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Computing with the collective intelligence of honey bees – A survey
Rajasekhar, Anguluri; Lynn, Nandar; Das, Swagatam; Suganthan, P. N.
2016
Rajasekhar, A., Lynn, N., Das, S., & Suganthan, P. N. (2017). Computing with the collective intelligence of honey bees – A survey. Swarm and Evolutionary Computation, 32, 25‑48. https://hdl.handle.net/10356/83447 https://doi.org/10.1016/j.swevo.2016.06.001
© 2016 Elsevier. This is the author created version of a work that has been peer reviewed and accepted for publication by Swarm and Evolutionary Computation, Elsevier. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1016/j.swevo.2016.06.001].
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Computing with the Collective Intelligence of Honey Bees – A Survey
Anguluri Rajasekhar, Nandar Lynn, Swagatam Das, and P. N. Suganthan
Abstract –Over past few decades, families of algorithms based The term swarm is used for an aggregation of natural creatures on the intelligent group behaviors of social creatures like ants, like fishes, birds and insects such as ants, termites, and bees. birds, fishes, and bacteria have been extensively studied and used The members in the swarm interact with each other without for computer-aided optimization. Recently there has been a surge any central supervision and they move based on the of interest in developing algorithms for search, optimization, and information obtained from their neighbourhood. In this paper, communication by simulating different aspects of the social life of a very well-known creature: the honey bee. Several articles a comprehensive survey of the computing algorithms based on reporting the success of the heuristics based on swarming, the social behaviours of honey bees is presented including mating, and foraging behaviors of the honey bees are being different variants of the bee-inspired algorithms and published on a regular basis. In this paper we provide a brief but applications of those variants to real-world optimization comprehensive survey of the entire horizon of research so far problems. undertaken on the algorithms inspired by the honey bees. The paper is organized in the following way. Section II Starting with the biological perspectives and motivations, we discusses the biological perspectives of honey bees and the outline the major bees-inspired algorithms, their prospects in the motivations behind the algorithms inspired by different respective problem domains and their similarities and activities of honey bee swarm. Section III outlines various dissimilarities with the other swarm intelligence algorithms. We also provide an account of the engineering applications of these algorithms based on the mating and marriage of queen bees. In algorithms. Finally we identify some open research issues and Section IV, studies based on developments of methods promising application areas for the bees-inspired computing involving foraging and communications between bees are techniques. reviewed. Section V provides an overview of the methods Keywords-Nature inspired computing, swarm intelligence, honey based on honey bee swarming. In Section VI algorithms based bees foraging, particle swarm optimization, bee colony optimisation; on spatial memory and navigation methods are discussed. Section VII presents a comprehensive outline of the I. INTRODUCTION algorithms based on the division of labor in honeybees. EES are four-winged flower-feeding flying insects having Finally, conclusions are drawn in Section VIII with a Bsimilarities with ants and wasps and they belong to the discussion of the potential future research issues. A summary family of Apoidea. They are well known for their pollination of the key concepts of some most representative bee-inspired and production of honey and beeswax. There are around algorithms along with the meaning of various metaphors 20,000 known species of bees organized in 7 to 9 recognized commonly found in the related literature is provided in Table families. Among all the categories of bees, bumblebees and 2. honey bees have a very peculiar life cycle which has attracted several researchers to study about the facts associated with II. HONEY BEES – BIOLOGICAL PERSPECTIVES AND them. These studies led to different theories which are highly MOTIVATIONS suitable to meet the needs of engineering applications. In a In nature honey bees create nests called ―hives‖ (consisting honey bee swarm, the tasks are dynamically assigned and the up to 20,000 individuals) and they work together following a bees adapts to the new environment in a collaboratively highly structured social order. The brief taxonomy involved in intelligent manner [S1, S2, S3]. the life cycle of bees is shown in Fig.1. The following section In the recent past, with the computational cost having been provides a brief description of the evolution of bees and their almost dramatically reduced, the researchers have drawn the role played in collection of nectar. ideas from nature to solve difficult computational problems. Among the population-based models for computer aided 1. Honey Bee Hive problem solving, the insect colonies exhibit a significant level of interaction through mutual co-operation and organizational This is the place where new bees take birth. The hive behavior which are necessary for survival in the life process. consists of a number of vertical combs. There are two kinds of Computer scientists observed that efficient metaheuristic comb cells; the worker cells and the drone cells. In due methods can be developed, based on the honey bees‘ course of time occasionally the bees build a third type of cells, intelligent behaviors of co-operation, allocating the task force the queen cells, in which the queen bees are reared. and finding the food source using the mutual interaction as guidance.
Note: Due to space limitation the supplementary reference list cited as [Sxxx] will not be published in print, but as an on-line document only. The list is appended with this version.
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i)Queen Bee (source) she should visit. At the end foragers carry the In general ―Queen Bee‖ refers to an adult mated female. collected nectar to hive. Her sole purpose in life is to lay eggs and to produce more ii) Communication: bees. She is the only female in the hive. A bee returned to the hive from a good food source ii) Drone Bees performs a kind of ‗dance‘ on the vertical comb. In Drones are the male honey bees developed from eggs that general these are given particular name based on the have not been fertilized. Drones mate with a queen in front profitability and distance of the flower (source). For of the hive through the phase of mating flight. instance, if the distance is beyond 150 meters the bee performs waggle dance, a particular figure eight dance to iii) Worker Bees share the information regarding the direction and distance Workers are the most populated non-mating female bees, of the food sources. Other workers follow the dancing bee constituting over 98% of the colony‘s population. The and then learn the direction and distance of the food worker bees play a major role in collection of nectar and in source based upon the dancing behavior. A waggle dance safe-guarding the hive from potential intruders through with a very short waggle run used to be characterized as a social interactions. Several bee colony based algorithms round recruitment dance. Forager honey bees of the imitate the collective intelligence shown by the worker species Apismellifera can perform tremble dance to bees. recruit more receiver honey bees to collect nectar from
the workers. Tremble dance resembles the waggle dance, however, a forager uses it when the foraging bee senses a long delay in dumping its nectar or a dearth of the receiver bees.
3. Honey Bee Swarming and Nest-site-Selection
Swarming is often considered to be the process in which bees abandon their hives and collectively move to perform various life-supporting activities. One situation includes rapid reproduction of honey bees in the colony resulting in the increase of population. The reasons may include abundant availability of nectar and favorable environmental conditions. On other time it may happen that the honey flow has been restricted or ailments which forces the worker bees to leave the hive. As soon as they emerge as a swarm they aim to construct a new site after deciding the most suitable site. The most experienced scout bees search a large area for a suitable new site. Bees that have found good sites return to the cluster
and the strength of their waggle dance becomes proportional Fig.1.The taxonomy involved in the life cycle of honey bees (in some sense) to the quality of the nest-site [S10, S11, S12].
2. Honey Bee Foraging and Communication 4. Spatial Memory and Navigation
Learning plays a vital role in foraging. Von Frisch and Often foragers (worker bees) come across a situation where Seeley are considered to be the pioneers in studying the finding a way between food source and hive becomes learning capabilities of honey bees. From different extremely difficult due to fractal oriented landscapes and experiments and many studies conducted by Von Frisch [S4, longer distances. Honey bees usually overcome this problem S5], Von Frisch and Lindauer [S6], Seeley [S7], Chalifman with the help of landmarks and celestial cues. According to [S8] and Lindauer [S9], it is observed that a single forager will Menzel et al. [S13], foragers use a map oriented organization visit the different flowers (food sources) in the morning. If regarding the spatial memory, which is based on the there is a particular kind of flower which has sufficient computations of land marks and celestial cues [S14, S15]. attraction and reward, the bee will visit that flower as many 5. Division of Labor times as possible for most of the day. Honey bees are quite skillful in associative learning. Division of labor refers to biases in the inclination of
i) Foraging: individuals to perform different tasks within a group [S16, Foraging process begins when the foragers (worker bees) S17]. According to Beekman et al. [S18], the bee colony leave the hive in search of food. Almost all flowers should divide its workforce and allocate the appropriate produce nectar to attract insects, primarily honey bees. A number of individuals for each of the many tasks. Even though bee uses its cognitive intelligence and also observes the each individual bee can perform every task in a hive, each bee neighboring bees and then determines to which flower can also be specialized for a particular task. The aforementioned taxonomy is a general representation of
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’ the life-cycle of bees and particular emphasis was provided Do mutation with P m only on the phases, which served as a source of inspiration for End if bee inspired computational methods. Literature study reveals End For that each phase has played a very important role in developing 8. Evaluate P(t) model that suited for many challenging applications. In the 9. End following sections we provide a comprehensive account of the algorithms/methods/systems that are developed based on the Many QBE variants were proposed for solving optimization behaviors mentioned in the above taxonomy. problems and also were used in various engineering
III. COMPUTATIONAL METHODS BASED ON QUEEN BEES, applications. Some noteworthy variants and applications MATING, MARRIAGE include economic power dispatch problem using QBE by Qin et al.[139]; design of fuzzy knowledge base controller using A. Queen Bee Evolution (QBE) QBE with weighted crossover operator [12, 13, 77]; parameter QBE strategy was first proposed by Jung [64] to enhance extraction of organic thin film transistors compact model the performance of Genetic Algorithms (GAs). According to using QBE by Moreno et al.[109]; designing DNA sequences Jung, QBE speeds up the convergence of GA by improving that satisfy combinatorial and thermodynamic constraints the exploitation and exploration capabilities. The basic using Bee Swarm Genetic Algorithm (BSGA) [195]; GA inspiration is as follows. In a bee colony, Queen is considered based on Multi-bee Population Evolutionary (BMGA) by Lu as a mother for all the bees and given hierarchal preference in and Zhou [90]; queen-bee crossover in GA for label- every task. In QBE, the fittest bee (representing the best constrained minimum spanning tree problem by Xiongm et solution) is considered as the queen in each generation, and is al.[192];Tuning the parameters of Boost Converter using allowed to crossover (mate) with other bees selected by the Queen-Bee-Assisted GA by Sundareswaran et al.[162]; tuning parent (candidate solutions) through a selection rule. This the scaling factors of fuzzy logic control using Modified increases the exploitation of GA at the same time this may Queen-Bee-based Genetic Algorithm (MQBGA) by lead to premature convergence. To overcome this problem and Mohammad et al. [S258]; designing fuzzy controller using to decrease the premature convergence rate some individuals artificial DNA assisted Queen Bee GA (DNA+QBGA) by in the QBE framework are frequently mutated resulting in Ming et al.[S259]. Vakil-Baghmisheh et al.[179] developed a improved exploration quality of the GA. hybrid algorithm that combined QBE with the Nelder-Mead The two key differences between normal Evolutionary algorithm to design the PID controller for a Gryphon robot; Algorithm (EA) and QBE are denoted with # symbol in the Jie-Sheng et al.[181, 182] proposed a new Bee Evolutionary pseudo-code of QBE provided as Algorithm 1. Usually in GA Genetic Algorithm (BEGA) to solve the aircraft landing the parents P(t) of NP individuals are selected by a selection scheduling problem and vehicle routing problems. In BEGA, mechanism like roulette wheel or tournament selection. On the self-adaptive crossover operator is adopted to increase solution other hand, in QBE, the set of parents consists of half of the accuracy and to avoid premature convergence. Huang et NP couples of queen bee Iq(t-1)(q=argmax fi(t-1), 1
4 search heuristics for improving the offspring solutions. The End For mating process between the queen and the drone encountered Generate new broods by crossover and mutation probabilistically during the flight, followed by feeding process operations by the worker. At initialization, bee population is randomly Employ workers to improve the broods generated and the solutions with better fitness values are Update workers fitness selected as queens and the rest as drones. Then, the mating While (best brood > worst queen) // fitness process can be probabilistically determined using the Replace the queen with best brood following expression: Eliminate the best brood from brood family End While -d/s P(Q,D)=e . (1) 4. End For
Here d is the absolute difference between the fitness of D The MBO model found a profound use in applications such and Q, and s is the speed of the queen Q. P(Q,D) represent the as different satisfiability problems by Abbass [1], [S21, S22, successful mating probability. If the mating is successful, a S23]; optimization of partitioning and scheduling by Koudil et sperm of the drone is added to the queen‘s spermatheca (this is al.[81] and solving infinite horizon-discounted cost stochastic like increasing a counter by unity). The mating flights are dynamic programming problems by Chang [23] (termed as reiterated until the energy of the queen is lower than a Honey-bees Policy Iteration (HPI)). predetermined threshold or the queen‘s spermatheca is full. Teo and Abbass [168] proposed a hybrid MBO with After each transition, the queen‘s speed and energy are annealing function. In the proposed method, the queen‘s decreased according to the following equations: mating flight trajectories are determined based on the (2) speed( t 1) . speed ( t ), probabilistic function of the queen‘s fitness. A conventional (3) annealing function is used in this context to intensify the energy( t 1) energy ( t ) step , search. Abbas and Teo used this hybrid method to construct where is a scaling factor and lies between 0 and 1, step is the pool of drones in [S24]. the amount of energy reduction after each successful mating or Yang et al.[197] proposed faster marriage in honey Bees transition. Algorithm 2 provides the set of heuristics to be optimization named FMBO algorithm with global performed in MBO approach. After completing the mating convergence behavior. In FMBO, the computation became process, the new broods (offspring solutions) are generated easier and faster by initializing the drones randomly and using crossover operation of the queen and the randomly restricting the conditions of iterations. To improve the selected drone solutions. The breeding process is repeated performance of MBO, Yang et al.[S25] judiciously merged until the number of broods reaches the required value. MBO with the Nelder-Mead method and applied to solve the Afterward, a binary mutation is applied to improve the Traveling Salesperson Problem (TSP). Yang et al.[S26] genotypes of the newly-born broods. proposed a hybrid method involving the Wolf Pack based Then, feeding of offspring solutions produced by queens are local search known as WPS-MBO for solving a few complex carried out by workers. As the worker action is constrained to optimization problems and also TSP as well. Vakil- only breeding (nursing), each worker can represent a local Baghmisheh and Salim [180] proposed a Modified Fast search heuristic function. The workers are selected according Marriage in honey Bee Optimization (MFMBO) and validated to their fitness values and then applied to enhance the the performance of the proposed approach on various offspring solutions. numerical benchmarks. Further the authors compared After the breeding process is over, the weaker queens are MFMBO with other bee algorithms like ABC, QBE, and replaced with the fitter broods until there is no more brood FMBO methods. fitter than any of the queens. The remaining broods with lesser Vakil-Baghamisheh et al.[S27] used this MFMBO to fitness are killed before starting the new mating flights. The predict the structure of the Met-enkphaline using torsion procedures are shown in Algorithm 2. angles representation and ECEPP/3 energy function. Salim and Vakil-Baghmisheh [150] presented three versions of the Algorithm 2. Marriage in Honey Bee Mating Optimization Discrete Fast Marriage in honey Bee Optimization (DFMBO1, 1. Initialize the workers and randomly generate queens DFMBO2, and DFMBO3) algorithm and discrete ABC 2. Apply local search (greedy criterion) to get best queen (in algorithm using three logical operators - OR, AND, and XOR. terms of fitness) The performance of their proposed methods was validated 3. For f = 1 to Max number of mating flights using four benchmark functions and was also compared with For i = 1 to Max number of queens ABC, QBE, and FMBO. Ping et al.[122] used MBO algorithm Initialize energy, speed and position via support vector regression models for forecasting output of Queen moves between states randomly the integrated circuit industry. Drone is selected probabilistically using Eqn (1) Thammano and Poolsamran [174] proposed a new Self- If (queen selects a drone) organizing model of MBO (SMBO) to improve the Sperm is deposited in spermatheca of queen performance of MBO. Unlike the original model, SMBO End automatically searched for the proper number of queens. The Update queen‘s speed and energy using Eqns (2) and problem space was partitioned into several colonies with its (3). own queens and later the queens were encouraged to compete
5 for a larger colony. Thereafter a greedy mechanism was used 6. Improve the newly generated set of solutions utilizing between the newly born brood and the queens. The fuzzy c- various available mutation operators as well as heuristic means clustering algorithm was employed to assign the drones functions according to their fitness. to the proper colonies. Performance of SMBO was validated 7. Sort new solutions based on their fitness values, selecting on six benchmark functions and compared to the original the best new solutions and best new trail solutions for MBO. The authors also applied SMBO to solve multi- next iteration objective optimization problems and its performance was 8. IF (new best solution better to previous one) compared with two well-known approaches, the Pareto Substitute the best solution archived evolution strategy and the Non-dominated Sorting 9. Else Genetic Algorithm (NSGA) [S226]. Keep the previous best solution 10. If termination criterion not satisfied go to step 5 C. Honey Bees Mating Optimization (HBMO) Algorithm 11. Else report the best solution and terminate. HBMO was introduced by Haddad et al.[50], [S28, S29] and it is a meta-heuristic approach similar to MBO in terms of In power systems and related areas, Niknam et al.[117] crossover and genotypes. This algorithm has five main stages: presented an efficient multi-objective HBMO for multi- mating flight, new brood creation, performing local search on objective distribution feeder reconfiguration problem (Niknam broods via workers, adapting worker‘s fitness based on the [S40], Niknam and Sadeghi [S41]). In MHBMO, several improvement obtained on broods and finally replacing weaker queens are used and the queens are considered as an external queens by the broods with better fitter values. A pseudo code repository to save non-dominated solutions found during the of this algorithm is provided as Algorithm 3. Similar to MBO search process. The objective functions are based on fuzzy and QBE, HBMO had been successfully applied to solve clustering technique, particularly to control the size of the many real-world optimization problems which are listed in the repository within given boundaries. Table 3. Niknam also proposed a new Chaotic Improved HBMO Amiri and Fathian [9] presented a two stage method in (CIHBMO) [115] based on the logistic and tent equations. which HBMO was integrated with Self-Organizing Feature CIHBMO is also used for solving multi-objective daily Map (SOM) neural network to solve the clustering problem. Volt/Var control in distribution systems and in non-smooth SOFM was used to determine the number of clusters and economic dispatch problem in the field of power systems cluster centroids and then HBMO method based on the k- [S42]. Niknam et al.[116] presented a new interactive fuzzy means algorithm ((HBMK) was employed to find the final method using modified HBMO for solving the Multi-objective solution. SOM with HBMK was compared with SOM with k- Optimal Operation Management (MOOM) problem. In this means and SOM with genetic k-means via a Monte Carlo method, the modified HBMO is combined with chaotic local study. Fathian and Amiri [S33, S34] applied the HBMOK search method to prevent premature convergence. Niknam algorithm to solve an internet bookstore market segmentation [114] also hybridized discrete particle warm optimization with based on customer loyalty. HMBO for solving the multi-objective distribution feeder Marinakis et al. [98-100], [S36, S37, S38] proposed the reconfiguration optimization problem. HBMO algorithm to handle the Vehicle Routing Problem Huang [58] proposed Plant Growth Simulation (PGS) (VRP) and termed as HBMOVRP. HBMO algorithm is algorithm enhanced HBMO to improve the local search combined with Multiple Phase Neighborhood Search-Greedy capability and overall computation of HBMO. The authors Randomized Adaptive Search Procedure (MPNS-GRASP) and used their approach to estimate the fault section in a power Expanding Neighborhood Search (ENS) algorithm. The system in practical scenario, and the results indicated that algorithm slightly modified the crossover operator and the enhanced HBMO was superior to comparative algorithms and workers‘ heuristic nature. This particular hybrid method was further it also avoids premature convergence. successfully applied to various TSP problems. Ghasemi [S230] applied a fuzzified multi-objective interactive HBMO to the environmental/economic dispatch Algorithm 3. Honey bee Mating Optimization problem. The approach was quite different from Niknam et 1. Start al.‘s HBMO method [116] involving fuzzy clusters. In multi- 2. Initialize the model and algorithm input parameters. objective IHBMO, the dominated and non-dominated 3. Randomly generate a set of initial solutions and rank the solutions are sorted by using Pareto dominance and the best solutions based on the fitness values keeping the best one solution is extracted by using the fuzzy set theory. The as queen and others as drones. performance of the multi-objective IHBMO was tested using 4. Use simulated annealing to select the set of solutions from IEEE-30 and IEEE-180 bus systems. The authors verified the the given search space to make a mating pool for superiority of IHBMO over other multi-objective optimization generating new trail solutions and replacing them with algorithms in terms of convergence characteristics and Pareto previous best solution if they are fit sets obtained. 5. Generate a new group of solutions (breeding process) by In image processing area, Horng et al.[56] applied HBMO- employing different predefined crossover operators and based snake algorithm to improve the detection of the concave heuristic functions (workers) between the best present region connected with control points of active contour. Li solution (queen) and trail solutions based on their fitness proposed improved HBMO-SNAKE algorithm by adjusting values obtained the step and replacing the model parameters in [S260]. Afarandeh et al. [3] proposed a new technique which used a so
6 called no-search scheme for fractal image compression and considered to be a chromosome encoding a candidate solution local search with HBMO. The proposed method was applied as in GAs. Some chromosomes having considerable fitness are to fractal image compression and gained superior performance regarded as superior chromosomes and others try to find over other compared fractal encoding algorithms. solution around the vicinity of the superior ones by generating Bernardino et al. [S44] applied a hybrid version of HBMO multiple solutions. to connect a given set of terminals to a given set of In an alternate development, Lucic and Teodorovic [91] concentrators and to minimize the link cost to form a explored bees‘ behavior and developed the models to tackle communication network. Chiu et al. [26] proposed a hybrid the combinatorial optimization problems. In this BS, (different heuristic which integrates PSO and HBMO methods for from that of Sato and Haigwara [151]), every bee colony has market segmentation that segments data into homogenous scouts and they are the bee colony‘s explorers. There is no clusters by using cluster analysis. guidance for the explorers when searching for food. Therefore, Yuan [S227] proposed Hybrid HBMO for assembly the scouts/explorers are characterized by low search costs and sequence planning problem in which multipoint precedence a low average in food source quality. However, in course of crossover was used to avoid from generating infeasible time, the scouts can accidently discover the rich, entirely solutions and to preserve the queen and broods‘ meaningful unknown food sources. In case of solving the difficult characteristics. The author also presented a novel hybrid combinatorial optimization problems, the bees discovered the HBMO algorithm in which a new encoding and decoding groups of the feasible solutions quickly. Among these feasible schemes were designed to fit the problem and simulated solutions, some could be proved as of very good quality. The annealing was employed to improve the broods. Shayeghi survival and progress of the bee colony depends on the rapid proposed parallel vector evaluated improved HBMO discovery and efficient utilization of the best food sources. (VEIHBMO) to tune the parameters of Power System The BS and its variants were mainly applied to traveling Stabilizer (PSS) in [S262]. The experimental results validated salesman problem in [92] and [S49 - S52]. that VEIHBMO algorithm performs superior to bacteria foraging algorithm and cultural algorithms on the PSS tuning 2. Bees Colony Optimization (BCO) problem. Inspired by the honey bees foraging behavior, Teodorovic IV. METHODS INVOLVING BEES FORAGING AND and Dell [170] proposed a powerful metaheuristic algorithm, COMMUNICATION called Bee Colony Optimization (BCO). BCO employs artificial bees as agents, which collaboratively solve the
A. Foraging involving communication based Methods complex combinatorial optimization problems. BCO ([169], Stumper and Broomhead [S48] laid the first steps to [S59], [S64]) is a more generalized and improved version of describe the nectar foraging of honey bees algebraically. Their the BS algorithm [91] and hence in this context we consider work later played a key role in the development of both of the algorithms more or less similar. computational methods for solving different problems based The BCO algorithm is mainly divided into the two on the characteristics of bees foraging. This idea also led to processes: forward pass and backward pass. The main idea the origination of various optimization algorithms, inspired by behind the algorithm is to exploit and explore the search space the honey bees‘ foraging behavior. During the last decade so that an optimal solution can be found in a predefined steps. there have been several algorithms of this kind. Some of the In each forward pass phase, each agent explores the search well-known heuristics based on foraging and communication space with a predefined number of moves which is applied to of bees that played a vital role in designing or optimizing the construct and/or improve the solution. Once the bees are real world applications are summarized in this section. acquainted with new partial solutions, they go back to the hive and start the backward pass phase. Methods Based on Foraging In backward pass, the artificial agents share information 1. Bees System (BS) about the quality of their solutions via waggle dances. With a 2. Bee Colony Optimization certain amount of probability value, the bees decide whether 3. Bee Colony Optimization Algorithm to abandon the created partial solution to become a 4. Artificial Bee Colony uncommitted follower or to dance and recruit the remaining 5. Bees Algorithm nest mates before they return to the patches or create partial 6. BeeAdhoc solution. This makes the bees with high fitness value to 7. Bee Swarm Optimization continue exploration once again in the same area. Thus, once 8. Virtual Bee Algorithm again the bees start to forage. Subsequently the forward pass 9. Miscellaneous Methods resembling Bee‘s Foraging phase takes place and the bees expand the previously created nature partial solutions. Then they perform backward pass and this process continues in an iterative fashion until a predefined 1. Bees System (BS) termination criterion is satisfied. Every follower chooses a new solution from the recruiters using the roulette wheel In 1997 Sato and Hagiwara [151] proposed a first selection. A brief pseudo-code of BCO is presented in computational algorithm based on bees‘ foraging behavior and Algorithm 4. called it Bee System (BS). In this approach each bee is BCO applications to numerous real world and computationally complex problems are listed in Table 2.
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schedule of the independent tasks of identical machines with a Algorithm 4.Bee Colony Optimization minimum completion time for all tasks. Davidovic et al. [S62] //B -- Total number of bees in the hive/ proposed parallelization strategies of BCO and validated on //NC – The number of constructive moves during each forward identical machines problem. Yueh-Min Huang et al.[59] pass proposed a new BCO with idle-time based filtering scheme for 1. Initialization solving the open shop scheduling problems, to reduce the 2. For I iterations do problem solving time. Taheri et al.[163]developed a novel Job 3. For all B bees do Data Scheduling (JDS) algorithm using Bee Colony (BC) i. Set i=1 // counter for number of constructive called JDS-BC to apply to simultaneous job scheduling and moves in the forward pass data replication in grid environments. Three different sizes of ii. Evaluate all possible constructive moves; test-grid were used to test the performance of JDS-BC.JDS- iii. According to the fitness obtained choose one BC provided invaluable insights into data-centric job move by using the roulette wheel selection. scheduling for the grid environments. In [S231], reserved BCO iv. i=i+1 if i<=NC Go to step (ii) was applied to grid scheduling to allocate the resources 4. End For properly. BCO was also used for scheduling the independent 5. All bees return back to the hive tasks on homogeneous multiprocessor systems in [33]. 6. Sort the bees using their fitness values obtained In [S229], the authors modified BCO by pattern reduction 7. For all bees B do (PR) and in [S230] by hybridizing with ACO to reduce the i. Backward pass computational time of solving TSP. In the parallel lines, ii. Every bee decides randomly whether to become Teodorovic [172] and Davidovic et al. [S63] used a new a recruiter or to become a follower via dances improved BCO variant (BCOi) for the p-center problem and fitness sharing (Transpiration Engineering) and showed that BCOi provided iii. For every follower choose a new solution by better results in less computational time. roulette wheel basis Forsati proposed improved BCO (IBCO) algorithm to 8. End For address the document clustering problem in [S263]. In IBCO, 9. If best solution obtained in iteration is global best, the cloning and fairness concepts were introduced to increase Update best-known solution the explorative power of BCO algorithm. The IBCO algorithm 10. End For was applied to data clustering and introduced IBCOCLUST. 11. Display the best result. The performance of IBCOCLUST algorithm was tested using large and high dimensional sets and compared with original Contrasting to several attempts made by contemporary BCO, k-means, GA and PSO based clustering algorithms to researchers in developing various enhancement strategies to show the superiority of IBCO over the competitors. BCO, Tereshko, Lee and Loengarov [173], [S66, S67] To enhance the exploitation ability, Moayedikia introduced developed a honey bee foraging model based on the reaction- weighted BCO (wBCO) algorithm in [S264]. In wBCO, global diffusion equation. The authors investigated the bee and local weights were considered, which allowed the bees to communication behavior and analyzed the mapping of search deliberately through the solution space. A new recruiter information about the explored environment. The empirical selection was also adopted to preserve the population study of BCO was performed in [S234] and the experiment diversity. In [S264], wBCO was employed to tackle feature was conducted using several numerical test functions. The selection (FS) problem. The performance of wBCO and FS- experimental results were compared against Particle Swarm wBCO were evaluated using several benchmark functions and Optimization (PSO), GA, Differential Evolution (DE) and datasets and compared with other BCO algorithms. artificial bee colony algorithms. The study confirmed that BCO had been used for various applications such as Genetic BCO is able to find high quality solutions within reasonable Clustering for Flexible Protein-Ligand [S228], automated CPU times. Software Testing [S232], Transit Network Design [S233], BCO was mainly used in scheduling problems. Few notable Nurse Rostering problem [175], Optimizing Type-1 and Type- approaches are as follows. Banarjee et al. [S55] combined 2 Fuzzy controller Design [S265], Sequential Ordering BCO with rough set based approach for modeling process and Problem [S266], the satisfiability problem in probabilistic supply chain scheduling which had multiple conflicting logic[S267] and was also adapted to current control strategy of criteria. Teodorovic et al. [171] proposed a new metaheuristic power factor (PF) correction for a Sheppard-Taylor termed as fuzzy bee system (FBS) in which the artificial bees converter[68]. communicated each other using the approximate reasoning and fuzzy logic rules. FBS was applied to solve the 3. Bees Colony Optimization Algorithm (BCOA) combinatorial problems. Teodorovic and Dell‘orco [S56] used this FBS system as travel demand management technique for Similar to BCO, in 2006, Chong et al. [28] introduced the solving the ride matching problem. Bee Colony Optimization Algorithm (BCOA) based on honey bee foraging and waggle dance behaviors. Although the basic McCaffrey [S57] used a simulated BCO in generation of framework of this algorithm is same as that of BCO, the pair-wise test sets with a minimal size. Yonghao et al. [S58] search heuristics involved are completely different and it is as used BCO along with fuzzy entropy in image segmentation. follows. Typically BCOA consists of a total of n foragers. In Davidovic et al.[32], [S61] applied BCO to the static scheduling problem. The goal of BCO was to find an optimal the course of iterations each forager fi constructs a solution and
8 promote their solutions among the foragers. Then according to In the above approach the foraging part is not discussed to the quality of its own solution, a forager decides whether to make the algorithmic description more general and left to the retain its previous solution or to discard it and adopt other readers‘ interest which can be found in Chong et al. [28]. forager‘s solution. Decision is solely left to the female bee and Wong et al.[S69] applied BCOA to TSP and compared it with after the decision is made, a new solution is created based on six other optimization methods, thus demonstrating the its current solution. superiority of BCOA in solving TSP. Wong et al.[191] applied According to Chong et al. [28], bees search their food an improved BCOA with big valley landscape exploitation to sources by foraging and waggle dance. Briefly, in BCOA, solve a job shop scheduling problem. Chong et al. [27] there are two phases: a dancing phase and a foraging phase. proposed a new BCOA algorithm which used an efficient During an iteration, each forager build ups a solution for the neighborhood structure to find the feasible solutions and given problem. Then with probability p, each forager fi (i∈[1, iteratively improved on prior solutions. The proposed n])on returning to the hive from nectar exploration attempts to algorithm was applied for solving job shop scheduling perform waggle dance within duration D=di.A, where di is problem [27] and TSP instances [S70]. In this approach based on profitability rating and A is the waggle dance scaling BCOA model is constructed similarly to that of the original factor. In this approach, the profitability rating is defined as version. To improve the prior solutions generated by BCOA, Pfi and is related to the objective function. Pfi can be obtained the algorithm is integrated with a 2-opt heuristic and the by the following equation: obtained results are tested on a set of benchmarks. The 1 comparative study showcased the superiority of the integrated (4) Pfi i , approach. 2-Opt algorithm was originally designed for finding Cmax routes in the travelling salesperson problem, and was later i where C max represents the fitness value of fi‘s current applied to GAs, simulated annealing, etc. The original 2-Opt solution. The average profitability rating of all the dancing local search prohibits routes from self-crossing by reordering foragers is given by: them. This provides a good chance of escaping from local 1 nd optima. Pfcolony Pf i , (5) To further improve the performance of BCOA with 2-opt, n d i1 Wong et al.[189] proposed two mechanisms: Frequency- where nd corresponds to the number of dancing bees while Based Pruning Strategy (FBPS) and Fixed-Radius Near computing the profitability rating. The waggle dance duration Neighbor (FRNN) 2-opt. Based on the accumulated frequency fi is given by: of its building blocks recorded in a matrix, FBPS produces a di = Pfi / Pfcolony . (6) subset of promising solutions to perform 2-opt whereas FRNN 2-opt exploits the geometric structure in a permutation of TSP Based on the probability r , each forager attempts to follow i sequence and the performance is validated on TSP. Wong et a randomly selected dance of another forager. The probability al.[188] proposed a hybrid version of BCOA and called it r is dynamic and changes according to the probability rating i BCOA with the Fragmentation State Transition Rule (FSTR). as shown in Table 1. If the probability ratio is low compared The FSTR helps BCOA to produce a tour by combining a few to the colonies, a forager is more likely to randomly observe fragments of cities. BCOA with FSTR was tested on 84 and follow a waggle dance on the floor. A successful benchmark problems with different dimensions ranging from combination of waggle dance and foraging constitutes 14 to 1379. Wong et al.[190] developed a bee colony iteration. The best solution during the iterative process is optimization framework by including local optimization and obtained at the end of iterations. The pseudo-code of BCOA adaptive pruning (besides elitism) in the BCO framework. The has been shown as Algorithm 4a. algorithm was tested on TSP and quadratic assignment Algorithm 4a. BCOA problems. Low et al.[89] integrated a multi-objective BCOA into automated red teaming process to find a set of non- 1. For i = 1 to Itermax //Total number of iterations// 2. For j = 1 to i // for every foraging bee // dominated solutions effectively from a large search space. a. Forage b. Save the best Solution 4. Artificial Bee Colony Algorithm c. Perform Waggle Dance In 2005, Karaboga proposed a simple algorithm for 3. End multivariate and multi-modal continuous optimization 4. End problems, known as the artificial bee colony (ABC) [69].
Table 1 Since its inception, ABC optimization algorithm has received huge attention from both practitioners and researchers on Profitability Rating ri intelligent optimization. In this sub section we begin with the basic version of the algorithm. We then shift our focus on the Pfi< 0.9.Pfcolony 0.60 works that made significant improvements in the algorithm 0.9.Pfcolony 1.155Pfcolony a) The Basic ABC Algorithm ABC classifies the foraging artificial bees into three groups 9 namely employed bees, onlooker bees, and scout bees. The 5. Store the best food sources obtained so far in a memory. first half of the colony consists of the employed bees and the 6. If a termination criterion is not met, go to step 2; second half consists of the onlooker bees. The bees searching otherwise terminate the procedure and display the best for food around the food sources are called employed bees. food source (solution) obtained so far. The bees which make decision to choose the food sources found by employed bees are called onlooker bees. The Two evaluations of the fitness function are performed in employed bees of abandoned food sources become scout bees. each generation of the ABC algorithm together with the fitness In ABC, each food source represents a candidate solution and Function Evaluations (FEs) performed by send scout phase the nectar amount of the associated food sources corresponds (line 4 in Algorithm 5). This slightly complex way of to the fitness value of the solution. calculating the FEs (in one generation we have 2*NP+s FEs, The employed bees are randomly initialized in the search where s is the number of scout bees re-initialization and NP is space. The employed bees are associated with each food the total population size) triggered some misconceptions by source and find the new food sources by using the search reporting the quality of results in swarm intelligence based strategy shown in (9). If the quality (fitness) of the new food research community. Recently Mernik et al. [103] pointed out source is better than that of the old food source, the old food these facts for the potential users of this algorithm in their source is replaced by new one. Otherwise, the old food source survey article. is retained. In a D-dimensional search space, the position of th b) Improved ABC Variants the i food source is represented as Xi = (xi1, xi2,…,xiD). After the information is shared by the employed bees, each of the onlookers selects a food source according to the probability Tsai et al. [177] was one among the first to make given by: improvements in the performance of the ABC algorithm. As FS the onlooker bees‘ movements are limited to the selected nectar source and randomly selected source, the authors Pi fit i fit k , (7) k 1 proposed an interactive ABC (IABC) algorithm. The main where FS is the total number of food sources. The fitness idea of this approach is to improve the relationship of the employed and the onlooker bees. The IABC algorithm used value fiti is calculated as: 1 Newtonian law of universal gravitation in the onlooker phase fit , (8) and the selection of onlookers was done using the roulette i 1 fX ( ) i wheel selection. Baykasoglu [18] proposed a new where f(Xi) is the objective function to be modification to ABC which uses shift neighborhood searches, minimized/maximized. The onlooker finds new food source double neighborhood searches and greedy randomized using the following eqn.: adaptive search heuristics. The modified ABC was applied to solve the generalized assignment problems and used penalty xnew, j xi, j r.(xi, j xk, j ), (9) function approach for handing the constraints. where k(1,2, …,FS) such that k i and j (1,2,…,D) are Banharnaskun et al. [S101] proposed distributed parallel randomly chosen indices, r is a uniformly distributed random ABC in which the bee colony was decomposed into several number within [-1, 1]. This is like replacing one random subgroups and performed optimization by using the message component of the i-th solution with an arithmetic passing technique. Wenping et al. [S103] and El-Abd [38] recombination of that component and the corresponding suggested cooperative approaches to ABC for solving component from another solution. The process conceptually complex optimization problems. In order to enhance ABC resembles the binomial crossover of another very powerful convergence rate in solving the constrained, composite and and elegant continuous parameter optimizer, called DE with non-separable functions, Akay and Karaboga [5] provided crossover rate Cr = 0. Similar to the employed bee phase, the more control parameters rather than the single parameter greedy selection is applied between the old and new food ‘limit’ in basic ABC. The parameters are as follows: sources. In this way, onlooker bees select good food sources. Modification Rate (MR) to determine number of variables to In both phases, each bee searches for a better food source until be perturbed, and Acceleration Factor (AF) which guides the a certain number of cycles called limit is exceeded. If the uniform random number generation in search equation. fitness value is not improved until limit, that particular bee However, this made the search strategy of ABC more similar becomes a scout bee. A food source is reinitialized randomly to the binomial crossover of DE and MR became closer, in in the scout bee phase and the search process continues until spirit, to the crossover rate Cr in DE. the stopping criterion is satisfied. The pseudo code is provided Ruhai et al.[95] integrated a communication strategy for in Algorithm 5. parallelized ABC optimization for solving numerical optimization problems. In this approach, artificial agents are Algorithm 5. Artificial Bee Colony Algorithm split into several independent subpopulations and the agents in 1. Randomly initialize food sources. different subpopulations communicate with each other using 2. Shift the employed bees onto their food sources and the proposed communication protocols. Parpinelli [126] determine their nectar contents quantitatively. proposed a sequential version of ABC enhanced with the local 3. Position the onlookers based on the nectar amounts search and investigated the parallelization of ABC algorithm obtained from the employed bees. using three parallel modes: master-slave, multi-hive with 4. Employ the scouts for exploring new food sources. migrations and hybrid hierarchical on the 3 numerical 10 benchmark functions with a high number of variables. Fitness learning based ABC with proximity stimuli Alam et al.[7] introduced Exponentially Distributed (FlABCps) was developed to enhance ABC‘s optimizing Mutation (EDM) into ABC. In ABC-EDM, the exponential ability [30]. The fitness learning with weight selection and distribution is incorporated to produce mutation steps with proximity stimuli helped to keep the balance between the varying lengths and to adjust the current step length suitably. exploration and exploitation search processing ABC. The The results verified that their method is better than other fitness learning based ABC algorithm was recently used for methods like PSO and ABC. Aderhold et al.[2] studied the solving the protein ligand docking problem [178]. Quantum- influence of the population size on ABC and investigated the inspired ABC (QABC) algorithm was developed to enhance role of onlookers (when it is useful). They also proposed two the diversity and computing capability of original ABC ABC variants for the position update rule. From their [S242]. The quantum concepts such as quantum bit, states experimentations it is clear that use of onlookers depends on superposition and quantum interference were used and tested hardness of optimization goal and also their new variants on the benchmark functions to prove that QABC was outperformed the standard ABC on the test functions competitive to quantum swarm and evolutionary approaches. significantly. In order to improve the poor exploitative search of ABC, Xiaojun and Yanjiao [S134] presented a Fast Mutation Powell method was used in [44] as the local search and the ABC (FMABC) algorithm. In this algorithm when choosing new search equation with the best individual from the current food sources, the onlooker uses the pheromone and the population. Powell ABC algorithm was evaluated using the sensitivity model in Free Search algorithm to that of constraint and unconstraint problems and compared to other traditional roulette wheel selection. Raziuddinet al. [S140] ABC and recent state-of-the-art algorithms. Its results showed introduced Differential-ABC (DABC) for solving the complex highest quality solution, fastest convergence and strongest multimodal and dynamic optimization problems. In DABC, robustness. ABC based on orthogonal learning was also bees update strategy is enhanced for improving the solution presented to address the issue of the poor exploitation of ABC quality. Banharnasakun et al.[15] modified the solution update algorithm in [43]. The Orthogonal Experiment Design (OED) rule of onlooker bees, in which the best feasible solutions was used to develop the Orthogonal Learning (OL) strategy found so far are shared globally among the entire population. and the search equation was modified like cross operator of They biased the solution direction toward the best-so-far GA. The variant ABCs with OL strategy were studied for the position and also adapted the radius of search for new search experience and OCABC offered the best in the solution candidates as the search progresses towards convergence. quality and the fast in global convergence rate. Kang et al.[65] presented a Rosenbrock Artificial Bee Colony To increase the convergence speed, a combinatorial solution (RABC) algorithm which combines Rosenbrock‘s rotational search equation was introduced and to avoid getting stuck in direction with ABC. In RABC, the exploration phase is the local optima, chaotic search technique was employed on realized by ABC and the exploitation phase is done by scout bee phase in the ERABC algorithm. Reverse selection rotational direction method. Their numerical results showed based on roulette wheel was used to preserve the diversity. that RABC performed better than the peer algorithms in terms ERABC algorithm was tested on 23 benchmark functions and of convergence speed, success rate, and solution accuracy. it exhibited good performance. The analytical study of various Mezura-Montes el al [104] tried to adapt ABC algorithm to diversity measures in ABC algorithm was also conducted in solve the constrained optimization problems by modifying [S246]. In [8], a two-fold modification of the original ABC selection mechanism, the scout bee operator and the equality algorithm was suggested: the ratio of employed and onlooker and boundary constraints. In [94], Luo et al. developed bees and number of changes of dimensions' value in each Convergence Onlookers ABC (COABC) algorithm in which a cycle. Various ratios of employed and onlooker bees were new search strategy with the best solution from the previous examined. The ratio with more number of onlooker bees iteration was used in the onlooker stage to improve the obtained better results. Two or three changes were made for exploitation. The roulette wheel selection mechanism was the dimensions' value in each cycle. The modified ABC performed based on nectar amounts of each food source. The algorithm was tested on well-known benchmark functions and experimental results proved that COABC outperformed ABC two modifications effected on the performance of ABC in the solution quality and convergence rate. Karaboga and algorithm in terms of solution quality and convergence rate. In Gorkemli [S237] proposed quick ABC (qABC) algorithm in order to find the new search direction, the onlooker bee which the local search ability of ABC was improved by foraging process was modified by combining the information modeling the foraging behaviour more accurately. Another of the best food sources (based on fitness/nectar value) and the Improved ABC (IABC) algorithm was developed by Li et al. information of the current food source‘s location in [S248]. [S238] by modifying the search process with the best-so-far The new ABC algorithm was tested using the well-known selection, inertial weight and acceleration coefficients which benchmark functions to show the superior performance and were borrowed from the realm of PSO. Fister et al.[39] was efficiency of the proposed ABC over original ABC algorithm. the first to develop memetic version of ABC algorithm by Mezura-Montes and Velez-Koeppel [106] developed a hybridizing ABC with two local search heuristics: the Nelder- novel algorithm called elitist ABC. In elitist ABC, all types of Mead algorithm (NMA) for the exploration and the random employed, onlooker and scout bees are modified to generate walk with direction exploitation (RWDE) for exploitation. The more diverse solutions. Mezura-Montes et al.[105] presented stochastic adaptation method was employed to balance the an adaptive variant of ABC based on smart flight and dynamic diversification and intensification of the search. tolerances. The elitist and adaptive ABCs are applied to solve the constrained optimization problems and verified in [105] 11 and [106]. Schirru[34] introduced ABC with Random Keys (ABCRK) for To overcome the drawbacks due to single variable solving a combinatorial problem in Nuclear Engineering. perturbation, one-position inheritance scheme [S243] and Omkar et al.[118] presented vector evaluated ABC opposite directional search were introduced to ABC algorithm (VEABC) algorithm to solve multi-objective optimization in [S244]. The performance of the improved ABC algorithm problem (optimizing laminated composite components). was tested using the numerical benchmark functions. Other VEABC is a parallel vector evaluated type, swarm intelligence works which concentrated majorly in improving the multi-objective variant of ABC. The performance of VEABC performance of ABC include Efficient and Robust ABC is validated using different loading configurations like algorithm by Xiang and An [S245], chaotic systems and uniaxial, biaxial and bending loads. opposition-base learning method were used in [S235] and Xiu et al. [S269] presented modified ABC (MABC) [S236], hybridizing with cat swarm optimization (CSO) by algorithm in which one position inheritance scheme was Tsai et al. [S128] for numerical function introduced to learn from the previous experience and the best- optimization,hybridizing with simulated annealing (SA) for so-far-searched solution was used as the guidance to increase solving global optimization problem [24] and hybridizing with the convergence speed. The MABC algorithm was tested on PSO for solving complex numerical optimization problems two mathematical functions and loudspeaker design problem. [S251]. Compared to ABC, GA, PSO and DE algorithms, MABC Rajasekhar et al.[142] presented Cauchy mutation ABC (C- converged faster as well as obtained a better solution in ABC)algorithm. They first validated C-ABC on numerical [S269]. benchmarks and then considered a real world application of Wei-Feng et al. [S270] developed a novel ILABC algorithm tuning Proportional-Integral speed controller for a permanent which was based on information learning. In ILABC, magnet synchronous motor (PMSM) drive. Similar to the subpopulations were divided by clustering partition. The Cauchy mutation proposed by Rajasekhar, Coelho and Alotto [29], [S136] modified original ABC and proposed Gaussian subpopulation size was dynamically adjusted according to the ABC algorithm and applied to Loney‘s Solenoid Benchmark last search experience. The two search mechanisms were Problem. The authors showed the suitability of ABC in designed for the communication in each subpopulation and problems relating to electromagnetic optimization. between the subpopulations. ILABC algorithm was evaluated In order to solve the multi-parameter optimization, dynamic using the CEC 2005 test functions in [S270]. ILABC obtained ABC (D-ABC) algorithm was proposed in which a dynamic significantly better performance than compared ABCs and ‗activity‘ factor was introduced to increase the convergence EAs in most of the test problems. speed and improve the solution quality of original ABC A parallel ABC (P-ABC) with a new search method was algorithm [S239]. The D-ABC was applied to mutli- introduced in [S271]. In P-ABC, the best solution was parameters optimization of support vector machine (SVM) and generated using the mutation operator to increase the better SVM parameters were resulted. The new ABC exploration and parallel search structure was used to promote algorithm with dynamic population size called ABCDP was the exploration. P-ABC was tested on peak-to-average power also introduced in which the population size was dynamically ratio reduction problem. P-ABC obtained good performances changed related to each iteration result and the algorithm was with low computational complexity. applied to tackle the economic and emission dispatch problem Horng proposed ABCOO algorithm for solving stochastic in the power system [S241]. gbest-guided ABC algorithm was economic lot scheduling problem in [S272]. In ABCOO, ABC improved by using the fitness value of global best solution algorithm was combined with Ordinal Optimization (OO) while calculating probability values associated with the food theory which relaxed the optimization goal from searching the sources [S247]. The improved GABC algorithm was tested on best solution to seeking the solution with high probability of IEEE 3 bust test system and applied to economic and emission success. The author verified the superiority of ABCOO by dispatch problem of the wind–thermal power system.ABC algorithm was also hybridized with DE to solve the optimal comparing with (μ, λ)-ES (Evolution Strategy), GA, and PSO reactive power flow problem in the power system [S250]. in [S272]. Sonmez [157] introduced ABC with adaptive penalty Mustafa et al. [S276] presented ABC with various search function approach (ABC-AP) to find the solution for truss strategies called ABCVSS algorithm. In ABCVSS, five search structural optimization problem and validated the performance strategies were proposed to search the solution and selected over five truss examples. Li et al.[85] came up with a new according to the characteristics of the problem to be hybrid Pareto-based discrete ABC algorithm for solving the optimized. The constant counter contents wereset for each multi-objective flexible job shop scheduling problem. Each strategy during initialization and used to determine the food source composes two components: routing and strategy during the search process. The ABCVSS was scheduling filled with discrete values. The author also evaluated using the numerical benchmark functions and introduced a new crossover operator which allows the bees to compared with EAs, DEs and PSOs in [S276]. learn valuable information from each other. In [S277], Shayeghi introduced chaos theory into ABC Vargas Benitez and Lopes [S126] proposed two parallel algorithm and proposed chaotic interactive ABC (CIABC) approaches for ABC: master-slave and hybrid-hierarchical for algorithm for solving economic dispatch problem. CIABC solving protein structure prediction problem. Haris et al.[53] uses chaotic local search operator to improve the local search proposed a computationally efficient meta-heuristic algorithm ability. Newton‘s law of universal gravitation is employed as based on ABC and Tabu Search (TS) concepts. Oliveira and 12 an interactive law between the employed and onlooker phase solution. The AABCLS algorithm was tested on 30 benchmark to enhance the exploration. Hence, CIABC benefits from the problems and obtained superior performance than original advantages of original ABC, universal law and CLS operators. ABC and recent ABC variants [S282]. The efficiency of CIABC algorithm was demonstrated by In order to address the poor exploitation problem of original testing on solving ED of the small and large scale power ABC, a Gaussian bare-bones ABC (GABC) algorithm was systems and comparing with other recent ABC algorithms. proposed in [S283]. In GABC, Gaussian bare-bones search Michiharu et al. [S278] presented ABC with reduction equation is designed to generate candidate solutions in the (ABCR) to improve the solution search accuracy and to avoid onlooker bee phase. The search equation uses the Gaussian premature convergence. The number of bees is sequentially distribution with dynamic mean and variance values and reduced to the predetermined number based on the fitness samples the search between the current solution and the best function evaluation count. The bees with good fitness value solution of current population. The generalized opposition- are selected and the rest with the worst evaluation values are based learning strategy is employed to generate new food eliminated. The effectiveness of ABCR was studied using the sources in the scout bee phase. The GABC performance is two-dimensional six test functions and compared with real- verified using shifted rotated benchmark problems and coded GA, DE, PSO and original ABC algorithm. compared with other ABCs and EAs algorithms. GABC Ismail et al. [S279] proposed ABC with distributed- performed significantly better in terms of solution accuracy based update rule called distABC algorithm. Instead of and convergence speed [S283]. differential solution update rule, the distributed-based solution update rule is used to prevent the stagnation behavior. The c) Hybrid ABC Variants distABC algorithm uses the normal distribution with the mean and standard deviation of selected two food sources to Xiaohu et al. [S115] proposed a hybrid of ABC and PSO generate the new candidate solution. The author evaluated the in which the valuable information are mutually shared distABC algorithm using 18 benchmark problems.The between the particle swarm and the bee colony. Kang et distABC performed better than or at least equally to other al.[66] integrated a popular local search algorithm called compared ABC algorithms in [S279]. Nelder-Mead simplex method into ABC and applied to Xiangtao et al. [S280] presented a self-adaptive constrained identify the parameters of concrete dam-foundation systems. ABC (SACABC) algorithm for solving the constraint Marinakiset al. [S86] presented a new hybrid ABC algorithm with GRASP concept for clustering problems. They also optimization problems. As the constraint handling methods, proposed a discrete ABC for feature selection (clustering the feasible rule is used in the employed bee phase and multi- applications) and validated performance of this new heuristic objective optimization method is used in the onlooker bee on various clustering datasets. Zhang et al. [S143] developed a phase. In both phases, a new search mechanism is introduced, chaotic ABC algorithm based on Rossler attractor to solve the which leads the new candidate solutions to search around the partitive clustering problem. random solutions of the previous iterations. The modification Duan et al. [37] proposed a hybrid method combining rate (MR) [5] is used to enhance the convergence speed of Quantum Evolutionary Algorithm (QEA) and ABC to SACABC algorithm. Ivona et al. [S281] also presented overcome the limitations of stagnation. In their method, ABC crossover-based ABC (CB-ABC) to solve the constraint is responsible for enhancing the local search capability as well optimization problem. In CA-ABC, boundary constraint as randomness of populations, which in turn will help QEA to handling method and dynamic tolerance were used for avoid the local optimum. Liu and Cai [88] developed the ABC handling the constraints. The solution update rules of Programming (ABCP) algorithm based on the randomized employed and onlooker bee phases are modified and crossover distribution, the bit hyper-mutation (similar to differential operator is used in scout bee phase. The performances of both mutation employed in DE) and a novel crossover operator. SACABC and CA-ABC algorithms were evaluated using CEC The authors claimed the superiority of ABCP by comparing 2006 benchmark suite for constrained problems and compared with original ABC. Guopu and Sam [203]were the first to with other ABC algorithms. The results showed that both point out that ABC search moves have an inclination towards constraint optimization algorithms are better or at least exploration than exploitation. To overcome this deficiency, the comparable to other compared algorithms. However, CA-ABC authors proposed gbest-guided ABC in which the information algorithm outperformed SACABC on solving the constraint of the best solution in the entire bee population was used to guide the search performed by other members, thereby optimization problem. enhancing the exploitation. This was close in spirit to the PSO Jadon proposed accelerating ABC with an adaptive local method. search (AABCLS) in [S282]. In AABCLS, the original ABC Pulikanti and Singh [S82]introduced a new hybrid approach algorithm is modified in two ways. The first modification is which combined ABC with a greedy heuristic and a local the solution update rule which forces the low quality solutions search. The proposed approach is applied to solve the to follow the best-so-far solution and encourage the high quadratic knapsack problem in [S82]. Sundar and Sing quality solutions to follow the best as well as the randomly [161]also presented a similar hybrid approach combining ABC selected solution. The second is the self-adaptive local search and the local search to solve the non-unicost set covering strategy in which the individual‘s search is self-adaptively problem (SCP). Banharnsakunet al. [S107] extended ABC adjusted to exploit around the neighborhood of the best with Greedy Sub-tour Crossover to enhance the precision and 13 applied it to TSP. Jiao et al. [S144] modified ABC and applied was used for addressing the exploration and exploitation in migration of mobile agent problem and compared with search. Besides, two enhanced strategies were introduced to other EA methods. Yeh and Hsieh[199]presented a penalty preserve the diversity: replacing the worst one in population guided ABC to solve the reliability redundancy allocation with the new solution in the onlooker phase and producing problem (RAP). new food source by performing several insertion moves to In [201], a bee recurrent neural network is optimized by the abandoned food source in the scout bee phase. ABC algorithm and then combined with Monte Carlo Ozturk [S273] presented a novel binary version of ABC. simulation (MCS) to generate the network reliability The improved binary ABC model was based on genetic prediction model. Hsieh et al.[57] presented an integrated operators and named as GA-ABC algorithm. In GA-ABC, system which combines wavelet transforms and ABC-RNN two-point crossover and swap operators were integrated as a for stock price forecasting and the performance of their genetic neighborhood generator to improve the global and approach is verified by predicting several international stock local search abilities. The GB-ABC was tested on dynamic markets. Wang et al. [S133] proposed ABC with Support image clustering and 0–1knapsack binary optimization Vector Machine (ABC-SVM) model to determine the problems. The results validated that GB-ABC is a suitable parameters of SVM and feature selection in building intrusion optimization algorithm for binary optimization, compared to detection system. Irani and Nasimi [61] proposed a hybrid other binary optimization algorithms. ABC-back propagation strategy (ABC-BP). In ABC-BP, the Kiran proposed an adapted binary version of ABC called local search ability of gradient-based back-propagation (BP) ABC in [S274]. To solve the binary optimization problems, strategy is combined with the global search ability of ABC. bin ABC-BP is applied to bottom hole pressure prediction in the solutions are converted into binary values before the underbalanced drilling a two phase flow through annulus. Ravi objective function specified for the problem is evaluated. Kumar and Rajasekhar [S125] also developed a new hybrid of ABCbin was tested on 15 test problems and compared with ABC and GA based on pipelining method of hybridization and binary versions of PSO and ABC variants. The performance applied for obtaining controller parametric gains in PMSM comparison showed that ABCbin is competitive and able to drive. offer better solution quality. Dongli presented binary ABC (BitABC) algorithm in d) ABC for Discrete and Binary Optimization Problems [S275]. The framework of BitABC algorithm is similar to ABC algorithm. However, the arithmetic mathematical The discrete variant of the ABC algorithm (DABC) was operator is replaced by the binary bitwise operator in the presented for the first time by Pan et al. [123] for solving lot- employed and onlooker bee phases. BitABC was compared streaming flowshop scheduling problem. Tasgetiern et al. with other three binary ABC variants and GA in [S275]. The [167], [S135] proposed modified discrete version of ABC by comparison was carried outing using 13 benchmark problems hybridizing with iterated greedy algorithms to find the and BitABC performed better than other binary algorithms in smallest total flow time for the permutation flow shop terms of solution accuracy, convergence speed and robustness. scheduling problem. Afterwards, Several DABC algorithms Li [S268] introduced a discrete ABC (DABC) algorithm are applied to permutation flowshop scheduling problem in for solving the molten iron scheduling problem. The author [165, 167]; to flexible job shop scheduling problem in [84, 86, introduced problem specific heuristics and presented 87]; to hybrid flowshop scheduling problem in [124, 125]; to population initialization method and neighborhood structures blocking flowshop scheduling problem in [46, 52, 144]; to for balancing the exploration and exploitation ability. The economic lot scheduling problem in [21, 22, 164, 166]; to algorithm was compared with GA, ABC and PSO algorithms parallel machine scheduling problem in [79]; and to some and obtained superior performance in solving hybrid flexible traveling salesman problem variants in [75, 76]. Recently Lia flow shop problem in the molten iron systems. and Pan [83] proposed a hybrid algorithm called TABC that synergises ABC with Tabu Search (TS) for solving the large- e) Real World Applications scale hybrid flowshop scheduling problems. Unlike the original ABC algorithm, in TABC, each food source While some of the researchers tried to focus on represents a string of job numbers. The authors used a novel development of convergence and quality of solutions of ABC, decoding method to tackle the limited buffer constraints in the many others tried to adapt the basic version to solve schedules generated. Four neighborhood structures were challenging real world engineering problems. In Table 3, we utilized to balance the exploitation and exploration abilities of include the representative references in which ABC was used the algorithm. A TS-based self-adaptive neighborhood to solve various practical problems. However, a few of strategy was adopted to impart to the TABC algorithm a noteworthy approaches are discussed here to provide a basic learning ability for exploring promising regions of the search insight to the readers. ABC had also been used in a wide space by using the neighboring solutions. variety of applications such as the power systems [S284] Effective discrete ABC (DABC) algorithm was proposed with job-permutation-based representation for solving the real- [S285], image processing [S286-S288], aerospace engineering world hybrid flowshop scheduling problem from a [S289], signal processing [S290], communication steelmaking process [125]. In the DABC algorithm, [S291],fuzzy systems [S292] and so on. neighbouring solution generation operator called multi swap 14 5. Bees Algorithm Similar to well established approaches like ABC, BA has Bees Algorithm (BA) was first developed in 2005 by Pham also showed its advantages in many computationally complex et al. [130] to solve the continuous and combinatorial problems that are highlighted in Table.2. optimization problems. BA is inspired by the honey bee food The early development and improvements of the BA are foraging behavior. In BA, a neighborhood search is combined carried out by Pham and Darwish [128], [S164]. The authors with the random search and the bee population is divided into described an enhanced version of BA in which the fuzzy two groups: scouts and recruits. The scout bees are responsible greedy selection criterion is used to search local sites. Pham et for exploring the search space and the recruit bees are for al. [133] proposed an improved BA to handle the dynamic exploiting the solution found by the scout bees. The optimization problem. In the proposed BA, the new search algorithmic parameters of BA are the number of scout bees operators are included and the newly formed individuals‘ (n),the number of sites selected out of n visited sites (m), the survival probabilities are enhanced by the new selection number of best sites out of m selected sites(e), the number of procedure. Packianather et al.[121] presented a new version of bees recruited for best e sites (nep), the number of bees the BA which uses pheromone to attract explore the promising recruited for the other (m-e) selected sites (nsp) and the initial regions of the search space and compared to the original BA size of patches (ngh). The site and its neighborhood and and showed that new version of BA gave an average stopping criterion are defined during initialization. improvement of 41% in convergence speed. Chen and Lien et In the first step, the BA starts with initializing the n scout al. [25] proposed a new optimization hybrid swarm algorithm bees randomly in the search space. Secondly, the sites visited by integrating the BA with the PSP termed as PBA. They also by the scouts are evaluated and the fitness value corresponds introduced a neighborhood-windows technique to enhance the to the quality of the solution. The algorithm proceeds until the search efficiency and a self-parameter updating technique to termination criterion is satisfied. In the sub-step (a), bees with avoid getting trapped into a local optimum in solving the high- good quality solutions are chosen as ―Selected bees‖ and the dimensional problems. The proposed technique is used to sites visited by them are selected for the neighborhood search. solve facility layout problem (FL) and compared the The best m<=n scout bees are selected and the rest are performance to that of BA and PSO. Tian et al.[S175] discarded. The selected bees are further divided according to developed a chaos quantum honey bee algorithm by combing their fitness values into e elite selected bees and the m-e non- chaos optimization and quantum computation to tackle the elite selected bees. Alternatively, the probability to be selected uncertain complex optimization problems such as transmission is determined by the fitness values. In sub-step (b), more bees system expansion planning based on random fuzzy chance- are recruited to follow the elite selected bees and search in the constrained programming. best site neighborhood. The number of recruit bees assigned to Xiaojing et al.[S180] proposed to use an adapted BA to each elite selected bees depends on the quality of the solution, identify fuzzy measures from sample data and the adaption is neq recruits for each elite bee and nsp recruits fir each non- based on needs of fuzzy measure extraction problems. BA was elite bee. At the assigned neighborhood, each recruit bee also hybridized with ABC to solve the constraint optimization performs a local search using the following heuristic step: problem in [176]. * Huanzhe et al.[S171] proposed an improved bees (IBA) xjj( x ngh ) ( rand (0,1). ngh .2) (10) algorithm for solving large-scale layout optimization problem If the solution found by the recruit bees is improved over without constraints, which differs from the original BA in the the best selected bee‘s solution, the best will be replaced by initialization and implementation of neighborhood search. improved solution. Otherwise, the previous best will be kept. Dereli and Das [35] presented a hybrid algorithm by In the end of substep (c) and substep (d), the scout population hybridizing heuristic filling procedure with BA to solve is filled up with these m solutions and the rest of bees i.e., n-e container loading problems a NP-hard optimization problem. bees are initialized with random solutions. In this way Abdullah and Alzaqebah[S254] proposed hybrid self-adaptive algorithm proceeds till it reaches the global solution or meets bees algorithm to solve examination timetabling problem, in the predefined criterion. Algorithm 6 summarizes steps which BA was hybridized with SA and late acceptance hill involved in BA. climbing algorithm to increase the convergence speed. The disruptive, tournament and rank selection strategies were used Algorithm 6. Bees Algorithm to select the sites to preserve population diversity. 1. Initialize the bees randomly in the search space Apart from numerical function optimization problems (that 2. Evaluate the fitness includes NP-hard, combinatorial problems etc) BA has also 3. While (! = termination criterion) been widely used in real world engineering problems. Fonseca (------New population is being formed------) et al.[41] devised the new variant of BA, which has the local a. Select the sites (solutions) search ability and the abilities to generate scout locations and b. Recruit bees to perform local search on selected solutions perform the waggle dance. The authors used this approach to and evaluate fitness solve the protein structure prediction problem in molecular c. Out of the solutions obtained (patch) select the best biology. Shermeh and Azimi et al.[153]presented a novel improvement hybrid intelligent system that automatically recognizes a d. Assign remaining bees to search randomly (scouts) and variety of digital signals. In this recognizer they proposed a evaluate fitness multilayer perception neural network with resilient back 4. End While propagation learning algorithm as classifier and optimized the 15 classifier design by BA. Shrme[154] investigated MLP neural performance, compared to the existing state-of-art algorithms network classifier with quick prop (QP) learning algorithm, like DSR, AODV and DSDV. In BeeAdHoc, two types of extended delta-bar-delta (EDBD), super self-adaptive back agents are mainly used for routing: scouts and forages. Scouts propagation (SuperSAB) and conjugate gradient (CG). The discover the new routings to the destinations. Foragers best features are selected by BA to be fed to the classifier. transport data packets while evaluating the quality of the Pham and Sholedolu [134] hybridized PSO with BA to train routes simultaneously. Mazhar and Farooq [101]made a prime Neural Networks for classifying wood boards according step in developing the secure routing model for bio-inspired different type of defects. MANET routing protocols and proposed a security Beesec In the area of electronics and communications, Pham et model for BeeAdHoc. al.[131] used BA in designing a two-dimensional recursive Artificial immune system (AIS) isa promising potential filters, studied the adaption of BA optimization technique in solution for solving MANET security problem. To challenge parallel and distributed computing [S169]. Ang et al.[S174] MANET security issue, Mazhar and Farooq[101] developed described an application of BA with new operators excerpted the AIS-based security model to detect the misbehaviors in from TRIZ methodology. BA is employed to optimize the BeeAdHoc and BeeAIS. Due to various reasons such as assemble sequence problem in a printed circuit board (PCB) dynamic topology, diverse flooding patterns, contention at the machine. They also made a case study taking various medium access control (MAC) layer, it is difficult to model constraints into consideration and claim that BA enhanced MANET routing protocols. To overcome this shortcoming, with TRIZ operators is performing well mainly in the PCB Saleem et al.[149]introduced two key performance metrics for assembly using a moving-board-with-time-delay type BeeAdHoc protocol: routing overhead and route optimality. machine. Dhurandher et al.[S178] presented a peer-to-peer file The metrics provide the unbiased analysis of BeeAdHoc searching bee (P2PBA) algorithm. In P2PBA, BA is used to protocol and its interesting behaviors. provide an efficient peer-to-peer file search in the mobile and Mazhar and Farooq [102]developed a dendritic cell based ad hoc networks (MANETs). distributed misbehavior detection system called BeeAIS-DC Ang et al.[S167] presented Pareto-based multi-objective BA for BeeAdHoc, to overcome the drawbacks caused due to AIS. to determine the minimum travelling time for a SCARA-type Saleem and Farooq [148] proposed a bee inspired power robot arm, considering the trajectory smoothness. The authors aware routing protocol called Beesensor. The simple bee agent compared the results with variant of GA, Nelder-Mead model is used and only little processing and network resources flexible polyhedron search etc and claimed the performance of are required. Compared to other ad hoc routing algorithms, their proposed approach. Shuo et al.[196] proposed a multi- BeeHive obtains better performance in the fixed networks objective Binary Bees Algorithm (BBA) to solve two-level while BeeAdHoc offers similar or better performance but at distribution optimization in the robot industry. The problem least energy cost. includes assigning missions to the robots and allocates the robots to home stations. Bhasaputra et al.[19]proposed another 7. Bees Swarm Optimization multi-objective Bees Algorithm (MOBA) based on principles To overcome the maximum weighted satiability (MAX-W- on multi-objective optimization. In MOBA, a clustering SAT) problem, Drias et al .[36] introduced a metaheuristic algorithm is included in order to determine Pareto-optimal Set called Bees Swarm Optimization (BSO), based on the foraging step size and applied to solve multi-objective optimal power behavior of real bees. Precisely, the main framework lies in flow problem which is validated on standard IEEE 30-bus the bees‘ strategy, where a colony concentrates its effort of system. harvest on a small number of areas such as the richest and Other miscellaneous yet notable approaches include, easiest of access, out of all the potential exploitation areas distributed and asynchronous bees (DAB) grid-based visited by them. Sadeg and Drias [146] presented a parallel approach, proposed by Go et al.[S179] to optimize the version of the BSO metaheuristic and compared the magnetic configuration in order to reduce the neoclassical performances of the sequential and the parallel algorithms in transport of particles in a nuclear fusion device. Moradi et solving instances of the weighted maximum satisfiability al.[108] investigated the application of BA in the finite problem. Akbari et al.[S186] proposed the so called Powerful element model updating. BA was applied on a piping system BSO which provides different patterns that are used by the to update several physical parameters of its FE model. Then, bees to adjust their flying trajectories. the numerical model is tested and the parameters obtained are In order to handle the stagnation problem, Akbari et al.[6] compared with the experimental ones. extended BSO to improve its performance using repulsion factor and penalizing fitness. The time-varying weights (TVS) 6. BeeAdhoc are introduced to obtain the trade-off between exploration and exploitation. They compared this BSO and extended approach Walker [S181] emulated the honey bees foraging behavior with existing algorithms on different test suites and claim that to assist customized internet routing and congestion their method produced excellent results. Later, Drias and avoidance. This exploration model constructed by Walker has Mosteghanemi [S187] designed BSO based web information been used by web search engine that builds the document retrieval to explore the prohibitive number of documents to warehouse for the indexers of web page. Wedde et al. [185], find the information needed by the user. [S185] presented a new efficient routing algorithm called Askarzadeh and Rezazadeh [11] proposed artificial bee BeeAdHoc, inspired by the honey bees‘ foraging basics. In the swarm optimization algorithm (ABSO) to identify the mobile ad hoc networks, this routing algorithm offers better 16 parameters of the solar cell model. Following the honey bees‘ models mainly in communication applications. intelligent collection and nectar processing behaviours, ABSO Information sharing within the social structure of honeybees algorithm identified the parameters of a 57 mm diameter results from Bee-to-Bee communication between distinct commercial silicon solar cell in [11]. The results demonstrated hierarchical levels as well as between members of the same ABSO algorithm‘s superiority to other methods. distinct levels. Centered on this supposition, Walker [S193] presented Tocorime Apicu, an information sharing model, to 8. Virtual Bee Algorithm combine information sharing and processing of the honeybees. The model is adapted to sync with information fluctuations Yang [198] proposed Virtual Bee algorithm (VBA) based occurred in internet communication. For similar kind of on honey bee foraging behavior. In VBA, the virtual bees are software application, Gordon et al. [S194] presented a randomly initialized in the search space. Each bee‘s position is distributed algorithm for generating any arbitrary pattern by represented each virtual food source. The nectar amount anonymous homogenous mobile agents on a grid. corresponds to the fitness function value of each position. The Inspired by the honey bees‘ dance language and foraging virtual bees explore and exploit the search space continuously. behavior, Wedde et al.[S195] presented a fault-tolerant, In due course of time they interact with other bees and pass adaptive and robust routing protocol and termed it as BeeHive the information of the food patches to other bees. The bee that algorithm, which does not need any global information and receives information will start foraging with these guide lines works with the local information. In the proposed protocol, for faster foraging. In this way, the solutions are found by the network regions called foraging zones are defined and the bee interactions between the bees. In 2010 khan et al.[S188] agents travel through these network zones and share implemented this VBA in designing supplementary damping information on the network to update the local routing tables controller for thyristor controlled series compensator (TCSC) (Wedde and Farooq [S196], [184]). Wedde et al. [S197] for improving the stability of power system. discussed the security threats of routing protocol. The protocol is extended into the security model to protect the beehive from 9. Miscellaneous Methods Resembling Bees Foraging in the threats. The extended protocol is termed as BeeHiveGuard. Nature Wedde et al.[187] integrated artificial immune system into BeeHive algorithm and named as BeeHiveAIS.BeeHiveAIS Quijano and Passino [S189, S190],[141] developed an and BeeHiveGuard are compared using the empirical algorithm for solving the optimal resource allocation ratification framework. problems. The algorithm is based on honey bee social Wang et al.[S198] proposed a QoSuni-cast routing scheme foraging. The authors proved that if several algorithms (of based on the beehive algorithm. Weddeet al.[186], similar kind based on foraging) compete each other in the [S199]introduced a completely decentralized multi-agent same problem domain, their algorithms‘ strategy is stable approach (termed BeeJamA) on multiple layers in which the evolutionarily and as per Nash equilibrium. Moreover, the car/truck routing problems are solving using the beehive authors showed that the allocation strategy is globally optimal adaptive algorithms. Navrat [S200]; Navrat and Kovacik in the single/multiple hives. The proposed theory was [S201]presented a web search approach based on a beehive successfully applied for solving dynamic voltage allocation metaphor. The beehive metaphor includes a dance floor, an problem related to interconnected grid of temperature zones. auditorium, and a dispatch room and can be used as the model Baig and Rashid [14],[S191] presented a different Honey to represent the web search processes. Navrat et al.[112] used Bee Foraging algorithm which performs a swarm based the beehive metaphor model to search for the user‘s collective foraging for improving its fitness (nectar amount) in predefined web-pages. The authors reported their experimental promising neighborhoods in combination with individual results in the paper and stated that in the search, the model scouting searches. Although their approach seemed to be bit select the best routes and rejected the bad ones. Olague and different it shares some similarities with BA proposed by Puente [S202] proposed honey bee search algorithm. As in the Pham. honey bee communication system, the 3D points are Based on self-organization of honey bee colony Lu and communicated to achieve an improved sparse reconstruction. Zhou [S192]developed a Bee Collecting Pollen (BCP) Thiscould be used in further visual computing tasks. algorithm based on self-organization of honey bee colony. They validated their algorithm on Travelling Salesman V. METHODS BASED ON HONEY BEE SWARMING benchmark. Ko et al.[80] proposed a self-adaptive grid computing protocol called Honeydews which draws its A. Decision Making and Nest-Site-Selection inspiration from adaptive bee foraging behavior in nature and Passino [127]was one among the first who laid steps in applied it to grid based applications. They also developed a establishing an abstract mathematical model for honey bee variant of Honey adapt, called HoneySort, for application to nest-site selection process. As said prior Nest-site selection is grid parallelized sorting settings using the master-worker a process of social decision making in which the scout bees model. via swarming locate several potential nest sites, evaluate them, B. Bee Dances and Communication and then select best sites by means of competitive signaling. So far models developed based on Bees Communication are Based on above intelligence, Passino developed a model and heavily used in the applications of mobile networks and validated that the model possesses the key features of the internets. This section briefs few significant contributions bee‘s decision-making process. Detailed information about made by researchers in developing efficient optimization 17 these works can be obtained in Seeley et al.[S203], Passino crux of algorithm lies in the optic flow of geo-spatial [S204]; Passino et al.[S205, S206] and Nevai et al.[S207]. information about surrounding location in the foragers. A practical application with respect to Nest-Site-Selection can be ascribed to work carried by Gutierrez and Huhns [49], VII. METHODS BASED ON DIVISION OF LABOR the authors came up with a new idea of introducing the nest Nakrani and Tovey[110] made significant contributions in site making decision behavior of bee in designing fault free solving server allocation problem for internet hosting centers software which is a robust fault tolerance technique via multi based on bees‘ intelligence. The hosting center host services agents thereby improving large scale, critical and complex on a pay-per-use and then dynamically allocates servers to system reliability. maximize their income. But due to various constraints B. Floral and Pheromone laying optimizing server allocation has been a serious issue and to In this context, Ashlock and Oftelie [10] studied to overcome this problem Nakrani and Tovey [S211]introduced a understand the nectar-gathering behavior of population of new honey bee parallel algorithm. They validated the efficacy virtual bees in a field of simulated flowers over several of honey bee parallel algorithm against omniscient, greedy hundred generations. They developed a mathematical model and optimal-static algorithms using synthetic and real request based on the Finite State Automata (FSAs) familiarly called as streams. As the server allocation is similar to honey bee Finite State Machines. Based on this structure an evolutionary forager allocation, the authors proposed a honeybee bio- algorithm is set up and the observations are made for different mimetic algorithm [111]. To highlight the superiority and parameters. adaptive nature of proposed approach they validated it on a Purnamadjaja and Russell [137] reported a paper about the benchmark followed by the comparison between conventional current progress of an investigation into the possibility of algorithms. using pheromone communication between members of a robot Gupta and Koul [S212] presented new swarm intelligence swarm. In this work they modeled the interaction between based architecture named SWAN for IP network management members of a robot swarm which is one form of pheromone to overcome the drawbacks of the traditional network communication in social bees and used in robotic systems to management. SWAN is inspired by the beehive‘s structure and rescue disable robots. According to their analogy, pheromone organization, which represents as an example for communication can offer the efficient communication between ―management‖ and ―division of labor‖. Therefore, in SWAN, robots. Purnamadjaja and Russell [138] also investigated the network is managed as collection of cells with many queen Bee‘s pheromone which has a number of crucial agents‘ assigned specific roles within the cell. functions in a bee colony. In a robotic system, one important Due to limited progress in defining efficient teamwork application is to allow the robots to follow their robot leader. architecture for task execution mechanism by collaborating the Following the queen bee‘s pheromones idea, the robot leader agent groups together and coordinating with each other, Sadik can release different chemicals to bring out different behaviors et al. [58] developed agent teamwork architecture to improve from other robot members. the performance and task execution efficiency. This architecture has its frame work inspired from honeybee teamwork strategies and they also made a short comparison VI. METHODS BASED ON SPATIAL MEMORY between the similarities of Honey bee and Agents team work. AND NAVIGATION Apart from all the intelligent foraging behavior of bees as Sadik et al.[S213] also used this strategy for software agents, discussed earlier, inspired by the bees‘ navigation behavior, which is deployed to work on distributed machines and named Bianco [20]developed a model framework to perform large- it Honey Bee teamwork architecture. scale navigation and mapping in robotics. Lemmens et al.[S208, S209] presented a non-pheromone-based algorithm VIII. POTENTIAL FUTURE RESEARCH DIRECTIONS WITH which combines bees‘ recruitment and navigation strategies. METHODS BASED ON HONEY BEES Based on their experimentation they claim that their proposed Although the literature reported rich amount of research and model i.e., non-pheromone-based algorithm performs more addressed various contributions made by researchers for effectively when collecting food. Their simulations revealed strengthening bee‘s based algorithms such as hybridization, that the proposed approach requires less computational effort. adding new heuristics, and adaptive mechanisms, yet there are Finally, concluding that their method is less adaptive to new research areas and application fields left to explore the pheromone-based algorithms in foraging. The proposed capabilities of bees‘ intelligence. In the following section, we approach uses a direct and straight way to reach to the put forth the important research future directions of Bees destination and it does not consider the obstacles. Thus, the intelligent algorithms. proposed non-pheromone-based algorithm is less adaptive in the obstructed environments. Later, Lemmens et al.[S210] 1) As all these methods are stochastic based methods and all introduced a new hybrid algorithm extended with inhibition of them initiates via uniform random sampling of the pheromones to enhance the adaptability. search space, the search would be effective if the Recently Das et al.[31]proposed a new and first of its kind, probability distribution is also considered while choosing optimization algorithm by synchronizing the ABC algorithm the initial population. Only few of contemporary and spatial memory and termed it as Spatially Informative researchers explored the influence of initial population on Perturbation-based ABC algorithm with saccadic flight. The the performance of the algorithm. The performance of the search technique relies on the random number generation 18 in bees family of algorithms (a few foraging methods like hybridization strategies can be borrowed from the other BA, ABC, BCO etc.). Hence, using the uniform techniques enjoying the hybridization. distribution can improve the search performance of the 5) From the introduction of EAs many papers are published algorithms. As most of the methods obtain the random with new methodologies, improvements, modifications to numbers from subroutine build-in functions available in improve the search method performance and few of them the programming languages which are not distributed more proposed novel bio-inspired strategies but only few of uniformly its worthwhile to make use of quasi random them made contributions in the theoretical understanding numbers or low discrepancy random numbers to obtain of which few of them are GAs, ES, EP (Evolutionary good convergence rates starting from the first iteration to Programming), BFO (Bacterial Foraging Optimization), the end while maintaining the quality of solutions. Most of HS (Harmony Search) [S217]-[S221]. However, analyzing common methods that are rampant in the usage are the Bees family algorithms is still remained open in the Vander-Corput, Halton, Faure and Sobol sequences for research, especially in the convergence property of the initializing the swarm. These initialization schemes algorithms. become handy in solving the global optimization problems 6) Of all the methods discussed above many papers published because of the variation of random numbers generated in are of Artificial Bee Colony (ABC) because of its simple every iteration/generation. exploitation and exploration structure which is balanced 2) Most of the EAs and swarm intelligent algorithms throughout the end of search. Many researchers pointed the (including bees) use normal mutation scheme normally weakness in the mechanism and presented their ideas for based on Gaussian distributions. The advancements of enhancing the performance yet there is still lot of remaining distributions which gives a supervisory control exploration that can be addressed to see true potential of over the distribution patterns came in to existence recently ABC in solving the challenging real-time problems that and distributions based on Cauchy, Levy, Laplace can be always remained as hurdles for state-of-art optimizers. incorporated in to the mutation schemes to control the step Few of them include, in ABC the onlookers choose their length of the bees‘ algorithms mainly in solving numerical food sources based on roulette wheel selection and hence optimization problems. Apart from these types of mutation algorithm may take more computations to select the food works based on incorporation of adaptive mutation sources so selection mechanism like rank-based, strategies which updates there mechanism in the due tournament etc., selections can be embedded. The limit course of iterations may lead to better performance in the parameter is been changed based on the problems, yet algorithms. Karaboga and Basturk [70] said that it will be wise to use 3) There are also few instances in which the search technique limit equal to product of number of onlookers and may struck at local optimum or may reach stagnation so dimensions, it is best suited for continuous optimization there requires some adaptive mechanism to exploit and problems and fails for discrete and higher dimensional explore the search space continuously and also to balance problems hence adaption of limit with help of some the searching (convergence) speed. So, it is possible to adaption strategies can enhance the global searching of think of adding speeding methods like Rechenberg‘s 1/5th algorithm. Apart from these new heuristics, hybridization rules and adaptive mechanisms such as including the discussed above can also be incorporated. isotropic, non-isotropic, and correlated self-adaptive 7) There is also almost unexplored area in the family of bees mechanism. Covariance matrix adaption strategies can also algorithms i.e., integrating the learning strategies of which be incorporated to determine the probability distribution quite interesting are opposition based learning, Rule based for mutation. These mechanisms seem mostly helpful learning (fuzzy approach), Ensemble methods, Reinforce insolving multi-modal functions and which are of current based methodology (obtained from machine learning). All interest in fields related to optimization. these strategies shown their outstanding capabilities in 4) Another potential research may be ascribed to memetic ameliorating performance of various search techniques and methods and hybridization of local methods in to the hence these techniques can be also handled bees inspired search process of bees to make the method more robust methodologies. Of which ensemble based learning is quite and quick. So, far researchers almost hybridized every new, and this comes from the field of machine learning method with another method to make the performance which is the concept of combining classifier to improve more effective. This poses constraint on time of overall classification performance. Interested readers are convergence and care should be taken while hybridizing suggested to go through this portal for further information with new search methods so that it shouldn‘t increase the www.ntu.edu.sg/home/epnsugan/. time complexity of the algorithm. A few of methods that 8) Recently scaling, grouping, adaption, micro population gained wide reputation in hybridizing (which act as local etc., related to number of individuals are drawing attention search strategies) with others EAs are Hooke Jeeves of researchers to have control over the population size method, Nelder-Mead simplex method, annealing strategy, [S222] [S223]. Many of these methods have been greedy search mechanism etc. and when coming to successfully applied to family of DE algorithms and there algorithms simulating swarming methods the search is immense chance to apply these techniques to bee family strategies can be enhanced with help of PSO (gbest and algorithms. The main concept of these to change the size pbest updating). Apart from these there is a probability of of population in the due course of iterations or to initialize adding new heuristics based on the problem and few less number of population with some additional operators 19 to mainly save the number of Functional Evaluations and there hasn‘t been much focus on theoretical aspects of many hence to reach the solutions in less number of epoch. of the algorithms and contributions in terms of exploiting 9) Real world optimization problems may very often come stability, convergence and chaos of the swarm remains with several linear and non-linear constraints which challenging problems in this community of algorithms. severely restrict the feasible search space, thus adding to Though NFL (No Free Lunch) theorem [205] pointed out that the challenges posed to an optimization technique. Bees finding cure all algorithms is difficult it‘s worthwhile to foraging based optimization techniques may be coupled choose an optimization algorithm that has advantage on with advanced constraint handling techniques to explore particular problem and research in that direction will enable in the potential of these methods on constrained optimization. developing robust algorithm which can attack problems that Such algorithms may also be investigated on problems are in parallel lines. Considering the various interesting results with dynamically changing constraints. provided by bees based algorithms we firmly believe that 10) Many-objective optimization problems [S224], [S225] these groups of algorithms have authority over various include more than three objective functions. The methods and will continue to serve as state-of-art optimization conventional MOEAs use the Pareto optimality as a tools in future. ranking metric and thus may perform poorly on these As a final note, in the field of the nature inspired many-objective functions. Hence, extending BA, BCO, metaheuristics, new algorithms are being published in ABC algorithms to solve multi-objective problems remains countless number of conferences and journals very frequently. open as a challenging field of future research. Inspirations for designing an optimizer are coming from diverse sources ranging from human beings to flu virus! But IX. CONCLUSION are these numerous algorithms really effective? Will they It has been almost two decades since researchers started to survive in the long run and in face of the challenges posed by develop different algorithms based on Honey Bees‘ collective real life problems? Or will their influence remain largely intelligence for complex and challenging optimization stipulated within the world of paper writing? In a recent problems that are not easily solvable by conventional methods article, Sörensen [159] expressed his concern on the current such as trial and error, linear and non-linear convex trends in metaheuristic research in the following way – ―… it programming. The literature studies reveal that there has been seems that no idea is too far-fetched to serve as inspiration to vast amount of articles which are cantered among the launch yet another metaheuristic. …..we will argue that this optimization algorithms simulating the collective behavior of line of research is threatening to lead the area of the bees. Hence, to make easy for the potential researchers to metaheuristics away from scientific rigor‖. contribute to the area of bees‘ based computational intelligent We believe careful benchmarking with proper performance methods we tried to provide brief yet comprehensive details of measures can filter out the junks and indicate the really the algorithms that are extensively used by the researchers. powerful natural computing methods for taking up the real We started with providing need for biologically inspired challenges. The research on honey bee inspired algorithms, in algorithms and elaborated the discussion on life cycle of near future should also be more scientifically structured and honey bees and its major roles that laid foundations for the rigorously validated. The ideas should be presented in a algorithms discussed. Fig 1 provides the glimpse of stages the metaphor-free language and more directly (a trend that is bee carries during her cycle and in subsequent sections we lacking in majority of the papers published on bees-inspired provided discussions on algorithms involved in its each stage. algorithms). Following this line, the researchers in this vibrant Starting with mating of honey beetill division of labour we area have miles to go before they can sleep! have provided a brief overview of more than dozen of algorithms. References To give a succinct and powerful grasp on a particular optimization we gave formal introduction of the most 1. Abbass, H.A. MBO: Marriage in honey bees optimization-A prominent algorithms and then discussed their developments, haplometrosis polygynous swarming approach. in Evolutionary modifications and applications on challenging practical Computation, 2001. Proceedings of the 2001 Congress on. 2001. IEEE. 2. 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Optimization", IEEE Transactions on Evolutionary Computation 1, 67. Table 2. Summary of some of the most representative honey bee inspired algorithms. Biological aspect Name of Algorithm and Metaphor Deciphered Features of the algorithm of the Honey Developers Bee Social Life Cycle Queen bee → fittest solution, which is Imposes a strictly elitist form of crossover Queen bees Queen Bee Evolution (QBA) allowed to crossover with other solutions, where the decision variables from the best by Jung [64] within the framework of a standard GA solution trickle down to different offspring with two mutation rates. solutions through crossover. Basically a modification of GA. Queen and drone → candidate solutions, Involves several heuristic methods and Bees mating and Marriage in Bees workers → local search heuristics for greedy local search in the framework of GA marriage Optimization (MBO) by improving offspring solutions (broods) as the new solutions (broods) are generated Abbas [1] by using crossover and mutation. Number of control parameters is high and their tuning is not always straightforward. Honey Bees Mating Queen and drone → candidate solutions, Very similar to MBO, the five stage Bees mating and Optimization Algorithm broods → newly generated candidate algorithm adapts the local search heuristics marriage (HBMO) by Haddad et solutions, based on the improvements of the newly al.[50], [S28, S29] workers → local search heuristics for generated solutions (broods). improving offspring solutions Bees → search agents, Sato and Hagiwara's BS generates multiple Bee System (BS) by Sato searching for food → exploring the search solutions in the neighborhood of the best Honey bees and Hagiwara [151]; space with low cost mathematical solution. In Lucic and Teodorovic's foraging alternative formulation by operators by some individuals of the alternative BS (mostly applied for Lucic and Teodorovic [91] population (scouts), combinatorial optimization) employs Bee colony → population or sub- additional exploring agents (scouts) for each population of candidate solutions, population of solutions. Food source → candidate solution, Quality of food source → fitness of a solution. Bee Colony Optimization Waggle dance → sharing the information Bees create partial solutions to the Honey bees (BCO) by Teodorovic and about quality of solution obtained by combinatorial optimization problem and go foraging and Dell [170] different search agents. on balancing between explorative forward communication (rest are similar to BS) pass and exploitative backward pass phases of the algorithm. Bees/foragers → search agents, Mostly applicable to combinatorial Honey bees Bee Colony Optimization Dance → sharing information about optimization problems, the foraging or foraging and Algorithm (BCO) by Chong fitness of current solution, nectar exploration part uses transition communication et al. [28] Recruitment → fresh start of building a probabilities similar to the ant colony solution, optimization algorithm. Following → continuing with the older partial solution, Nectar → destination state 25 Bees → search agents, Most popular bees foraging based algorithm Food sources → candidate solutions, for continuous optimization (later extended Nectar amount → fitness value of a for discrete and binary optimization solution, problems). The explorative coverage of Honey bees Artificial Bee Colony (ABC) Employed bees → generate solutions in search space, especially form multi-modal foraging and by Karaboga [69] the neighborhood of existing ones, functional landscapes can be poor. The communication Onlooker bees → share information from neighborhood exploration in onlooker bees employed bees and randomly choose some phase is by forming an arithmetic solutions for further exploration, recombination of a randomly selected Scout bees → neighborhood exploration dimension of the current solution with the of newly initialized solutions that replace corresponding dimension of another solution older ones (which could not be improved available. by neighborhood explorations). Flower/food source/site → candidate The algorithm combines a neighborhood solution, search strategy with global search and can Bee colony → population of search be used for solving both continuous and Honey bees Bees Algorithm (BA) by agents, combinatorial optimization problems. foraging and Pham et al. [130] Profitability → fitness of a solution, However, the exploration of the search space communication Flower patch → neighborhood of a is not somewhat intelligently guided and the solution, neighborhood search may waste FEs Recruitment procedure → to search considerably. further the neighbourhoods of the most promising solutions, site abandonment procedure→ re-initialize some of the poorer solutions. Scout → agents discovering new routes to Bees' BeeAdHoc by Wedde et al. destination, An efficient routing algorithm for mobile ad communication [185][S185] Forager → transport data packets as well hoc networks. as evaluate the quality of the routes simultaneously. Table 3. Summary of applications of the bees inspired algorithms Sub areas and problem Types of Bees Algorithms used and References Hybridization Queen Bee Queen Bee with GA [64], Improved Bee Evolutionary GA (BEGA) [107] Honey Bee Mating Optimization HBMO with simulated annealing [S261] Marriage in Honey Bees (MBO) MBO with annealing approach [168] , MBO based onNelder Mead [S25], MBO-Wolf pack search method [S26] Bee Colony Optimization (BCO) Simulated Bee Colony Optimization [S57] Artificial Bee Colony ABC-PSO [S115], Differential ABC [S140],Hybrid Quantum evolutionary algorithm (QEA) with ABC [37], G-best guided ABC [203], Memetic ABC using Nelder Mead [39], Simulated Annealing based ABC [24] Modification of Bee intelligence Based on Heuristic Methods MBO Fast-MBO (FMBO)[197], Modified FMBO [180] BCO BCO enriched with elitism, local optimization and adaptive pruning [190] ABC ABC with Banach spaces[140], ABC involving hyper-mutation and a novel crossover operator [88],Cooperative approaches oriented ABC [38], [S103], Adaptive control mechanism in ABC [5], Elitist ABC [106],Smart flight and dynamic tolerances in ABC [105],ABC with ripple communication strategy [95], Parallelization of ABC [126], Adapting of onlooker bees [2], Best-so-far selection ABC [15], ABC embedded with Deb‘s heuristic rules [71], RosenbrockABC[65], Parametric tuning of ABC [S77],ABC with exponentially distributed mechanism (ABC-EDM) [S111], Fast Mutation ABC [S134], Powell method based ABC [44], ABC with Saccadic Flight Strategy Bees Algorithm (BA) BA with fuzzy greedy selection criterion [128], BA with pheromone-based recruitment [128], Improvised initialization oriented BA [S171] , parallel bees algorithm [93] Bee Swarm Optimization (BSO) Parallelized BSO [146] Electrical Engineering Economic Dispatch Modified QBA[118], HBMO [S42], BCO[16], ABC [S78, S84, S94, S95], BA[82][S177], BA with Pareto Dispatch [S162], Fuzzy HBMO [45], Hybrid BCO and Quadratic Programming [17], Enhanced BSO [S257], Incremental ABC [S240], ABC with Dynamic Population [S241], GbestABC [S247] Boost Converter & PI/PID Controller, Queen Bee Assisted GA [162], Hybrid Genetic ABC [S125], Cauchy Mutated ABC [142], BCO [68] inverter Capacitor Placement, compensator Queen Bee Assisted GA [S214], Virtual Bee Algorithm [S188], Bees Algorithm [S176] Distribution System‘s network HBMO [S43], ABC[143][S127], Modified ABC [S91], Priority ordered constrained search along with ABC configuration [S129], Hybrid HBMO and Fuzzy sets [117], Chaotic Improved HBMO [115], Efficient Multi Objective HBMO [S40, S41], fuzzy method based on HBMO [116], A hybrid HBMO and Discrete PSO [114], BCO [S65] Optimal Power flow ABC [S215], Hybrid DE-ABC [S250] Load Profile Clustering HBMO [S45] HVDC and FACTS BA [S168], Multi-objective BA[60] Fault location Enhanced HBMO [58] 26 Solar Cells Artificial bee swarm [11] Engineering Design, Control System and Robotics Fuzzy Controller in Robotic Systems Modified queen bee evolution based GA [13], A Novel Parent Selection Operator in GA [12], BA [S154][135] PI/PID Control Queen Bee with nelder-mead [179], ABC [ S112], Chaotic and Non Chaotic Systems ABC [S113, S110, S111] Automatic Voltage Regular Systems ABC [S146] Robot Motion path planning and ABC [S216], HBMO[S32] navigation Aircraft control Chaotic ABC[194], Evolutionary Genetic Algorithm and Clustering Method [182] Robotic Arm Bees Algorithm [S151, S165, S167]. Engineering and Mechanical Design Bees Algorithm [S156, S157, S159, S166, 124, S172], Artificial Bee Colony [4] Machining and milling Process ABC [S79, S80, S81, 94, S108] Container over loading problems hybridized heuristic filling procedure with BA [35] Swarm Robots Distributed BA [S252] Civil Engineering Vehicle Routing Improved BEGA [181], HBMO algorithm with Multiple Phase Neighborhood Search-Greedy Randomized Adaptive Search Procedure (MPNS-GRASP) and the Expanding Neighborhood Search (ENS) [99], [S36], Integrated Bee and Fuzzy System [S52], decentralized multi-agent approach (termed BeeJamA) [S199] Transportation Engineering Bee System [91, 92], [S50], Multi-Agent Systems [S51], BCO[169, 170], BCO [S233] Traffic Mitigation, Ride Matching Fuzzy Bee System [S56], BCO [S60] Problems, p-center problem BCO [172][S63] Travelling Sales Man Problem (TSP), BCOA [S69], BCOA with the Fragmentation State Transition Rule (FSTR) [188],An efficient BCO with Probabilistic TSP, Euclidean TSP Frequency Based Pruning [189],BCO with local search [S70], Greedy Subtour Crossover method with ABC (ABC-GSX) [S107], HBMO involving GRASP and ENS [98], [S39], Fast Bee Colony [S229], Hybrid Ant Bee Colony [S230] Optimal Reservoir operation HBMO [S28, S29], [51] Water Distribution Networks HBMO [50, 156], [S30, S31] Structural Analysis NelderMead Simplex combined with ABC [66], BA[108] Design of Truss structures ABC with Adaptive Penalty function [157], Modified ABC [158],[S132], Parallel vector evaluated type, swarm intelligence multi-objective variant of ABC (VEABC) [118] Multi-zone dispatch systems BA [S170] Weighted Ring Arc-Loading Problem Efficient traffic loading algorithm-ABC [S121] Pattern Recognition and Image Processing Data Clustering, Mining& Feature HBMO [S33, S34], HBMO along with GRASP[100], ABC[73, 202],[S99], Chaotic ABC [S143], Selection BA[132],[S158], ABC and GRASP [S86], BSO [S255] Fuzzy Clustering BA [S161] Image Compression HBMO- Linde-Buzo-Gray (LBG) [55] Adaptive Image Restoration ABC [S142] Active Contour Model HBMO [56], HBMO-SNAKE [S260] Fractal image compression Local no-search scheme along with HBMO [3] Image analysis and pattern recognition HBMO [S47], ABC [S90] Image segmentation, Fuzzy entropy and Bee Colony Algorithm [S58], ABC [96] Segmentation of MR brain images FCM improved ABC algorithm [S109] Target recognition for aircraft ABC optimized edge potential function (EPF) approach [193] Image Edge Enhancement ABC [S88, S89] Multilevel Image Thresholding ABC [S100], [54] Blind image de-convolution BA [S253] SVM Dynamic ABC [S239] Signal Processing Communication signals recognition BA and MLP neural [154] Blind signal-type classification BA[48] Routing and wave length assignment BCO [S53] PAPR Reduction of OFDM signals ABC [183] Electronic Engineering Intrusion detection system ABC-support vector machine algorithm [58] CMOS inverter, Multilevel inverter ABC [45], [S104], BA [78] Multiple Sequence Alignment problems ABC [17, 33], [S105,S106] Multiplier-less non-uniform filter bank ABC [97] trans multiplexer Loney‘s solenoid benchmark problem Gaussian ABC [29], [S136] Electronic devices and circuits ABC [145], [S146], Queen Bee Evolution [195], improved ABC [S244], modified ABC [S269] Design of digital filters ABC [74],[S123], BA [131] Antennas ABC [S138, S139], ABC with inverse fast Fourier technique [S139], BA [47, 48, 152] PCB assembly optimization BA [S159], BA enhanced with TRIZ operators [S174], ABC [S131] OFDM ABC [183], ABC enhanced with Tabu search [53] Computer Science Engineering Software test optimization framework ABC [63], [S117], BCO [S232] Task allocation problems HBMO [67], distributed BA [62] Reliability redundancy allocation Penalty guided ABC [199] mobile and ad hoc networks (MANETs) peer-to-peer file searching with BA [S178], Bee Adhoc[185], BeeAIS with Dendrite cell approach [S184] 27 Routing protocols BeeSec [S182], BeeAIS[101], BeeSensor[148], Bee Adhoc[149], [S183] Exploring of information Bee Adhoc [S181], BSO [S187], Approach based on information sharing and processing models of honeybees [S193], BeeHive Metaphor [S200, S201], [112] Max weight satisfiablity Cooperative BSO [36] Satisfiability Problems (SAT) MBO with GSAT and random walk [S21], A single queen bee based MBO [S22], MBO with annealing approach [S23], Multilevel BSO [S256] Knapsack problem, Quadratic Knapsack ABC [S82, S83, S102] problem, Multi-dimensional knapsack Set Covering Problem (SCP) ABC with local search [161] Graph coloring problem Hybrid ABC [40] Server allocation in internet hosting Division of labor phenomenon [110, 111],[S211] centers Improving efficiency of software agents Honey Bee Team work architecture [147], [S213] Stochastic dynamic programming Honey-Bees Policy Iteration [23] Spanning Tree, Quadratic Spanning Tree QBE crossover with GA [192], ABC [155, 160], [S137] Sensor Networks ABC [S85, S86, S96, S97, S98, S249] Scheduling BCO [33, 163], Reserved BCO [S231] Sequence Planning HBMO [S227] GPU Parallel Bees Algorithm [93] Market Segmentation and Scheduling Market Segmentation Integration of self-organizing feature maps and HBMO [9], HBMO-PSO [26] Environmental integrated closed loop ABC [S120] logistics model Scheduling BCO [32],[S61], Parallelized BCO [S62], BA [S153], BCO algorithm with idle-time-based filtering [59], Discrete ABC [123, 167], [S135], BCOA [27, 28], BCOA with big valley land scape [191], ABC [81], [S116], ABC with Random Key [S122], BA [204], two-stage ABC [42], Effective ABC [125], discrete ABC [124], Hybrid ABC[83] Bio Informatics DNA sequences Multiobjective ABC [S141], BA [S152] Protein related and structure ABC [S92, S93], Parallel ABC [S126], Modified MBO [S27], BCO [S228] Protein conformational search BA [S160], BCO [41] Artificial Neural Networks Training of Feed-forward ANNs ABC : [70] [S73], BA [136], Complex Neural Fuzzy System [S142] Medical Pattern classification problems ABC [S74], [120] Evapotranspiration problem ANN-ABC [119] S-system models ABC-NN [200] Wavelet Latin Hypercube Sampling Bee Recurrent Neural Network (BRNN) optimized by ABC algorithm with Monte Carlo Simulation [201] Bottom hole pressure prediction hybrid ABC-back propagation strategy (ABC-BP) [61] Wood defects BA [S148], BA with SVM [S155], Hybrid PSO-Bees Algorithm [134] Control chart pattern recognition BA [S149, S150] Forecasting output of IC industry Marriage in honey-bees optimization algorithms [122] Financial forecasting problems HBMO [S39], ABC-Recurrent Neural Network [57] Nuclear Engineering Fusion reaction ABC enhanced with grid type computing environment [S119], Distributed and Asynchronous BA [S179] Fuel Management Optimization ABC with Random Keys (ABCRK) [34] Others Multi-objective problems Multi-objective HBMO [117], Chaotic Improved HBMO (CIHBMO) [115], [S42], CIHBMO with local search [116], Pareto BCO[S55], multi-objective BCO [89], Multi-objective ABC [124],[S79, S80, S81, S95 S118,S141], Pareto-based ABC [85],Vector Evaluated ABC [118],Multi-objective BA [19, 60, 82, 129, 152], Binary Bees Algorithm [196], BA with Pareto Dispatch [S162], Pareto based BA [S167], Modified MBO [S226s] Constrained Optimization BEGA [182], MBO [1], [S21, S22, S23], HBMO [S31] ABC [4, 5, 105, 106, 155], [S72, S122, S129], modified ABC [71], BA [204], Face Constrained Problem: hybrid ABC and BA [176] Multimodal & Dynamic Optimization ABC [S75, S140], BA [S123, S170], Labor division [147], Honey bee behavior [186], Honey-Bees Policy Iteration [156], Differential-ABC [S140], BeesAdHoc[101], Honey bee foraging [14], [S68],[S191] Stochastic optimization problems BA [S163] Multivariate Improved ABC [140] High dimensional and large-scale HBMO [99], ABC [4], [S75, S76], Bees navigation [20] Multidimensional ABC : Numerical Function Optimization [72], Engineering Design Problems [4] BA : Numerical Function Optimization[S147], Environmental/Economic power dispatch [82], orthogonal frequency division multiplexing [152], optimal allocation of FACTS [60] Miscellaneous Portfolio optimization: BCO [S54], ABC [S124], Two level distribution problem: Bio inspired Bees Algorithm [196], Direction Finding of ML Algorithm ABC [S113], Sudoku and NP Complete Problems : ABC [S87] Direction Finding : ABC [S114], Inverse Heat Conduction: ABC [S130], Non-Traditional Machining: ABC [S145], Coordination of overcurrent relays: BA [S173],Nurse Rostering: BCO[175]; timetabling problems: Self-Adaptive BA [S254], Plant Cycle Location Problem [S35], Power System State Estimation [S43],[113] 28 Supplementary Reference List [S1] Michener, Charles D. 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