1 Genetic Algorithms in Wireless Networking: Techniques, Applications, and Issues Usama Mehboob, Junaid Qadir, Salman Ali, and Athanasios Vasilakos

Abstract—In recent times, wireless access technology is be- his landmark 1950 paper on machine intelligence [5]. Holland coming increasingly commonplace due to the ease of operation used the biological metaphor of chromosomes to refer to and installation of untethered wireless media. The design of strings of binary symbols encoding a candidate solution to wireless networking is challenging due to the highly dynamic environmental condition that makes parameter optimization a the given problem. Holland proposed using the computational complex task. Due to the dynamic, and often unknown, operating analogues of the biological evolutionary processes of random conditions, modern wireless networking standards increasingly mutation, crossover, and natural selection [6] to enable popu- rely on machine learning and artificial intelligence algorithms. lations of chromosomes to get increasingly better at problem Genetic algorithms (GAs) provide a well-established framework solving. The underlying premise is that given enough time, the for implementing artificial intelligence tasks such as classifica- tion, learning, and optimization. GAs are well-known for their process would converge towards a population that contains a remarkable generality and versatility, and have been applied in chromosome (or chromosomes) that solves the given problem. a wide variety of settings in wireless networks. In this paper, Apart from the mutation and crossover operators, The design we provide a comprehensive survey of the applications of GAs in of a GA framework also involves other design issues such wireless networks. We provide both an exposition of common GA as genetic representation (encoding), population initialization, models and configuration and provide a broad ranging survey of GA techniques in wireless networks. We also point out open fitness function formulation, and a selection mechanism. More research issues and define potential future work. While various recently, researchers have also proposed the use of altruistic surveys on GAs exist in literature, our paper is the first paper, techniques in an evolutionary framework that involve cooper- to the best of our knowledge, which focuses on their application ation as a fundamental primitive [7]. in wireless networks.

A. Motivations for using GA I.INTRODUCTION 1) Generality and Versatility: GAs apply in a wide variety The study of nature is a rich source of inspiration for of settings and can be easily molded to particular problems. researchers working in the area of artificial intelligence and GAs constitute a very general meta-heuristic technique which machine learning. In particular, the human brain and the can be thought of as the sledgehammer of the craft of algo- biological process of evolution have helped develop and guide rithms, much like the technique of artificial neural networks research in the neural network, and the evolutionary algorithms (ANNs). In particular, GAs can be readily invoked in areas communities. A genetic algorithm (GA) is a metaheuristic that do not yield readily to standard approaches, or when computational method [1], inspired from biological evolution more specialized techniques fail. GAs are capable of solving [2], that aims to imitate the robust procedures used by various extremely large problems that have large search spaces. GAs biological organisms to adapt as part of their natural evolution. are very good at navigating through huge search spaces to GAs have been successfully used in fields as diverse as air- heuristically find near optimal solutions in quick time. In ad- craft industry, chip design, computer animation, drug design, dition, GAs can work even when the objective function is not arXiv:1411.5323v1 [cs.NI] 19 Nov 2014 telecommunications, software creation, and financial markets exactly known since GAs rely only on an objective function’s [3]. evaluation (without necessarily knowing the objective function The field of genetic algorithms (GA) was established by explicitly). Although GAs do not guarantee optimality, GAs John Holland who investigated the evolution of complex are generally useful in practice. Bhandar et al. [8] showed that adaptive systems (CAS) comprising interacting genes, starting although GAs do not guarantee convergence to an optimal in the early 1960s, and culminating in the publication in solution, GAs avoid local optimas with a high probability 1975 of his seminal book on this topic [4]. The idea of through the use of mutation and crossover operators. embedding computers with learning inspired from evolution goes back even further as Alan Turing proposed a “learning 2) Adaptiveness and Online Problem Solving: To under- machine” which would parallel the principles of evolution in stand adaptivity in changing conditions, we will initially develop the idea of a ‘landscape’ both as a metaphor (in which Usama Mehboob ([email protected]), Junaid Qadir (ju- we visualize ourselves as climbing a landscape in pursuit of [email protected]), and Salman Ali ([email protected]) are with the Electrical Engineering Department at the School of Electrical the highest peak) and as a mathematical object (in which the Engineering and Computer Science (SEECS), at the National University of value of the function maps to the elevation of the landscape). Sciences and Technology (NUST), Pakistan. Junaid Qadir is an Assistant Pro- Building upon the metaphor of fitness landscapes, and the fessor at SEECS, NUST. Athanasios Vasilakos ([email protected]) is a Professor of Computer Engineering at the University of Western Macedonia, insight of GAs as stochastic search algorithms, two landscape Greece. models of relevance to optimization through GAs have been 2 proposed by Page [9]. Rugged landscapes are landscapes in the high performing basic building blocks. which there are many peaks, valleys, and troughs (and not 4) Parallel Nature and Scalability: Traditional theory of a single peak). Rugged landscapes assume that the fitness GAs presumes that GAs accomplish the culmination by dis- levels do not change; in evolutionary systems, however, the covering, emphasizing, and recombining the good traits of fitness function is also dependent on context, and on the chromosomes in a vastly parallel manner. GAs incorporate behavior of other competitors. This can be captured by the multiple solutions together in a ‘population’ of solutions. GAs metaphor of dancing landscapes—which are adapted from use evolutionary techniques to test and improve the solutions rugged landscapes. When a landscape ‘dances’, local peaks by using techniques such as mutation, crossover, selection, may change, making a solution that was earlier optimal no and recombination. The parallel nature of GAs renders it as a longer a peak. suitable optimization framework for scalable problem solving Traditional techniques from optimization theory assume in a wide range of applications. static and well-known topologies and are not suited to dynamic environments. In many problems of practical interest, our 5) Support For Multiobjective Optimization: Many prac- focus is more on satisficing (i.e., finding a sufficiently good tical problems in wireless networks require optimizing for solution that satisfies one’s purposes) rather than on optimizing multiple parameters (that may potentially conflict with each (i.e., finding the best possible solution). A key benefit of other). An important characteristic of GAs is that it can easily GAs is that they are well suited to the optimization task in support joint optimization of multiple objectives. Support for the dancing landscapes that characterize wireless networks (in multi-objective optimization—in which the considered objec- which there is interaction between the various adaptive wire- tives may potentially conflict with each other—is of significant less nodes and interdependency between the various node’s practical interest in wireless networks. Issues related to multi- decisions). GAs are well suited for building metaheuristic objective optimization are introduced in [10]. adaptive algorithms that can provide satisfactory performance 6) Support for Global Optimization: Unlike network mod- in changing network conditions. els such as the multi-layered perceptrons (which make local Another important aspect of GAs is that it is an online changes so as to find the local minima), GAs are suited to adaptive algorithm that that can operate in unknown environ- finding the global optima due to a number of properties: ments in an online fashion. Such an ability is crucial in various • They search by means of a population of individuals. control settings in wireless networks in which decisions have • They work with an encoding of the multiple parameters. to be made automatically in run-time to cater to dynamic chan- • They use a fitness function that does not require the nel parameters. In dynamic channel conditions that typically calculation of derivatives. exist in most wireless networking configurations, optimization • They search probabilistically. is an elusive moving target since the optimal solution keeps changing as the conditions change. In online adaptive opti- 7) Easy Implementation: GAs are computationally sim- mization algorithms, there is a fundamental tradeoff between pler compared to other complementary AI techniques such exploration—which involves looking for potentially better as neural networks since they require only swapping and previously unexplored solutions—and exploitation that implies shifting of genes in chromosomes (unlike neural networks that the use of previously known good solutions. Exploration in require adders for its multiple hidden layers). GAs are easily effect is an attempt to find good adaptive building blocks and implemented and can be rapidly prototyped in digital signal exploitation is the use and propagation of adaptations that processors (DSPs) or field programmable gate arrays (FPGAs). are known to perform well. We can envision mutation and In addition, GAs are highly amenable to successful implemen- recombination of genes as analogous to exploration, whereas tation on modern parallel and cloud computing architectures natural selection can be envisioned as a form of exploitation due to its inherently parallel nature. [9]. In ever changing dynamic environments, such as wireless networks, it is important to always keep on exploring. Hol- B. Contributions of this Paper land’s original GA work used schema analysis to show that, This paper offers a comprehensive survey of the applica- under qualifying assumptions, GAs can achieve near-optimal tions of GAs in wireless networking. In addition, we also exploration and exploitation tradeoff. provide a self-contained introduction to the GAs. The aim of this paper is not to provide an exhaustive survey1, but 3) Ability to Find Good Building Blocks: By working in to provide a representative sample of important works along terms of a population of candidate solutions, genetic algo- with a comprehensive listing of the various applications of rithms can exploit the diversity of solutions to find building GAs. We also highlight the application of GAs in wireless blocks—known as schemas in literature—which are substrings networking configurations such as wireless mesh networks of chromosomes that denote high performing elements of (WMNs), mobile ad-hoc networks (MANETs), cellular net- the overall solution [4]. In the context of biological genet- works (CNs), wireless sensor networks (WSNs), and cognitive ics, schemas correspond to constellations of genes working together to help an organism adapt; evolution proceeds by se- 1The sheer breadth of GA literature precludes an exhaustive survey, the lecting these constellations (or building blocks) through natural exhaustive bibliography created by Goldberg et al. in 1997—which is a excellent reference to the pool of GA literature—amassed more than 4000 selection. Using genetic operators such as recombination and publications. With the unabated interest in GAs, it will be no surprise if an crossover, GAs can evolve better solutions through mixing of updated bibliography contains more than double the original references. 3 radio networks (CRNs). While a lot of material exists on TABLE I: Acronyms used in this paper. GAs—including various textbooks [6] [11] [12], as well as Acronym Expanded Form generic survey papers [13] [14]—a focused survey article on ACO Ant Colony Optimization the applications of GAs in wireless networking is missing in AP Access Point literature. This paper will be useful to networking researchers ANN Artificial Neural Network interested in applying GAs in particular, and metaheuristic BER Bit Error Rate BFWA Broadband Fixed Wireless Access and evolutionary techniques more generally, in the context of BS Base Station wireless networks. According to the best of our knowledge, BSP Broadcast Scheduling Problem this is the first survey paper that provides an extensive survey CAC Call Admission Control CBDT Case Base Decision Theory of the applications of GAs in general wireless networks. CSM Cognitive System Module CN Cellular Network CDMA Code Division Multiple Access C. Organization of this Paper CR Cognitive Radio CRN Cognitive Radio Network We provide the necessary background on GA theory, work- DCA Dynamic Channel Assignment ing and common techniques used to carry out the evolutionary DSA Dynamic Spectrum Access process in Section II. The applications of GAs in wireless DSPRP Dynamic Shortest Path Routing Problem FA Forward Ant networks—such as routing, channel allocation, load balanc- FCA Fixed Channel Assignment ing, localization, and quality of service (QoS)—are listed in FPGA Field Programmable Gate Array Section III. We highlight the various lessons learnt through GA Genetic Algorithm GP Genetic Programming years of GA research, in terms of common pitfalls as well as GPRS General Packet Radio Service guidelines for successful implementation, in Section IV-B. In iGA Island GA Section V, we highlight open issues and suggest directions for HLB Hybrid Load Balancing ILP Integer Linear Programming future work. Finally, this paper is concluded in Section VI. LISP List Processing (Programming Language) LLF Least Loaded First To facilitate the reader, acronyms used in this paper are LTE Long Term Evolution collected in Table I as a convenient reference. MAC Media Access Control MANET Mobile Ad-hoc Network MDP Markov Decision Process II.BACKGROUND:GENETIC ALGORITHMS MOGA Multi-Objective GA MSC Mobile Switching Center A detailed GA taxonomy is provided in Figure 1. This NN Neural Network taxonomy diagram exhibits the breadth of GA’s applications NSGA Non-Dominated Sorted Genetic Algorithm NSGA-II Non-Dominated Sorted Genetic Algorithm-II as described in this section. NSGS-IIa Adaptive NSGA-II NSGA-IIr Random NSGA-II PGA Parallel GA A. GA Terminology pNSGA-II Parallel NSGA-II QoS Quality of Service Since the field of GA is inspired from the biological genetic RNC Radio Network Controller evolution, the field uses a number of biological metaphors RSS Radio Signal Strength in its terminology. The purpose of this short subsection is RSSI Received Signal Strength Indicator SA Simulated Annealing to introduce these biological metaphors in the context of SGSN Serving GPRS Node applications of GAs in wireless networking. We introduce the SINR Signal to Interference and Noise Ratio terminology through the following list. SNR Signal to Noise Ratio SOGA Single Objective GA • Organism: It represents the entity (e.g., a radio parameter, SP Shortest Path or a wireless resource) being optimized. ssNSGA-II Steady State NSGA-II SWN Software Defined Wireless Network • Population: It refers to the ensemble or collection of UMTS Universal Mobile Telecommunications System organisms undergoing simulated genetic evolution. WLAN Wireless Local Area Network • Chromosome: It encodes a particular solution to the prob- WMN Wireless Mesh Network WSGA Wireless System Genetic Algorithm lem under study. (Biologically, a chromosome contains an organism’s genetic makeup.) • Fitness: It represents the utility of the current chromo- • Mutation some. (In evolutionary theory, fit chromosomes are passed : It represents a random change of an allele (or on through heredity while unfit chromosomes die out due the value of a gene). • Selection to the natural phenomenon of the ‘survival of the fittest’.) : The process through which the ‘fittest’ sim- ulated organism survives while the unfit solutions are • Gene: It is the basic building block of the chromosome defining a particular feature of the simulated organism. weeded out. (Each chromosome can contain a number of genes.) • Allele: Each gene can take several alternative forms, each B. Number-of-Objectives Based Classification of which is called an allele. • Locus: It is the position on the chromosome containing 1) Single-Objective GAs: Single objective GAs (SOGAs) a particular gene of interest. are popular when it comes to optimize single objective with 4

Fig. 1: Taxonomy of Genetic Algorithms scalar fitness function. They are computationally less exhaus- instance of a MOGA framework known as Non-dominated tive but are required to run multiple times using different Sorting Genetic Algorithm (NSGA). weight vectors to optimize multiple objectives as in case of a) Non-dominated Sorted Genetic Algorithm (NSGA): multi-objective GAs [15]. NSGA is a class of multi-objective optimization algorithm 2) Multi-objective GAs: In a multi-objective optimization, that works at improving the adaptive fit of a population to there are multiple objectives that need to be simultaneously the Pareto front constrained by a set of objective functions. optimized. In such a scenario, a single solution may not be NSGA can also be seen as a case of an evolutionary algorithm suitable to multiple objectives. A solution may be best in from the domain of evolutionary computation. The population one objective but worst in other cases. The overall system within the algorithm is sorted into levels or sub-populations, is optimized, in all directions, by multiple solutions. These which are based on the arrangement of the Pareto dominance. categories of solutions are non-dominated solutions that lie on Major similarities between the population members of each the Pareto front. Each point in Pareto front is optimal, since no sub division are calculated against the Pareto front, and the single solution exists that may improve one objective vector resulting class, along with its similarity measure, is then without degrading at least one other objective. Almost all the utilized to promote a solutions front that is non-dominated. solutions lying on the Pareto front would be compromises Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is a relative to multiple objectives. There are various objectives widely used computationally fast and elitist MOGA approach in wireless networking that need to be optimized such as [16]. NSGA-II variants include the following: the signal to interference and noise ratio (SINR), the power • Steady State NSGA-II (ssNSGAII): A steady state version consumption, and the bit error rate (BER). The Pareto front is of the generational genetic algorithm. illustrated through an example in Figure 2 with two conflicting • Parallel NSGAII (pNSGA-II): A variation of the NSGA- objectives: A is a non-dominated point with the objective of II wherein the algorithm takes advantage of the different minimizing power at the cost of BER, while the point B cores of a computer in order to evaluate the individuals corresponds to the objective of minimizing BER at the cost of a function in parallel. of power consumption. Both objectives cannot be achieved • Random NSGAII (NSGA-IIr): NSGA-IIr is a variation of simultaneously so a compromise solution has to be adopted. NSGA-II wherein the three basic operations including Multi-objective GAs (MOGAs) can be employed in almost evolution, mutation and crossover are selected using a every optimization setting provided that chromosomes encod- random seed to generate new individuals. ing and objective function are appropriately accounted for. • Adaptive NSGA-II (NSGA-IIa): This approach works on Details and applications of MOGAs are discussed next in the same principles as NSGA-IIr but the operators are Section III. In this section, we will describe one particular adaptively selected through a random process. 5

C. Other Types of GAs

1) Adaptive GA: To prevent GAs from suboptimally con- verging to a local optima, a number of adaptive techniques have been recommended for adjusting parameters such as crossover probability, mutation probability, and population size. These techniques constitute adaptive GAs. In contrast to simple GAs that rely on fixed control parameters, adaptive GAs utilize information about the population in each gen- eration to adaptively adjust the probability of crossover and mutation. 2) Parallel GA: Parallel GA (PGA) can be categorized into three subcategories: (i) master-slave GA; (ii) island GA (also referred to as distributed GA or coarse-grained GA); and (iii) cellular GA (also called fine-grained GA). Amongst these three configurations, the Island PGAs (island GA, or iGA, for Fig. 3: A flow chart of a typical genetic algorithm [20] short) are best suited to wireless networking since they allow control of the migration policy unlike the cellular PGAs— which require local communication at all agents during each and indeed commonplace, to define the population randomly, generation of the PGA—and the master-slave PGAs that the convergence process can be accelerated by starting with require the master and slaves to constantly communicate. an appropriately defined population. Each candidate solution 3) Distributed or Island GA: Distributed GA divide a large defined in the population is known as an individual, with population into several smaller subpopulations that interact each individual encoded in an abstract format named as a weakly. Parallel GAs, on the other hand, are primed to speed chromosome (in a metaphorical reference to the encoding role up execution by implementing the sequential GA on several of chromosomes in biological genetics). Various evolutionary computation engines. Amongst the distributed GA approaches, techniques (mutation, crossover, etc.) are then applied on the island GA approach is important and is popularly used the population. In every generation, multiple individuals are in wireless networks [17] [18]. It works by separating the stochastically selected from the current population with fitter population into sub-populations called islands. These islands individuals being more likely selections (due to the genetic cooperate with other islands through the migration of indi- principle of ‘survival of the fittest’). The selected individuals viduals. In island GA, the GA runs on each node with the are then genetically modified (mutated or recombined) to possibility of good solutions migrating between nodes. These form the next generation of the population. The usage of migrations are performed in accordance with the migration genetic operators and stochastic selection allow a gradual policy that controls the ‘when’ and ‘how’ of the individual improvement in the ‘fitness’ of the solution and allow GAs movement. In the island GAs, there is relatively infrequent to keep away from local optima. migration between island models thereby implying reduced In the following subsections, we will provide more details inter-agent communication requirements compared to master- about the various steps involved in problem solving through slave GA and cellular GA [19]. GAs. 1) Encoding into Chromosomes: Genetic algorithms oper- ate by initially defining a population of candidate solutions (each of which is called an individual). Individuals are encoded in an abstract representation known as a chromosome (which may be problem specific although representation in strings of 1s and 0s is common; in the related field of ‘genetic pro- gramming’, the encoding is in terms of snippets of computer code). The population size can be a significant factor in GA performance and efficiency. In particular, the performance of GAs can poor when the population size is very small [22]. The encoding of candidate solutions in the form of chro- Fig. 2: Pareto front illustrated for two objectives mosomes can also be of variable length. Such variable length encoding is well suited to problems such as shortest-path routing problem that compares paths of different lengths. As an example of variable length chromosome encoding, refer D. GA Components And Operators to the work of Ahn et al. [23] in which the routing path is A flow chart of a typical GA is provided in Figure 3. The encoded in the chromosome as a sequence of positive integers operation of a GA-based framework starts by initially defining representing node IDs of the nodes enroute the end-to-end a population of candidate solutions. While it is acceptable, routing path. Each locus of the chromosome corresponds to 6

e) Value Encoding: Direct value encoding is useful in problems that deal with complicated values (such as a real number). Use of binary encoding method in this (a) Binary Encoding. Most common encoding type in which each chromosome is represented using a binary string. case would be very difficult. In value encoding, every chromosome is a string of some values. Values can be in any arbitrary form including numbers, characters, or any other complicated object. While value encoding is a good approach for some problems, it often requires new (b) Permutation Encoding. Useful for ordering problems in which each crossover and mutation operators defined specifically for chromosome represents position in a sequence. the problem. f) Tree Encoding: Tree encoding is used for expressions or evolving programs, specifically for genetic programming (GP). In tree encoding, every chromosome or gene is in (c) Value Encoding. Chromosome are strings of some a tree form of some objects, like commands in program- values (which can be form numbers, real numbers, chars, ming language or a function. Programming language like or some other complicated object). LISP is mostly used for this, because genetic programs in it are encoded in this form and can be easily parsed as a tree structure, thereby facilitating mutation and crossover to be performed relatively easily.

For illustrative purposes, an example binary encoding, permutation encoding, value encoding, and tree encoding is presented in Figure 4.

(d) Tree Encoding. Every chromosome is a tree of some Encoding example: Consider an example encoding of radio objects (such as functions or commands in programming parameters in chromosomes and genes for GAs. The inherent language). difficulty in such a representation is the large relative differ- Fig. 4: Illustration of basic types of encoding schemes used ence between radio parameters. For example, frequency range by GA (Adapted from [21]). of 1 MHz to 6 GHz with step size of 1 Hz would require more than 30 bit genes, while modulation has only handful of techniques so it would require far less bits. Chromosomes can, therefore, utilize large number of bits for frequency the order of the node in the end-to-end routing path with the while utilizing small number of bits for the modulation gene. source node always represented by the gene of first locus. The To make GAs independent of which radio it is optimizing, length of the chromosome is variable but is upper bounded by the variable bit chromosomes representation is suggested by N (the total number of network nodes). Scaperoth et al. [24] in the context of software defined radios Several encoding schemes for GA exist including: (SDR). a) Binary Encoding: Binary encoding is the most common 2) Fitness Function: The fitness function, sometimes called approach, mainly because initial GA-based works used the objective function, offers a mechanism for the evaluation this encoding. In binary encoding every chromosome is of the individual chromosomes. Fitness function can be single a string of bits, i.e. 0 or 1. Binary encoding provides objective, or multi-objective. The fitness function is devised many possible chromosomes even for a small amount in a way that the individual chromosome is its variable of alleles. On the other hand, this encoding is in some input parameter. Fitness function ensures that the chromo- cases not natural for many problems and in other cases somes passed on to the next generation are not violating corrections need to be made after mutation or crossover. any constraints. It assigns a fitness score to each individual b) Octal Encoding: The chromosome is represented in octal depending on the quality of the individual in terms of the numbers (0-7). optimization goals and objectives. In particular, for the fields c) Hexadecimal Encoding: The chromosomes are repre- of both genetic algorithms and genetic programming, each sented using hexadecimal numbers. (0-9, A-F). design solution is represented as a string of numbers referred d) Permutation Encoding: Permutation encoding can be to as the chromosome. In fitness evaluation, after each round used in GA for ordering problems, such as task ordering of completed simulation or testing, N worst design solutions problems, or the ‘traveling salesman’ problem. In per- are deleted, and N new ones from the best design solutions mutation encoding, each chromosome is a represented are created. Each design solution thus needs to be awarded a as a string of numbers, which is actually a number in a figure of merit, which indicates how close it came to meet the sequence. In some problems, for some types of mutation overall specification. This is achieved by applying the fitness and crossover, corrections must be inculcated to leave function to the simulation or test results obtained from that the chromosome in a consistent form, viz. it should be solution. corrected to ensure that it has a real sequence in it. Genetic algorithms require much effort in designing a work- 7 able fitness function. Though a computer might generate the new horizons and new traits. Mutation helps to diversify the final form of the algorithm, it takes a human expert to define population, thus helping GAs to avoid local optima and pave the fitness function since an inefficient function can result in the way towards global optima. Several types of mutation convergence to an inappropriate solution, or no convergence at techniques exist including: all. Speed of execution of the fitness function is very important, • Bit-string Mutation: The mutation of bit strings occurs, since a typical GA needs to be iterated many times in order through bit flips at random positions of chromosomes (as to produce a usable result for a non-trivial problem. Hence, illustrated in Figure 5). fitness function requirements include: • Flip Bit: This mutation operator takes the chosen genome • Minimum fitness computation time of candidate solution. chromosome and inverts the bits, i.e. if the genome bit is • Precise model definition for fitness computation. 0, it is changed to 1 and vice versa. • Removal of noise from the fitness function values. • Boundary: This mutation operator replaces the chromo- Two main categories of fitness functions exist: one where some with either upper or lower bound in a random man- the fitness function does not change over time (as in the ner. This can be used for float and integer representation case of optimizing a fixed function, or testing with a fixed of chromosomes. set of test cases) and the other where the fitness function is • Non-Uniform: The probability that the extent of mutation mutable (as in the case of co-evolving the set of test cases will go down to 0 with the next generation of chromo- or in niche differentiation). Another way of defining fitness some is increased by using non-uniform mutation. This functions is in terms of a fitness landscape that depicts the keeps the population from stagnating at early stages of fitness level for each possible chromosome. Definition of the the evolution process. It also alters solution in later stages fitness function may not be straightforward in many cases. In of evolution. The mutation operator can only be used for some scenarios, it becomes very hard or impossible to come up float and integer chromosome genes. even with a guess of what fitness function definition might be. • Uniform: This operator replaces the score of the chosen This difficulty is solved by ‘interactive GA’, which outsources chromosome with a uniform random value selected in the evaluation to external agents including humans. The function range of the user-specified upper and lower bounds. This is calculated iteratively if the fittest solutions produced by GA mutation operator can only be used for integer and float are not in the desired range. genes. There are various strategies for assignment of fitness values • Gaussian: This operator adds a unit Gaussian distributed to the subject population. The ‘aggregation-based’ strategy random value to the selected chromosome. If it falls sums the objectives into a single parameterized objective outside of the boundary of user-specified upper or lower value, e.g., an aggregation of weighted-sum. The ‘criterion- bounds for that chromosome, the new value is clipped. based’ method transitions between the objectives during the This mutation operator is used for integer and float selection phase of the algorithm. Every time an individual is strings. chosen for reproduction, a potentially different objective will dictate which member of the population will be copied into the mating pool. In the ‘Pareto dominance based’ methods, different approaches like dominance depth, dominance count, and dominance rank are used. The dominance rank dictates the number of individuals by which certain individual is dominated. In the dominance depth, the population is divided Fig. 5: Illustration of mutation and crossover operation. into several fronts and the dominance depth reflects the front to which an individual belongs. The dominance count is 4) Crossover: The crossover process is essentially an at- the number of individuals that are dominated by a certain tempt to exploit the best traits of the current chromosomes and individual. to mix them in a bid to improve their fitness. This operator Fitness function example: The evaluation of the solution is randomly chooses a locus and exchanges the sub-sequences at the heart of GAs since it is on the basis of fitness values before and after that locus between two parent chromosomes that GAs evolve solutions and remove poor individuals. It can to create a pair of offspring. A crossover point is randomly be thought of as the performance metric for the optimization chosen. There can be multiple crossover points to aid more algorithm. As an example, for the routing problem, the fitness exploration. In biological systems, crossover is much more can be equated with high average throughput (f = t : i i rampantly observed than mutation, often as much as a million where f is the fitness of ith individual and t is its average i i times more frequent [25]. Crossover along with mutation throughput), low delay (f = −d ) where d is delay perceived i i i provides the necessary ‘evolutionary mix of small steps and by the ith individual. For classification problems, the fitness occasional wild gambles’ to facilitate robust search in complex function can be some measure of the error. Realistic fitness solution spaces [26]. functions are typically much more complex than this toy In GAs, crossover is viewed as synthesis of best practices example, and can depend on many factors. and mutation is viewed as a method of spontaneous inspiration 3) Mutation: The mutation operator is used for exploration and creativity. The evolution can start from a population with randomly altering genes in chromosomes to discover of completely random individuals and can evolve to better 8 solutions through survival of the fittest after application of ge- and splice’ approach, a change in length of the children netic operators. The selected individuals (or chromosomes) are strings occurs. The reason for this difference in length is genetically modified (mutated or recombined) to form the next that each parent string has a separate choice of deciding generation of the population. The usage of genetic operators crossover point. and stochastic selection allow a gradual improvement in the • Three Parent Crossover: In this method, the child chro- fitness of the solution and allow GAs to keep away from local mosome is derived from three parents which can be optima. randomly chosen. Each bit of first parent is compared with bit of second parent to see if they are the same. If the bits are same then that corresponding bit is taken for the offspring otherwise the bit from the third parent is taken for the offspring chromosome. • Ordered Chromosome Crossover: In some cases, a direct swap may not be possible. One such case is when the chromosomes are in an ordered list. The N-point crossover can be used for ordered chromosomes, but always requires a corresponding repair process. Some of the approaches for ordered pair crossover include cycle crossover, position based crossover, alternating position crossover, edge recombination crossover, sequential con- structive crossover and voting recombination crossover. 5) Selection: Selection in GA allows individual genomes to be chosen from a population for later recombination or crossover (breeding). This operator performs the selection of Fig. 6: Illustration of examples of one point, two points, and chromosomes from population for reproduction. The fitter the uniform crossover methods (Adapted from [27]) chromosomes, the more likely they are to be passed on to the next generation. A number of selection techniques has been Several methods exist for crossover of chromosomes which employed in GAs to carry out the survival of the fittest from use different data structures [6]. a pool of individuals [28]. A common selection procedure may be implemented in the • One-Point Crossover: A single crossover point on both parent’s chromosome strings is selected. All data beyond following way: that point, in either organism chromosome, is swapped • The fitness function is evaluated for each individual and between the two parent strings. The resulting strings are is then normalized for algorithm use. The fitness value of the new children chromosome. each individual chromosome is typically normalized by • Two-Point Crossover: Two-point crossover requires two the aggregation of all fitness values to ensure that all the points to be selected on the parent chromosome strings. resulting fitness values sums up to 1. Everything between the two points is swapped between • The population is then sorted in descending order of the parent chromosome strings, producing two child fitness values. chromosomes. • Accumulated normalized fitness scores are calculated. • Uniform Crossover and Half Uniform Crossover: The Accumulated fitness value of an individual equals the sum uniform crossover approach uses a fixed mixing ratio of fitness scores of all the previous individuals and its between two parents strings. Unlike one-point and two- own fitness score. Accumulated fitness of the previous point crossover, this approach enables the parent chro- individual must always be 1—Any other value can be mosomes to contribute at the whole chromosome gene used as indication of a wrong normalization procedure. level rather than at the segment level. For example if • A random number R is chosen in the range 0 to 1. The the mixing ratio is 0.5, the offspring chromosome has first individual whose summed up normalized value is approximately half of the genes from first parent and the greater than the number R is selected. other half from other parent, although cross over points This selection method is called fitness proportionate selec- can also be randomly chosen instead. In the half uniform tion or roulette-wheel selection, since the procedure is repeated crossover method, exactly half of the non-matching bits until there are enough selected individuals. If instead of using a are swapped between the chromosomes. First the number single pointer that is spun a number of times, multiple equally of differing bits, or the Hamming distance, is calculated. spaced pointers are used on a wheel that is spun once, the se- This number is then divided by two; the resulting number lection process will be called ‘stochastic universal sampling’. depicts the number of bits that do not match between the The selection process will be a tournament selection process two parents, and will thus be swapped. An illustrative once there is repeated selection of the best-fitted individual example comparing one point, two points, and uniform from a randomly chosen subset pool. This will be further crossover is presented in Figure 6. called truncation selection once we take the best half, third • Cut and Splice: In the crossover variant called the ‘cut or some other proportion of the individuals. 9

There are also other selection mechanisms that do not take TABLE II: Applications of genetic algorithms in wireless into account all individuals for the selection process, but only networking (covered in Section III-A) those that have a fitness value, greater than a given constant. Application Discussed in Other algorithms select the individual from a restricted pool Routing Section III-A1 and Table III where only a constrained percentage of the individuals are Quality of Service (QoS) Section III-A2 and Table IV allowed, based on their fitness scores. Retaining the best Load balancing Section III-A3 and Table V individual chromosomes in a generation unaltered, in the next Bandwidth allocation Section III-A4 and Table VI. Channel allocation & assignment Section III-A5 and Table VII. set of generation, is called elitist selection or elitism. It is Localization Section III-A6 and Table VIII considered a successful variant of the general procedure of Wireless AP placement Section III-A7 and Table IX constructing a new population pool. General Applications Section III-A8 and Table X The main selection techniques used by GAs are summarized in the following list. networking in a wide variety of contexts. We will firstly • Relative Tournament Evaluation: In relative tournament, describe the various applications of GA in wireless networking two parents are compared randomly and the one with high in Section III-A. We will then provide a network-type based fitness value is selected to be the parent of next gener- classification of GA application in Section III-B. Finally, we ation. Winning chromosomes are awarded by adjusting will discuss ‘hybridization’ proposals that combine GAs with their weight corresponding to the objective function. This other techniques in Section III-C. weighting increases the importance of that chromosomes relative to others. A. Application Based Classification • Roulette Wheel Selection: Roulette wheel selection is a way of choosing mother and father chromosomes from In this section, we will discuss the applications of GAs in the population in a way that is proportional to their wireless networking. In particular, we will discuss routing, fitness. The chromosomes with higher fitness have high QoS, load balancing, channel allocation and assignment, local- chances of being selected using this technique. ization, WLAN AP placement, and other general applications, in this particular order. The organization of this section is • Relative Pooling Tournament Evaluation: In this tech- summarized in the Table II. nique, each parent is thrown in a competition with the individual chromosomes in population, independently. 1) Routing: The problem of shortest path routing problem The individual that is the winner of maximum number of is a well-studied problem in literature. GAs are well suited tournaments gets a chance to be passed into next genera- to the routing problem allowing convenient mechanisms for tion through reproduction. This technique is comparable developing adaptive routing solutions. GAs have been used for to the proposed method in Horn et al. [29] of fighting developing routing solutions in a variety of wireless settings two individual against various subsets of population. This as summarized in Table III. Ahn et al. [23] have tackled this technique is computationally intensive, and thereby can problem through GAs. The routing table for each source- stress GA deployment due to the computational overhead. destination pair needs to be constructed first. Obviously, the • Elitism: Elitism is a method to store and use previously number of possible routes between two nodes heavily depends found best-suited solutions in subsequent population gen- on the network topology. If the network is densely connected erations of GA. In a GA approach that uses elitism, the or the size of the network is large, the number of possible statistic related to the population’s best solutions does routes of a source-destination pair becomes huge. Hence, it is not degrade with generation. Maintenance of archives impossible to list all the possible paths in the routing table. A for non-dominated solutions is an important and critical predefined number of routes are randomly generated and fed to issue. The final contents of archive usually represent the population pool, and chromosomes are then optimized. In the result returned by applying the optimization process. It is simulation, crossover and mutation are run on variable length highly effective and common to employ the archive as a chromosomes. Infeasible solutions are also kept in check. The pool, from which guidance is taken for the generation of paper discussed the issues of path-oriented encoding, and path- new solutions. Some algorithms use solutions available based crossover and mutation, which are relevant to the routing in the archive exclusively for such purpose, while others problem. tend to rely on the archive to varying degrees accord- Yang and Wang [34] studied how GAs can be used for ing to settings of related parameters. The computational dynamic shortest path routing problem (DSPRP). Algorithms complexity of maintaining the archive which involves like Bellman-Ford and Dijkstra perform well in fixed infras- checking for non-dominance of newly generated solutions tructure but on dynamic scale, high computational complexity suggests relatively modest size of bounded archive [30]. renders them unacceptable. A DSPRP model is built up in this paper using GAs. A specialized GA is designed for the shortest path problem in MANETs. Several immigrants and III.APPLICATIONS OF GASIN WIRELESS NETWORKING memory schemes that have been developed for GAs for gen- After providing background on GAs in the last section, eral dynamic optimization problems are adapted and integrated we are now in a position to survey the applications of GAs into the specialized GA to solve the DSPRP in MANETs. in wireless networking. GAs have been applied in wireless The experimental results indicate that both immigrants and 10

TABLE III: Using genetic algorithms for routing in wireless networks

Project & Network No. of Technique used Brief summary reference objectives Ahn and Ramakr- MANET SOGA Integer coded, variable length Unlike Dijkstra and Depth-First Search (DFS) algorithms, multiple ishna [23] chromosomes solutions can be found for shortest path routing that have same cost using GAs. Cheng et al. [31] MANET MOGA Distributed multipopulation GA A distributed GA approach incorporating multi-population with random immigrant schemes solves the shortest path routing in MANET. Gen et al. [32] LANs SOGA Integer coded GA for random A priority encoding scheme is proposed using GAs to represent and distributions optimize all possible paths in network graph. Davies et al. [33] WAN SOGA Simple GA with unbiased cod- A GA approach continuously re-routes and assigns weight to traffic ing scheme paths to implement adaptive control over dynamic routes and network topology. Yang et al. [34] MANET SOGA GA with immigrants and mem- A GA proposed for investigating effectiveness and efficiency of GAs ory scheme with immigrants and memory schemes in solving the dynamic shortest path routing problem in the real-world networks. Badia et al. [35] WMNs SOGA ILP formulation with GAs GA addressed the routing and link scheduling problem when ILP cannot cope with computational complexity of large WMNs. Al-Karaki et al. WSN MOGA Centralized GA and ILP A metaheuristic algorithm that solves the joint problem of optimal [36] routing with data aggregation to optimize the network lifetime while retaining the energy and latency efficiency. Lorenzo and Gal- CN MOGA Sequential GA A sequential GA solves the NP-hard problem by optimizing relay isic. [37] topology while eschewing the inter-cell interference. Apetroaei et al. WSN SOGA Tree coded GA on spanning tree GA inspired spanning tree topology for WSNs that adapts (according [38] topology to the nodes, residual energy) to maximize the usage of the network. Yen et al. [39] MANET SOGA Prüfer number encoding A GA strategy for energy efficient routing by maintaining the energy balanced nodes in entire MANET distribution. Chiang et al. [40] MANET SOGA Tree sequenced coding A GA based on sequence and topology encoding employed topology crossovers to solve the multicast routing constraints efficiently.

memory schemes enhance the performance of GAs for the nodes are encoded and fed to GA in the form of population DSPRP in MANETs. chromosomes. GA then uses evolutionary techniques to select In MANETs, all the nodes communicate over wireless the best chromosomes by evaluating them against a partic- links without any established infrastructure. MANETs are well ular fitness function, which can be in the form of different suited to environments in which there is no fixed infrastructure constraints related to bandwidth, QoS, and channel allocation, or when the infrastructure is not trusted. In such networks, a etc. In another work, Salcedo-Sanz et al. [43] proposed mixed common strategy is to form clusters where each node is linked neural-genetic algorithm for the ‘broadcast scheduling prob- to a clusterhead for efficient routing with other nodes that are lem’ (BSP). The algorithm solves this optimization problem in not in its direct range. GAs have been used in such cluster- two stages: firstly, it finds a feasible solution, and secondly it based routing schemes for MANETs. Al Gazal et al. [41] obtains maximal transmission throughput by employing fittest have proposed a GA-based protocol named ‘cluster gateway chromosomes through GAs. A track of interference and frame switch routing protocol’ (CGSRP) to select the clusterhead matrix are kept and the channel slots are assigned accordingly. to carry out communication between nodes. Clusterhead must Nodes that are 1-hop away are not assigned the same slot have enough resources, power, and bandwidth to avoid dangers to avoid mutual interference. After finding feasible solutions, of bottlenecks. This scheme works by encoding each node’s these solutions are encoded in chromosomes. Multiple GA unique ID in the chromosomes. The chromosomes have infor- operators—such as mutation, crossovers—are then applied mation about cluster-head, members, number of links in each leading to maximized throughput. cluster-head. The encoded chromosomes are then evaluated The use of hybrid GA algorithms have been proposed for against certain criteria as defined by the fitness function routing in wireless networks. Cauvery et al. [44] proposed (which may incorporate features such as load balancing and using ant algorithms, combined with GAs, for route discovery. bandwidth conservation). Each chromosome’s fitness is then It was observed that the use of ant algorithm leads to reduction evaluated. The process of the survival of the fittest leads to in the size of the routing table. We note here that ant- an optimum selection of nodes as cluster-heads that optimally colony-optimization (ACO) algorithms belong to the broader utilize resources. class of AI known as swarm intelligence. While GAs cannot GAs have also been proposed for use in multicast and use global information of the network, the use of ACO and broadcast routing in wireless networks. A study on multicast GA techniques in tandem leads to independent exploration routes optimization using GAs is done by Banerjee and Das of the network helping in effective computation of routes [42]. An on demand routing scheme with GAs is discussed between any pair of nodes. The proposed algorithm creates an to meet bandwidth, delay constraints while maintaining the initial population, determines the forward-ants, generates new QoS in wireless networks. Chromosomes from different pools populations using genetic operators and fitness evaluation, and are randomly concatenated to obtain a multicast solution. In finally updates routing table. The hybrid algorithm performs doing so, all possible routes between source and destination well in not only generating routes between pair of nodes but 11 also for achieving efficient load balancing. composition, and requires less computation for large networks. Sub-tree crossover exchanges the task nodes and updates 2) Quality of Service (QoS): With increasing prevalence the QoS vector from the leaf nodes to the tree’s root. A of multimedia applications (such as video conferencing and standardized and comprehensive fitness function verifies the streaming), and the development of high-speed wireless com- whole QoS process plan. Results have showed that the tree munication technologies, efficient and reliable QoS provision- based models have lesser overhead than the traditional GAs ing has become increasingly important. Modern multimedia with serial chromosomes while offering excellent replanning applications place rigorous QoS demands for different param- and service composition. eters like bandwidth, delay, and jitter [71]. This motivates the development of effective resource allocation schemes that can 3) Load Balancing: GAs have been proposed for use in ensure QoS while also satisfying these strict QoS constraints. various load balancing solutions for various wireless network- In this section, we will describe the various GA-based QoS so- ing configurations in literature (as shown in Table V). lutions that have been proposed in literature. This information There are three main types of load balancing categories: is presented in summarized form in Table IV. (i) strongest ‘received signal strength indicator’ (RSSI); (ii) Various analytic approaches have been proposed in literature least loaded first (LLF); (iii) hybrid load balancing (HLB) including those that rely on Semi-Markov decision process incorporating RSSI & LLB. These techniques fall under the (SMDP) theory for optimal call admission control (CAC) category of network-centric load balancing, and are applied on [72]. These methods unfortunately fail to scale to large-scale a network scale to achieve global optima, unlike user-centered networks where the decision and action space is large. GAs techniques that are more likely to achieve local optima only. can provide near optimal solutions in large-scale complex Chromosomes consist of randomly assigned individuals to networks. Xiao et al. [73] presented an effective near optimal an access point. Crossover and mutation are performed on GA-based CAC approach for large-scale wireless/ mobile individuals and fitness evaluation is done. Both load balancing networks. The chromosomes encoded are binary strings where and congestion control problems have been addressed. QoS 1 and 0 represent the acceptance and rejection of calls by CAC. has also been addressed by assigning different weight to users, These chromosomes are randomly generated and then evalu- depending on its service requirement like streaming and media ated against fitness function of channel utility and constraints. etc. Experimental results and analysis showed that microGA Evolution of best traits leads to near optimal solutions for outperforms macroGA at first but in the long run macroGA QoS. This scheme offers adaptive QoS to multi-class users does better load balancing by pushing more congested users while being computationally less intensive compared to the towards peripheral APs. SMDP approach. Ozugar et al. [82] proposed the multi-objective hierarchical A multi-objective GA (MOGA) approach on multicast QoS mobility management optimization for UMTS networks to routing is proposed by Roy et al. [49]. To deliver on-demand distribute the load among different parts of network such QoS, different solutions are kept in an optimized pool. Multi- as serving GPRS nodes (SGSN), radio network controllers ple solutions are offered depending upon the service demands. (RNC), and mobile switching centers (MSC) in addition to A MOGA approach optimizes the prioritized objectives as performing the role of minimizing cost for location update in stated in the user QoS requirements. A similar approach for these intricate networks. QoS aware web-based service under strict constraints and Selecting resource-rich nodes for trivial tasks creates an optimizing the targeted QoS parameters is done by Canfora imbalance in energy distribution among nodes resulting in the et al. [51]. It is shown in this study that the widely adopted demise of multicast service. To mitigate such a possibility, optimization approach of linear integer programming is unable Yen et al. [39] have proposed an energy-efficient GA routing to offer non-linear QoS functions. GAs can be employed to in MANETs. The algorithms proposed in [39] continuously work with non-linear QoS attributes. In yet another MOGA observe the condition at various nodes and improve the en- work, Roy et al. have proposed QM2RP as a QoS-based ergy balance by replacing the weaker nodes with energy-rich multicast routing protocol framework for mobile wireless nodes. An extended Prüfer encoding scheme is proposed for cellular networks [56]. The proposed protocol determines near- energy efficient exchange of leaf nodes through mutation and optimal routes on demand while working with potentially crossover. In this way a substantial reduction in convergence inaccurate network state information. The protocol considers time is achieved, thus prolonging the service duration effi- a number of QoS optimization metrics including end-to-end ciently. delay, bandwidth, and residual capacity. GAs have also been proposed for load balancing at APs in IEEE 802.11 WLANs for efficient distribution of bandwidth With the increase in number of service candidates, the among users. Scully and Brown [70] have discussed MicroGAs traditional chromosome model for QoS optimization becomes and MacroGAs to address the problem of load balancing. cumbersome in web services. To address this, Gao et al. A comparison of MicroGAs and MacroGAs has been done [74] studied a ‘tree based GA’ for optimizing QoS. This by Kumar et al. [83]. MicroGAs has a population of five model is faster than traditional GA since it offers impulsive individuals leading to brisk evolution. chromosomes coding and decoding and present run time integration of QoS resources. Chromosomes are represented 4) Bandwidth Allocation: The problem of bandwidth allo- in series of nodes and all the leaf nodes execute the process. cation under QoS constraints in wireless networks is typically A tree characterizes the structured model for different QoS a complex task. A proper bandwidth allocation scheme must be 12

TABLE IV: Using genetic algorithms for QoS optimization in wireless networks

Reference Goal No. of Technique used Brief summary objectives Resources Scheduling for QoS Sherif et al. Resources allocation with SOGA GA with reallocation of Accelerate allocation through crossover and mutation. Reduces [45] call admission control unused bandwidth computation of NP-hard problem. Dynamic assignment of net- work resources and bandwidth Gozupek and Scheduling under interfer- MOGA Binary encoding with GA based sub-optimal schedulers for maximizing the throughput Alagoz [46] ence constraints random seeding and improving the latency in CRNs. Cheng and Packet level resource allo- SOGA Karush-Kuhn Tucker An effectual hybrid GA optimizes the QoS provisioning and Zhuang [47] cation (KKT) and GA driven resource allocation to keep a balance between performance and approach computation. Lopez et al. Transmit power control MOGA GA with call admission MOGA approach adopted to maintain the transmit power of CRs, [48] for maximum utility control while maintaining the QoS and optimizing the spectrum access. Roy et al. [49] Energy efficient resource MOGA Depth first search with On demand QoS routing scheme has been proposed based on end scheduling NSGA user needs. A solution meeting the constraints is offered from an optimized pool of chromosomes. QoS for Multimedia and Web-Services Jiang et al. [50] Multi-Constrained QoS SOGA Variable length chromo- A scalable QoS aware web service composition is introduced for web-services some GA using GA for diversified functionality through cut and splice operation of mutation and crossover. Canfora et al. QoS service composition SOGA GA with ILP and elitism GA approach for web based QoS services with non-linear aggre- [51] gate functions while meeting a set of constraints. Li et al. [52] Video On Demand MOGA GA with interference GA is employed to leverage multi-source, multipath solution to model design a concurrent video streaming environment in WMNs, along with route discovery. Energy-Efficient QoS Multicast Routing EkabtaniFard et Energy Efficient QoS MOGA NSGA-II A hierarchical energy efficient routing protocol, for two tier WSN al. [53] routing in clusters networks, under tight QoS constraints, is developed using MOGA optimization with NSGA-II. [54]. GAMAN Topological Multicasting SOGA Tree coded GA with A GA for MANETs (GAMAN) is proposed by Barolli et al. [55]. multi-population The algorithm works locally on smaller population and offers promising QoS for ad-hoc networks. QM2RP [56] QoS-based multicast rout- MOGA Tournament selection A QoS-based mobile multicast routing protocol using multi- ing and niched Pareto objective genetic algorithm. optimization Cui et al. [57] Optimizing conflicting MOGA Depth-first search algo- A MOGA approach is used to optimize multiple multicast routes QoS parameters rithm and GA lying on Pareto front. Lu et al. [58] Energy efficient QoS mul- MOGA Tree structured coding Proposed GA solves QoS by constructing a multicast tree with a ticast routing minimum energy cost and bounded end-to-end delay. Yen et al. [59] Multicast routing through MOGA Tree coded flooded GA A GA based method is proposed for multi-constrained QoS flooding multicast routing, while incorporating elitism, to optimize the computation time. Huang and Liu QoS Aware Multicast MOGA Greedy and family com- A hybrid GA along with greedy algorithm mitigate premature [60] Routing petition with GA convergence problems to avoid local optimas. Sun et al. [61] Multi-constrained MOGA Spanning tree encoding The evaluated GA can optimize the cost of the multicast tree, optimization maximum link utilization, the average delay selection of the long- life path. Abdullah [62] Modified QoS Routing MOGA Variable length encoding A GA approach look for the best QoS route, using route mutation, Protocol to optimize the design of MANET routing protocol by improving packet delay and throughput.

Route Discovery Gelenbe et al. Autonomous route discov- SOGA GA with distributed Proposed autonomous route discovery in cognitive packet net- [63] ery with GA CPN protocol works (CPNs) with GAs. Paths discovered by CPN are provided to GA which then produces new routes using evolutionary techniques Cauvery and Route discovery through SOGA GA with Ant algorithm A hybrid algorithm (combining ant algorithms and GA) is pro- Visvanatha [44] mobile agents posed to reduce the size of routing table and help in routing among autonomous peers.

Queue Management at Routers (AQM) Fatta et al. [64] Designing FPI controller SOGA GA with fuzzy logic Fuzzy proportional integer (FPI) controller is purposed and FPI for AQM parameters are controlled by GAs dynamically to optimize active queue management (AQM) policies. Selamat et al. Query Retrieval for active SOGA Integer coded distributed A GA with mobile agents search system (MaSS) is proposed to [65] AQM GA minimize the query retrieval cost while maintaining a reasonable path delay. 13

TABLE V: Using genetic algorithms for load balancing in wireless networks

Reference No. of Technique used Brief summary objectives Wireless Mesh Networks Hsu et al. [66] SOGA GA with Dijkstra algorithm A hybrid GA coupled with Dijkstra’s algorithm look for the best available paths with bounded delays and low cost network configuration. Zeng et al. [67] SOGA GA with greedy algorithm and bi- Load balanced disjoint clustering is done by a GA coupled with greedy algorithm nary encoding for efficient distribution of network resources.

Mobile Ad-hoc Networks Yen et al. [39] MOGA GA with Prüfer number coding In time-critical load balancing scenario, GAs inspired strategy is applied in multicast tree to balance the energy consumption, leading to prolonged network lifetime. Cheng et al. SOGA Distributed GA with multi- A dynamic GA evaluates the fitness of each feasible clustering structure against load [68] population and immigrant schemes balancing metric.

Wireless Sensor Networks He et al. [69] SOGA 1-to-1 mapping of nodes to genes The application of GA to find a load-balanced connected dominating set (CDS) to in chromosomes be used as a virtual backbone of WSNs.

Wireless Local Area Networks Scully and SOGA MicroGA & MacroGA A comparison of MicroGA and MacroGA is done against QoS attributes like Brown [70] throughput and load balancing. MicroGA performs better in brisk load balancing under time constraints.

TABLE VI: Using genetic algorithms for bandwidth allocation in wireless networks

Reference No. of Techniques used Brief summary objectives Lin et al. [75] MOGA GA with adaptive inheri- A prioritized bandwidth allocation scheme for transmitting medical patients data is tance probability applied for multimedia sub-streams. Kandavanam et al. MOGA GA with variable neigh- A hybrid GA optimizes the residual bandwidth allocation to routing links for multiclass [76] borhood search approach traffic in all networks. Karabudak et al. [77] SOGA GA with Markov Decision The proposed GA scheme minimizes handoff latency by using elitism technique to Model and Elitism allocate the maximum network resources to admitted calls. Vendanthan et al. [78] SOGA GA with greedy algo- A GA approach to efficiently utilize the bandwidth for different incoming call streams rithms to maximize the revenue generation. Riedl [79] SOGA GA with local search GA approach with bandwidth and delay metrics optimizes the IP traffic engineering in heuristics wireless networks. Kobayashi et al. [80] MOGA Distributed GA A distributed GA works by utilizing both local and global optimization in parallel on networks nodes to utilize the network resources and bandwidth. Qahtani et al. [81] SOGA GA for asynchronous A genetic routing algorithm (GRA) is designed to allocate bandwidth to virtual path transfer mode (ATM) subnetworks in a wireless network. adopted to overcome the problem of limited wireless resources resource utilization and fair distribution of bandwidth in all and utilize the channel allocation efficiently. Various GA-based the networks while keeping in view the network constraints. approached have been proposed in literature as solutions to the problem of bandwidth allocation in wireless networks. We 5) Channel Allocation and Assignment: With the rapid will describe a sample of these works (a tabulated summary proliferation of wireless and cellular networks, and the prob- is presented in Table VI. lem of limited frequency spectrum, the problem of channel An accelerated GA approach with dynamic adjusting of assignment and reuse has become very important. The recent mutation and inheritance probability is proposed in [75] as a advancement in wireless technology has enabled many high- solution to the bandwidth allocation problem in WLANs. The speed data services leading to an upsurge in number of wire- probability of mutation and crossover is made dependent on less users. Since the frequency spectrum is a limited resource, the individual chromosomes fitness. This approach is shown to there is a great emphasis on the reuse and sharing of frequency quickly converge to global optima while substantially reducing amongst the ever-increasing user base. The goal of channel the number of generations as well as the computation time. In allocation is to maximize frequency reuse by minimizing the another work, Sherif et al. [45] proposed a GA-based approach number of channels required to cover all the network cells. to analyze the network bandwidth allocation using a predeter- There has been a lot of GA-based work done in the area mined range of QoS levels (high, medium, low) declared by of channel allocation and assignment in wireless networks (a each multimedia substream. The proposed algorithm assigns summary of which is provided in Table VII). We discuss some the best available QoS level to each substream depending important GA-based channel allocation/ assignment works upon the availability of bandwidth resources in network. below. In the case of network congestion, the algorithm tries to Broadly speaking, there are three main constraints that chan- preserve resources by degrading the quality of some admitted nel assignment algorithms in wireless networks must consider: calls. Using this technique, the algorithm attempts maximum (i) co-channel interference constraints—which requires that 14

TABLE VII: Using genetic algorithms for channel allocation/ assignment in wireless networks

Reference No. of Techniques used Brief summary objectives Channel allocation in CRNs Zhao et al. [84] MOGA Quantum computation A hybrid GA implemented to decrease the search space and ease the mapping process with GA [85] between the channel matrix and qubit chromosomes. Bhattacharjee et al. MOGA Comparison of GA with Channel assignment optimization for single cell cognitive network using GA. [86] interference graphs Friend et al. [17] SOGA Distributed Island GA An Island GA, solves the channel allocation through dynamic spectrum access in cognitive radio networks. ElNainay et al. [18] SOGA Distributed Island GA A localized island GA cooperate with other cognitive network nodes to utilize the available spectrum opportunistically and efficiently through channel allocation. Ali et al. [87] MOGA Luby transform codes and A GA assisted resource management scheme is presented for reliable multimedia GAs delivery.

Channel allocation in cellular networks Zhenhua et al. [88] MOGA Immuned GA with elitism A modified immune GA, integrating immune operators, and minimum separation encoding to obtain the conflict free channel assignment in cellular radio networks. Pinagapany and SOGA Parallel GA with decimal A GA based scheme used to solve both fixed and dynamic channel assignment problems Kulkarve [89] encoding in multi-cell cellular radio network. Jose et al. [90] SOGA GA with Elitism and fit- Diversity guided Micro GA in cellular radios to optimize frequency/channel reuse in ness entropy fixed channel assignment problem. Lima et al. [91] MOGA GA with immigrants and Two adaptive GAs for locking and switching channel, solve the dynamic spectrum memory schemes access problem through distribution of channels among cell in cellular networks.

Channel allocation for broadband wireless networks Wong and Wassel SOGA GA based dynamic chan- GA based technique incorporated channel segregation to maximize the throughput in [92] nel allocation broadband fixed wireless access networks. Fang et al. [93] SOGA GAs with video coding Evolutionary technique alongwith Reed-Solomon coding and SNR matrix allocate scheme channel rates for scalable video transmission. the same frequency or channel cannot be assigned to two dif- since a neural network’s output critically depends on the the ferent radios simultaneously; (ii) adjacent channel interference initial values. In the case of GAs, they possess crossover and constraints—which requires that adjacent frequencies not be mutation as their key strength to escape local optimas. GAs, assigned to adjacent channels simultaneously; and, (iii) co- therefore, have far better chances to overcome the channel site interference constraints—that requires minimum spacing allocation problems such as (i) co-channel interference (ii) between a pair of frequencies assigned to a channel must have adjacent channel interference and, (iii) co-site interference. minimum spacing. GAs are applied on clusters in cellular networks and it is Kassotakis et al. have proposed an approach based on hybrid showed that if the number of cells in one cluster are increased, genetic approach—that combines genetic algorithms with local the convergence rate is decreased leading to an increase in the improvement operator—for channel reuse in multiple access number of generations due to the reuse of the same frequency telecommunication networks [94]. The proposed scheme aims among different cells. GA comes handy in keeping the cluster to establish the maximal number of connections while mini- size optimum for efficient frequency distribution among cells. mizing the number of isochronous channels. Wong and Wassel Ngo and Li [98] presented a modified GA to contribute in [92] investigated the channel allocation for a ‘broadband conflict free channel allocation and spectrum efficient assign- fixed wireless access’ (BFWA) networks. A channel allocation ment in cellular radio networks. There are generally two kinds matrix keeps track of channel parameters for conflict free of channel assignments: (i) fixed channel assignment (FCA)— assignments. It is observed that as the network grows, cen- where channel slots are pre-allocated to cells, and (ii) dynamic tralized scheme would offer unacceptable signaling overhead. channel assignment (DCA)—where channels are assigned GA is used for distributed channel where each access point upon request. FCA generally outperforms DCA under heavy (AP) transmits the interference power of the entire available traffic load. This algorithm, called the genetic-fix algorithm, channel to a control unit. Control unit employs GAs and ranks generates and manipulates individuals with fixed size, and the chromosomes of channel priorities according to fitness hence greatly reduces the search space. Furthermore, using the value of interference. Crossover and mutation rate are also set minimum-separation encoding scheme, the required number of to promote the best channels and explore the new channels. bits for representing solutions is substantially reduced. Experimental Statistics have revealed that better SNR gain (more than 14.5 dB) and throughput is achieved with GAs in 6) Localization: The task of determining the location of a comparison with the other two dynamic channel assignment wireless node is known as localization. Localization is impor- methods: (i) least interference [95], and (ii) channel segrega- tant in many different settings (such as military monitoring tion [96]. services and disaster management) for providing location- A study on GAs in channel assignment in cellular networks aware services. GAs have been used to assist the localization is performed by Kim et al. [97]. This paper reports that neural process in various wireless settings. In this section, we will networks are more likely to get trapped on a local optima provide an overview of such work. A tabulated summary of 15

TABLE VIII: Using genetic algorithms for localization in wireless networks

Reference Goal No. of Technique used Brief Summary objectives

Zhang et al. Node localization with MOGA GA with simulated A GA approach for centralized architecture to optimize the [99] random distributions annealing localization in WSN with least mean localization error. Yun et al. [100] Centroid localization SOGA GA with fuzzy logic A hybrid GA with fuzzy membership is developed for edge weights to localize the nodes using received signal strength indicator (RSSI) information. Tam et al. [101] Localization with ad- SOGAs MicroGA as post- A single objective MicroGA, using smaller population worked out hoc positioning system optimizer with APS best to improve the localization accuracy in APS for both isotropic (APS) and an-isotropic topologies. Nan et al. [102] Sensor nodes localiza- SOGA GA with elitism and A real-coded version of GA utilizes roulette wheel selection with tion partial map crossover Integer coding, thus, helping in achieving precise node localization (PMX) in sensor networks. Yun et al. [103] Localization with RSSI SOGA GA and fuzzy logic Calculation of edge weight with reference of anchor nodes, fol- system lowed by modeling through fuzzy logic functions and optimization by GA in the end.

TABLE IX: Using genetic algorithms for wireless AP placement optimization

Reference No. of Objec- Technique used Brief Summary tives

Wireless Mesh Networks Smadi et al. Bi-Objective GA with ILP A Joint clustering and gateway problem is addressed by GAs for placement of [104] GA hybrid free space opticals (FSO) to supplement the gateway capacity in WMNs Xhafa et al. Bi-objective GA on grid area with rectangular Proposed GAs to optimize the connectivity and user coverage area of mesh [105] GA mutation and crossover network through optimal placement of nodes in the area.

Mobile Ad-hoc Networks Kusyk et al. MOGA Distributed forced GA with evolu- A GA alongwith traditional game theory, running at each node in autonomous [106] tionary game theory network, helps nodes deciding their mobility and organization. Sahin et al. SOGA Distributed forced GA A Distributed GA adjust speed, location, and direction of mobile nodes over a [107] geographical terrain for military applications. Hoffman et al. SOGA GA with TDMA table and time slot A GA approach to gateway allocation in aeronautical networks and TDMA [108] exchanges. resource scheduling to minimize the latency.

Wireless Sensor Networks Youssef and SOGA GAs on pre-calculation generic A GA places the WSN nodes for disjoint clustering and minimizes the number Younis [109] routing table of hops between sensor and nodes to have efficient intra-cluster communication. Tripathi et al. Bi-objective GA and Genetic Programming GP improves the deployment, while GA optimizes the node placement for [110] (GP) maximum coverage in WSN. Pandey et al. MOGA GA with greedy algorithm and ‘bi- A hybrid GAs along with greedy algorithm optimizes the node placements for [111] nary integer linear programming’ traffic balancing, in two tier hierarchical heterogeneous WSNs. (BILP) Xu and Yao SOGA GA with integer coding and order A GA approach worked on optimal placement of WSN nodes in grid area full of [112] mapped crossover (OMX) hindrances and obstacles to match in real-time environment. some sample works are presented in Table VIII. inferior and sub-optimal solutions with the optimal ones. In the approach of centroid localization [100], proposed in [100], A simple way to localize the nodes is to deploy GPS, but GAs and fuzzy logics are used by each node to perform installing GPS in thousands of closely placed nodes is im- self-localization by estimating the edge weights based on the practical. A better approach is to employ GPS in a few nodes, received signal strength (RSS). called anchor nodes, and apply techniques to locate all the other nodes relatively, with reference to multiple anchor nodes. 7) WLAN AP placement: Since the arrival of IEEE 802.11, Tam et al. [101] proposed localization technique in which WLAN services are widely adopted with the predominant each node finds its position relative to three anchor nodes, WLAN setting being infrastructure mode (in which the topolo- thus, enabling each node to locate itself through triangulation. gies around APs). Optimizing the placement of WLAN APs This information is then broadcasted to base station where plays a substantial role in maximizing the throughput and data a centralized GA works as a post-optimizer, thus, leading rate of WLANs. In this section, we will summarize the various to precise network graph with each node’s location known. proposals for using GAs in WLAN AP placement. A tabulated Zhang et al. presented the centralized GA with simulated summary is presented in Table IX. annealing [99] to minimize the error in position estimation A multi-objective GA (MOGA) approach for WLAN AP of nodes in WSNs. This approach is also based on anchor placement (with the objectives of minimizing the number of nodes localization scheme. Simulated annealing is local search APs and maximizing SNR) has been described by researchers technique and it avoids pre-mature convergence, by mixing in [130]. GA-provided solutions have lesser variance implying 16

TABLE X: Using genetic algorithms for general applications in wireless networks

Reference Network No. of Technique used Brief summary Type objectives Area Coverage Xhafa et al. [105] WMNs Bi-objective Rectangular mutation & A GA approach is used to maximize the ‘giant component’ and GA crossover coverage area in WMNs while using multiple distribution strategies of client nodes. Alba et al. [113] MANET MOGA Broadcasting updates from base A hybrid broadcasting protocol using evolutionary algorithms. A station running GA MOGA approach is used to optimize metropolitan-scope MANET coverage and usage. Hu et al. [114] WSN SOGA GAs with schedule transition op- Hybrid GA with scheduled transition and forward encoding scheme erations finds the maximum number of disjoint cover sets to enhance the disjoint covered sets in areas. Sahin et al. [115] MANET MOGA A Distributed forced GA A forced GA is proposed letting the nodes decide their movement, direction and speed through molecular force equilibrium to get maxi- mum area coverage Lai et al. [116] WSN SOGA Integer coding GA Based scheme with one-to-one mapping of genes and sensors to find maximum disjoint sensor covers to prolong the network life span. Quintao et al. WSN SOGA GAs coupled with mathematical GA based heuristic approach with integer linear programming (ILP) [117] modeling and ILP and mathematical formulation to solve dynamic network coverage problem.

Network Planning and design Bhondekar et al. WSN MOGA GA model for grid deployment A GA decides the transmission ranges and the active/ sleeping nodes [118] in WSN topology while accounting for connectivity, energy, and other application specific parameters. Jourdan et al. WSN MOGA GA for non-linear objectives A MOGA approach design the Pareto optimal layouts for WSN nodes [119] depending upon the sensing and communication range. Pries et al. [120] WMNs SOGA Tree coding GA operators like subtree crossover and cell crossover, respectively, are employed in solving small and large-scale WMN gateway opti- mization problems. Ayyadurai et al. CN SOGA Single cell optimization An addaptive GA for dynamic system reconfiguration optimizes the [121] resource allocation in cellular networks. Ghosh et al. WMN SOGA Binary encoding of nodes A dynamic mesh topology design, using GAs, while maintaining low [122] network cost and path redundancy at base station for reliability. Sheen et al. [123] CN MOGA Joint optimization A GA for maximizing joint multi-cell CN system efficiency, through optimizing relay stations (RS) placement, frequency reuse pattern, and maximizing throughput to enhance the end user experience. Chiaraviglio et CN MOGA Hybrid GA with centralized GA based switch off strategies for enabling sleep modes in base al. [124] sorting of base stations stations to design energy efficient cellular networks.

Cluster Optimization Zeng et al. [67] WMN MOGA Greedy algorithm with GAs A hybrid GA meets the QoS and load balancing constraints separately by constructing the graph and dividing the WMNs in disjoint clusters. Hussain et al. WMN SOGA Cluster optimization through GAs augmented the network life when compared with LEACH [126] [125] distributed broadcasting by employing energy efficient data dissemination and optimizing the cluster distances. Zhang et al. [127] WSN SOGA Simulated annealing (SA) [128] A GA approach provided the energy efficient WSN topology by improving the data aggregation rate and minimizing the intra-cluster distances. Huruiala et al. WSN SOGA Centralized GA A GA running on BS coordinate with nodes to minimize latency and [129] power consumption for routing under tight constraints. that a larger number of area points within the network would Another important application of GAs is in the optimization have average SNR. Statistical analysis reveals that MOGA of AP placement in cellular and mobile networks. Since approach generate solutions with a high SNR data profile. finding the set of coverage areas whose sum is the maximum covered area is an NP-hard problem, GAs come handy. Lieska Optimizing the radio coverage inside buildings is as im- et al. [132] have explored in their study the combination of portant as outdoors radio optimization. WLANs are mostly simulation and evolutionary techniques. Radio coverage areas used inside homes and offices to provide mobile and Internet are obtained by the series of BS with received power greater coverage to subscribers. Nagy and Farkas [131] have studied than -60dbm. Algorithm works by selecting the chromosomes the problem of optimizing the placement of indoor Base based on required BS. The chromosomes are than evaluated Stations (BS) while taking in account the effects of floors, against constraints of power and SNR; afterwards, the healthy ceiling, and walls on signal propagation and path losses. GA chromosomes are allowed to reproduce leading to global used the microwave propagation model to account for the convergence of the entire network. This fitness function can effect of influence of brick, concrete, wood, furniture, and be modified to include other constraints based on network glass obstacles. Different weighting coefficients were assigned requirement. A major advantage of a GA, therefore, is its to each obstacle and parallel heuristic approach of GA is used ability to adapt to multiple situations and problems. to optimize the coverage results within indoor environment. 17

8) General Applications: A survey for solving computa- in the networking configurations of wireless sensor networks tionally difficult problem, through GAs, in wireless networks (WSNs), wireless mesh networks (WMNs), cognitive radio is presented by Das et al. [133] in his book “Handbook of networks (CRNs), cellular networks (CNs), and software- Bio-Inspired Algorithm and Applications”. It has been shown defined wireless networks (SWNs). that GAs have the potential to solve any optimization problem provided that proper modeling and chromosomes encoding 1) Wireless Sensor Networks (WSN): WSNs have emerged has been performed. In this section, we will cover some as an exciting technology that can be used to monitor the phys- of the other miscellaneous applications of GAs in wireless ical world. WSN is composed of self-organizing, miniaturized networking (that we have not covered in previous sections). A sensors nodes, running on batteries, and communicating over tabulated summary of these applications are presented in Table wireless links. The major challenge in WSNs is to provide X. We describe some of these applications here; some other ap- area coverage with minimum WSN nodes while preserving plications are discussed when we cover network-configuration the resources and energy consumption. based categorization of GA applications in Section III-B). Jia et al. [137] addressed this problem through MOGA for energy efficient coverage control in WSNs. The algorithm GAs have been proposed for energy efficient planning and provides a mechanism to cover the maximum deployed area management of cellular networks by enabling sleep modes in with minimum number of WSN nodes. Since connectivity and base stations [124]. Johnson and Samii [134] have proposed coverage are both dependent on each other so this problem a GA based approach to find the best node distribution is addressed by MOGA approach by achieving the Pareto with optimized antenna pattern and SNR. The authors have optimal front. This is a non-dominated problem so it comprises employed simple binary coding scheme for a pool of randomly of multiple solution individuals that are evaluated against generated chromosomes for different nodes distribution and two fitness function coverage area and sensor used rate. The evaluated their fitness against the fitness function (in which N MOGA approach applied performs well in maximizing the is the total number of nodes): area covered with least computation. Another advantage is 1 X that it avoids partial solutions in whole search space and reset F itness = max − P ath_length (1) N i sensor nodes once in whole network simulation. i Frentinos and Tsiligiridis [138] studied an adaptive WSN The winner chromosomes (having minimum cost of path design based on MOGA. Individual with random placement length) are more probable to be inherited in the next gener- of nodes are utilized as population and GAs decides which ation. This approach is also applied for random encoding of sensors would be active and which would act as clusterhead. antenna pattern and transmission power. Random designs are encoded and fed to GAs and the winner Churn prediction and forecasting have application in almost chromosomes are going to decide the network infrastructure all the real world phenomenon including medical, finance, including clusterheads and active or passive nodes along products sale, telecommunications and network. Forecasting with signal strengths. From evolution of characteristics, it the future sale and growth in turbulent markets like telecom- was shown that generally, it is more favorable to have large munications is always a big issue for product managers. Even number of sensor nodes with low energy rather than having approximate insights can yield large profit return in the long lesser number of sensors with high energy consumption. This run. Venkatesan and Kumar studied GAs for forecasting [135] application of adaptive GA in WSN can lead to increase in the magnitude of future sales, time period to peak sales and network life span while maintaining network properties close the value of sales during peak time. Considering the significant to optimal value as well as it helps in adapting sophisticated advantages of accurate forecast of product lifecycle, GAs are decisions about operating modes (clusterheads, active nodes used to estimate the diffusion model based on previous data with optimal signal range). points. GAs are fed with several critical factors like price, Extending the life span of any WSN network is active competitive intensity and network effects in obtaining better area of research. Different schemes have been proposed like predictions during growth phase. Since GAs are inherently centralized monitoring GA for keeping active and passive parallel, so, different scenarios can be taken care of while nodes in network. A similar approach has been discussed by making predictions. Study shows that predictions by GAs Jin et al. [139] to cut the energy consumption in WSNs. A are robust and accurate in predicting the future growth of a GA is used for independent cluster formation to reduce the market. Pendharkar [136] presented the hybrid GA with neural communication distances thus bringing the route cost down. networks to forecast the churn in cellular network services. Experimental results showed that by keeping the number of The hybrid algorithms optimize the objectives after learning cluster to 10% of total nodes, results in 80% reduction in and assigning weights to certain parameters. Results obtained path cost and communication distance as compared to random from GA method are shown to be more accurate than statistical distribution of WSNs. In another work, Sengupta et al. [140] models but are computationally expensive. have proposed an evolutionary multiobjective sleep-scheduling scheme for differentiated coverage in WSNs. B. Network Type Based Classification Zhang et al. [141] used GA to extend the work of Niculescu In this section, we will describe the applications of GAs in and Nath on network localization in WSNs [142]. The central wireless networking categorized according to the type of wire- idea is to employ GPS enabled nodes, called anchor nodes, in less network. In particular, we will present GA applications the network and to have all the other network nodes estimate 18 their position through 1-hop distances to the anchor nodes. The umented in a paper authored by Rondeau et al. [146]. This locations are then flooded by each node to the clusterhead paper presented the adaptation mechanism of a cognitive which uses the location information to construct the graph engine, implemented by the authors, that used GAs to evolve of the entire network. By using standard GA operators like a radio’s parameters to make them best for the user’s cur- mutation and crossover, the proposed GA based approach rent needs. A ‘wireless system genetic algorithm’ (WSGA) was able to better estimate locations resulting in lesser mean is also proposed to realize adaptive waveform control and position error than other algorithms in literature such as the cross-layer optimization [146]. GAs have also been used for ‘semi-definite programming with gradient search localization’ building distributed parallel solutions, using the technique of (SDPL) [143] and the ‘simulated annealing based localization’ island genetic algorithms, to mitigate the channel assignment (SAL) [144]. problem in CRNs [17]. An island GA divides the overall In another work, Hussain et al. [125] have studied and sim- population into subpopulations known as islands, which then ulated GAs for centralized hierarchical WSNs. The proposed interact by migrating individuals to the other island. More scheme comprises a hierarchy of layers with the BS being details of parallel genetic algorithms, and of general parallel at the top layer and the clusterheads and the sensor nodes meta-heuristics, can be found in the survey [19] and [147], occupying the bottom layer. GAs are used to construct clusters respectively. with a clusterheads and other nodes. The BS layer keeps track a) MOGAs for optimization of CRNs: Multi-objective of the entire cluster through their clusterheads. A GA approach optimization aims at estimating a true Pareto front opti- minimizes the average cluster distances while simultaneously mization in wireless medium depending upon the external increasing the total number of transmissions. After configuring environment parameters. These radio environment parameters sensor nodes in optimized formation, the data transmission serves as genes and are encoded in binary strings, which phase follows. form chromosomes. These chromosomes are evaluated against 2) Wireless Mesh Networks (WMNs): WMNs provide a fitness function regularly in successive generations. After popular mechanism for the provisioning of cost-effective realizing sufficient fitness or completing predefined number of wireless broadband connectivity. WMNs are composed of generation, these set of transmission parameters are sent for (potentially mobile) mesh clients and (typically fixed) mesh updating new radio configuration. Due to variation in radio routers that connect over a relatively static multihop wireless channel characteristics and spectrum availability, a cognitive network [145]. To address the issue of efficient placement of radio has to maintain time varying QoS while optimizing mesh routers, Xhafa et al. [105] employed GAs to optimize different parameters such as BER, throughput, power con- the user coverage area and connectivity of mesh network sumption, and interference. through optimal placement of nodes in an area. Chromosomes MOGAs have been used extensively for optimization of are designed in rectangular grids having information of both cognitive radio networks (CRNs) [28]. The foremost aim of clients and mesh router nodes. Crossover is implemented cognitive engine (CE) is optimizing the radio parameters for to preserve the chromosomes traits by randomly exchanging best QoS and secondary goal is to observe and learn for adap- parent and child router nodes from one cell to another in grid tation. To achieve these goals cognitive engines have (i) cog- area, thereby promoting high scoring chromosomes. Mutation nitive system module (CSM)—for modeling and learning (ii) is then utilized to randomly migrate a router to another grid Wireless System Genetic Algorithm (WSGA)—for actions (iii) and recalculating the fitness. Various models can be adopted Wireless Channel Genetic Algorithm (WCGA)—for hardware for distributing client nodes such as the normal, uniform, and implementation of radio parameters. These parameter and ra- exponential distribution. GAs are excellent in computing the dio traits called genes represent chromosomes, are modulation, mesh router placements and always succeed in achieving the frequency, spreading, filtering, and FEC coding, etc. Different connectivity, irrespective of client distribution, however, area objectives are optimized based on relative weights assigned to coverage is subjected to client nodes in network area. them using multi-objective approach. These objectives include 3) Cognitive Radio Networks (CRNs): Cognitive radio net- optimizing BER, power consumption, interference and MOGA works (CRNs) offer a potential solution for improving the approach is applied on population and chromosomes, which spectrum utilization in the world of limited spectrum. In performs best in most of the objective, are chosen as new set dynamic spectrum access (DSA) based CRNs, the secondary of radio parameters. users of a network aim to utilize the spectrum opportunistically Case Base Decision Theory (CBDT) for Initialization of to offer QoS for secondary users without causing any interfer- GAs: Since the secondary objective of CR is to adapt and ence to licensed primary users. Such DSA based CRNs utilize evolve with changing environmental parameters by updating cognitive radios (CRs) that incorporate various AI techniques radio configurations. So a CR system must be provided with for intelligent decision making [20]. The main benefits of a memory database that continuously monitors and learns GA applying GA in CRNs are that: (i) it is conceptually easy to outcomes in real-time optimization. As the system matures, understand; (ii) it is inherently amenable to parallel solutions with the passage of time, each new optimization would take and therefore can be easily distributed; and that (iii) GAs lend less time to achieve global optima. More thoroughly speaking, support to multi-objective optimization and performs well in CE keeps track of previous objectives and the winner chromo- noisy unknown environments. somes. So whenever a new objective or case is encountered, An early application of GA techniques to CRNs is doc- it is compared to previous cases in memory and chromosomes 19 of the case/objective having maximum similarity and utility are used to partially initialize the GA population for current objective. Rest of the population is randomly generated to not only maintain diversity but also to help in achieving optima in lesser number of iterations. This adaptation scheme is carried out through algebraic manipulations with the independently constructed channel availability matrix, the interference ma- trix, and the channel reward matrix (which are each kept up to date about the external radio environment conditions) [148]. Rieser [149] presented a biologically inspired cognitive radio model, using modern AI techniques. This model is based on adaptive cognitive engine that learns the radio environment, optimizes the radio parameters, and presents the best possible experience to secondary user. He built his foundation of GA based technique on original Mitola [150] proposed technique of software radios. He gave insights on all the popular AI Algorithms and how ineffective they are in evolving as compared to GAs, when faced with unanticipated radio channel environment. He applied GA to hidden Markov Fig. 7: Cognitive Engine Architecture with WCGA, CSM, and model for error modeling in uncertainties in radio channel WSGA [28] environment. Wireless channel GA has its foundation on these radio environmental modeling. The biologically inspired cognitive engine serves and parallel through the use of GA operators. This developed evolves well in unanticipated radio channel environment, testbed consists of multilayered cognitive engine inspired by which make it usable for military purpose and emergency human brain evolution. The architecture is shown in figure. It situation. This whole cognitive architecture works in multiple provides multilayered scaled functionality with sensing radio steps. Firstly, the engine gathers the channel information parameters at both MAC and physical layers. It uses three which is then subjected to machine learning techniques such algorithms that can be co-located in same radio or distributed as learning classifiers. After learning and modeling, these to multiple radios. This cross-layered cognitive engine archi- information are taken up to alter the radio configurations for tecture is shown in Figure 7. Another GA-based software tweaking appropriate settings [28]. Wireless system GA treats testbed for cognitive engine (CE) is proposed by Kim et al. the radio as the analogue of a biological creature, and makes [151]. A two-step GA is used to avoid problem of optimizing optimized discoveries to keep the appropriate balance of radio the biased dominant parameters. To implement this, GA based parameters. The cognitive engine architecture, with WCGA, iteration is run for channel selection and transmitter parameters CSM, and WSGA, is displayed in Figure 7. We will only selection separately. Simulation of this testbed demonstrates briefly explain below the main infrastructural components of that bandwidth and transmit power converge to optimal values the cognitive engine developed by Rieser. with in few iterations of GAs. 1) Wireless Channel Genetic Algorithm (WCGA): WCGA 4) Cellular Networks (CNs): Next generation wireless net- takes the information about radio channel through phys- works have to cope with the massive increase in multimedia ical and MAC layer and constructs a statistical model service along with cellular data. This motivates the devel- based on external channel environment. This information opment of self-consolidating networks that are capable of is then forwarded to CSM. making intelligent decision to offer the best user quality of 2) Cognitive System monitor (CSM): CSM incorporates the experience (QoE). Ayyadurai et al. [121] presented an adap- capability of learning and adaptation. CSM after learning tive GA to optimize the cellular networks spectral efficiency and generating appropriate action goals instructs WSGA through dynamic allocation of resources, between the relay [28] for actions leading to different radio configurations. stations and the base stations. Population adjustment came 3) Wireless System Genetic Algorithm (WSGA): WSGA along the way to improve the search capabilities leading to receives the channel model by CSM with fitness function quick optimum. Chiaraviglio et al. [124] presented the energy and initial chromosomes. WSGA performs all the GA efficient deployment of cellular networks by leveraging GA to computation through mutation, selection and crossover, minimize the power consumption and number of transmitter thereby helping to select the best chromosomes. These in cells. This involves employing sleep modes, where, a base chromosomes are, in fact, different radio configurations, station decides which nodes should be powered on, depending which are then used for implementing new radio set- on number of active users in given cell. tings. A conflict free channel assignment is an NP-hard problem. b) Cognitive radio (CR) testbeds: Rieser [149] devel- A powerful GA incorporating immune operators including oped a biologically inspired cognitive radio CR testbed. A immune clone, immune vaccination, and immune selection number of cognitive theories are developed and evaluated in has been proposed by Zhenhua et al. [88] to mitigate the 20 interference constraints and obtain a conflict free channel study and analyze competitive interaction between two or assignment. Vaccination involves changing some bits of a more self-interested rational agents. The field of evolutionary gene to have an improved fitness value. Elitism keeps the game theory utilizes the concepts of evolutionary computing population diversity and minimum separation encoding helps and genetic algorithms in the backdrop of a game-theoretic in keeping a frequency distance among individual channels. background [154]. Evolutionary games have been used in A similar approach has been studied by Pinagapany and a wide variety of contexts in networks including coopera- Kulkarve [89] for solving both dynamic and fixed channel tive sensing [155], multiple-access-control and power control assignments in cellular networks. Channel compatibility ma- [156], routing games [157], network selection games [158], trix is constructed first to record the violation of individuals. congestion control [159], adaptive TCP [160], and for dynamic After that, cell and bandwidth information are encoded in bandwidth allocation [161]. The interested reader is referred to individual chromosomes, which are then subjected to crossover a chapter on this topic in a recently published book on game and mutation. Jose et al. [90] offered low computational micro theory in wireless and communication networks [162] for a GA with elitism strategy to solve the fixed channel assignment detailed treatment. (FCA) problem. The proposed algorithm spotlighted how to keep diversity by varying mutation probability to avoid local 2) Combining GAs with Reinforcement Learning: Rein- optima. forcement learning, unlike supervised learning, is a tech- In cellular networks, it is desirable to minimize the call nique where agent has no prior knowledge of transitions drop and call blocking probability. Mobile cellular networks and learns along the way through experience and interaction are often evaluated against the criteria of dropping probability with the environment. We note that evolutionary algorithms of current calls and the blocking probability of new calls. Lima like GAs are related to reinforcement learning as they relies et al. [91] studied two adaptive GAs for locking and switching on exploration and exploitation [163]. More specifically, GA channel to solve the dynamic spectrum access problem in utilizes the genetic operators of mutation and recombination as cellular networks. The proposed fitness function evaluates the procedures for exploration along with selection procedures to capacity of each channel for new calls and also keep tracks exploit known good solutions. Reinforcement learning can be of existing calls. The algorithm takes care of randomness by carried out both by searching through the policy space or the allowing random immigrants and parameter adaptation to keep value-function space. Genetic algorithms can be thought of as exploring new option for each channel. reinforcement learning scheme of the policy space searching 5) Software Defined Wireless Networks (SWNs): In recent variety. Policies are encoded in chromosomes and determinis- times, software defined networking (SDN) has been proposed tic procedure is used to evaluate the cumulative fitness of the as a new architecture for conveniently operating and managing agent the follows a given policy. According to evolutionary diverse wireless networks. SDN is generally understood to principle of survival of the fittest, only good policies are entail (i) the separation of the control and data plane; (ii) adopted while failed or weaker policies are relinquished [164]. the control of multiple data planes by a single controller; and the iii) development of new sophisticated control abstractions 3) Combining GAs with Graph Theory: In order to produce [152]. Wireless networks using SDN principles are referred to robust dynamic graph-theoretic solutions, graph theory can as software defined wireless networks (SWNs). Although this be combined with GAs in particular, and with evolutionary networking configuration is relatively new, the use of GA has algorithms more generally. The combination of graph theory been proposed in SWNs. For example, Bojic et al. have pro- with evolutionary algorithms is known as evolutionary graph posed a small-cell mobile backhaul resource manager, based (EG) theory in literature. Ferreira et al. [165] have applied on GA, that interworks with software defined management EG theory in MANETs with known connectivity pattern for [153]. developing efficient practical routing protocols. The dynamic behavior of network is captured through evolving graphs. There are various metrics that can be used for determining C. Hybridization: GA With Other Techniques optimal routes in EG-based models with known connectivity GAs is a useful framework that can be profitably used in a patterns, including the three metrics of shortest, fastest, and wide variety of settings. It is also possible to use GAs with foremost proposed in [166]. These metrics determine respec- other adaptive algorithmic approaches such as game theory, tively the minimum number of hops, the minimum time span, reinforcement learning (RL), graph theory, fuzzy logic based and the earliest arrival data. Ferreira et al. [165] utilized and quantum theory based systems. Such a symbioses is not at the foremost journey metric along with the EG theory. The all antithetical from the theme underlying the GA framework proposed algorithm can estimate the congested nodes and which encourages pluralism in preference to relying on any suggest the parallel paths. In another work, a bio-inspired one solution; it is often the case that we can perform better graph theoretic solution for ensuring energy efficiency in by combining the best parts of different solutions as building cooperative communication networks has been proposed in blocks. In this section, we will describe hybrid approaches that [167]. The presented algorithm combine the graph theory combine various techniques with the principles of GAs. with evolutionary techniques to the let the nodes operate in decentralized fashion for intelligent decision making, and do 1) Combining GAs with Game Theory: Game theory is forwarding by selecting energy conserving nodes. a mathematical decision framework through which we can 21

4) Combining GAs with Fuzzy Logic: Fuzzy logic is a IV. PRACTICAL ISSUESAND LESSONS LEARNT logical system that can entertain logical variables that take In this section, we will summarize the main insights and continuous values between 0 and 1 instead of discrete values lessons learnt through decades of GA research that can guide of either 0 or 1 (as in classical digital logic). Fuzzy logic successful problem solving through GAs. We first describe is as an effective method for knowledge representation, con- common pitfalls in Section IV-A, and then describe some trol implementation, and cross-layer optimization in wireless guidelines and insights for successful GA implementation in networks [168]. Fuzzy logic is well suited for knowledge Section IV-B. representation in wireless networks since network conditions in wireless networks are often incompletely and imprecisely A. Common Pitfalls known. Fuzzy systems that utilize fuzzy logic are highly suited to problems with imprecise, noisy, and incomplete input While GAs provide a useful framework for problem-solving information. GA can be used for both optimizing the fuzzy in a wide variety of domains, it is not a panacea. In this section, membership function as well as the fuzzy rules that drive the we will highlight some deficiencies of GAs and how it may fuzzy control system. The intersection of hybrid technologies be incorrectly applied. of GA, fuzzy logic, and other AI techniques (most prominently 1) Genetic Drift or Bias: In GAs, there is a risk of neural networks) is studied in the research theme of ‘soft slow convergence and settling for local minimas, especially computing’ [169]. The trend of genetic fuzzy systems for soft with inappropriate choice of model parameters. While GAs computing applications is less developed than the trend of can often converge to the global optima in the majority of neuro-fuzzy systems, especially in the context of industrial applications, there are no mathematical guarantees to this control applications. Nonetheless the use of genetic fuzzy effect. In particular, a GA can get get stuck in the vicinity techniques is popular for both communication systems [170] of a suboptimal point if it lacks population diversity, or if has and wireless networks [103]. an inappropriately small population. Such a phenomenon is known as ‘genetic drift’ or ’genetic bias’. Certain problems 5) Combining GAs with Quantum Theory: Quantum theory cannot be solved by means of simple genetic operations. This derives its root from quantum mechanics, i.e., mechanics is mainly due to the choice of poor fitness functions that gen- of atoms. A comparative study has been performed in [85] erate poor chromosome blocks. There cannot be an absolute between quantum GA and classical GA. Quantum GA proves assurance that a GA will be able to find a global optimum— to be faster and more robust then classical GA for traveling this can especially be a problem when the population has a sales person problem. A quantum GA is proposed in [171] lot of subjects. to solve the NP-Complete QoS metrics problem in WSNs. Quantum GA operate on qubit as a smallest unit of infor- 2) Using GAs for Real-Time Applications: Like most other mation, that serves as a linear superposition of two states, AI techniques, GAs are not well suited to real-time application i.e., 1 and 0. A rotation gate is applied to keep the diversity that require guaranteed response times due to its stochastic of population in quantum GA. Quantum GA behaves more and heuristic nature. In addition, the response time of GA effectively than traditional GA for larger input set owing to can have significant variance depending on the various control its linear superposition states. parameters and population initialization. This potential pitfall should be kept in mind if GAs are used for online learning 6) Combining GAs with Local Search: A very common and optimization in wireless networks. In particular, QoS form of a hybrid GA, sometimes referred to as Memetic algo- requirements in wireless networks may put constraints on rithms [172] in literature, is created by combining GAs with achieving the optimum decision in limited time forcing GAs local search techniques and to incorporate domain-specific to terminate after predefined number of iterations. knowledge in the search process [27]. This can help produce 3) GA Deception: It has been reported in literature that stronger results but at the cost of higher computational costs. certain objective functions, referred to as GA-deceptive func- The local search operator is applied to each member of the tions, can be very difficult to optimize. With such deceptive population after each generation. Memetic algorithms have functions, combination of good building blocks may result in been used in the context of wireless networks for various very bad chromosomes, causing the building block theory to tasks such as energy-aware topology control [173] and cell fail. A potential solution to this problem is using messy genetic assignment to switches [174]. algorithms [3].

7) Combining GAs with Other Metaheuristics: A popular B. Implementation Insights area of research is combining GAs with heuristic methods like ant colony optimization (ACO), neural networks (NN), and 1) Setting Population Size: The size of the population in a fuzzy logics to solve the dynamic constrained multi-objective GA can be a major factor in determining its quality and con- optimization. In particular, there has a been a lot of work in vergence speed. Generally speaking, larger populations result applying GAs for adjusting the connection weights and the in better solutions. A few studies have addressed the problem connectivity itself in NNs [175]. Notwithstanding the amount of determining exactly how large a population should be to of work done, there is a lot of scope for further optimization ensure a certain quality [176] [177] [178]. For a moderately and improvement. complex problem, a population of 50 to 100 chromosomes 22 can serve as a good default value [179]. The precise choice of non-trivial and context-dependent. While this criteria depends the population size depends on the problem complexity and on the number of objective functions, and the number of the number of search variables. While it is typical for the variables, a default value of 2.5 times the population size can population size to remain fixed from one generation to the be used as a reasonable maximum generation count estimate next, it can also be made to grow or contract depending on [179]. the rate of convergence, and other factors such as the current genetic diversity. V. OPEN ISSUESAND FUTURE WORK 2) Designing Solution Encoding and Fitness Function: GAs have become a powerful tool for solving almost any The efficiency, processing power, and the convergence of kind of an optimization problem–subject to proper modeling GAs depend critically on how the solution is encoded in and encoding of chromosome. GAs are contributing in mili- the form of chromosomes and on the formulation of an tary, disaster management, spectrum utilization, and network appropriate fitness function. This is the first necessary step optimization. There are numerous challenges in devising an towards an efficient implementation. There is no one-size-fits- appropriate GA based solution including suitable definitions all solution here, and the correct model choice depends on of population size and evaluation function (which is typically what is most useful for the problem at hand. The encoding of non-trivial to define). In this section, we provide the recom- chromosomes should be carefully considered. While a majority mendation on scope of future research on GAs in the field of of implementations utilize bit representation, due to the ease networking. with which crossover and mutation can be implemented, other representations, utilizing data structures, may be appropriate A. Theoretical Results for GAs for the considered problem and should also be considered [27]. A lot of effort has focused on providing theoretical un- Since there can be numerous encoding and formulations, this derstanding of why and how GAs work but rigorous results step involves considerable ingenuity. Some guidelines on these have been slow in coming. Some of the results, such as “No issues are provided in [22] [180]. Free Lunch”, have sobering implications. Simply stated, no 3) Setting of Mutation and Crossover Rates: The optimiza- free lunch implies that all search algorithms perform equally tion of the control variables of genetic algorithms (such as the when averaged over all problems. This further entails that if setting of mutation and crossover rates) plays an important we are comparing GAs with other search heuristics (such as role in the performance of a GA based framework. A GA hill climbing or simulation annealing), even if GA performs framework can avoid prematurely settling in a suboptimal rut better for some class of problems, the other algorithms will by emphasizing exploration using mutation. Various solutions necessarily perform better on some problems outside this class. have been proposed to the problem of genetic drift/ bias GAs are also population-based heuristics; even as the entire including fitness sharing [181], crowding and pre-selection population is improved by GAs, the same cannot be guaranteed [182]. Bhandari et al. [8] showed that the probability of for an individual existing within that population. There is a fast convergence increases by seeding the initial population need for enhanced theoretical understanding of various facets with high scoring chromosomes. As a general rule-of-thumb, of GAs to lay a strong foundation upon which the GA user’s crossover and mutation rates of 0.6 and 0.001 have been pro- trust can be safely placed. posed for large population sizes (of ∼100), with corresponding values of 0.9 and 0.01 proposed for small population sizes (of B. How to Exploit Problem Specific Knowledge? ∼30) [22] [180]. Sastry et al. [27] similarly recommend a Techniques like GA and neural networks are often resorted mutation probability of .05 and a crossover rate of 0.6 with a to as black-box solutions to complex problems where the population size of ∼50. A tabulated summary of mutation and mechanisms to be used for problem solving are not well crossover rates generally recommended by the GA community understood. Even without problem specific knowledge, GAs and accepted as de facto ‘standards’ are presented in Table XI. can allow insights to develop thorough identification of sim- ilarities between highly fit individuals [6]. GAs exploit this 4) Computation of Fitness Values: In many problems, information by combining highly fit similarities to explore the computation of the fitness function can be extremely beyond the currently known best solutions. When the subject computationally intensive, thus motivating research in fitness knowledge is available, in the form of good understanding of approximation [184]. An important practical issue is to de- the underlying problem and plausible candidate solutions, it termine ways of modeling large complex systems so that the is desirable to exploit this information to expedite GA’s pro- fitness value can be computed without executing the real-world gression towards a solution. One way of embedding problem- system itself (which can be impractical in many situations). specific information in the GA system is by seeing GAs with 5) Setting of Termination Criteria: Assuming the pop- good structures and populations thereby accelerating search ulation, and the various GA control variables, have been and learning progress. However, the use of problem specific set up properly, the GA will improve towards the optimal knowledge to generate specialized heuristics or operators can solution over successive generations. In light of potentially entail some loss of generality of the GA system [6]. The slow convergence, it is very important to for timely problem question of how to embed wireless-specific subject knowledge solving with GAs to devise a suitable termination criterion into the GA frameworks is very much an open research issue that defines a ‘good enough’ solution. Defining these criteria is requiring further exploration. 23

TABLE XI: Summary of GA paramater settings guidelines generally accepted by the GA community

De Jong and Spears [180] Grefenstette [22] Sastry et al. [27] Carrol [183] (Micro GA) Population Size 50 30 50 5 Number of Generations 1000 Not Specified Not Specified 100 Mutation Rates 0.001 0.01 0.05 0.02; 0.04 Mutation Types bit flip bit flip Not Specified jump and creep Crossover Rate 0.6 0.9 0.6 0.5 Crossover Type 1 or 2 point (typically, 2 point) 1 or 2 point (typically, 2 point) Not Specified Uniform

C. Efficient Multi-Objective and Distributed GAs VI.CONCLUSIONS The development of practical algorithms for wireless net- We have provided a survey of the applications of genetic works often requires the use of multi-objective optimization algorithms (GAs) in wireless networking. In addition to pro- performed in a distributed fashion. Currently, the most popular viding a self-contained introduction to common models and approaches in wireless networks depend on centralized GA configurations of GAs, we have also provided a detailed [116]: e.g., in mobile cellular networks, the GA runs on the survey of applications of GAs in wireless networking. We BS and helps decide the cluster size and nodes deployment. have categorized the applications of GAs in wireless network- In wireless networks, there is often a need to distribute the ing both according to the wireless networking configuration, computational load to various network nodes. This can be and according to the different kinds of GA techniques. We done by a locally run GA on each node combined with local have also highlighted pitfalls and challenges in successfully search techniques for robustness. There is an ongoing research implementing GAs in wireless networks. Finally, we have on dynamic cluster design based on multiple metrics. We can highlighted a number of open issues and have identified also use distributed GA to provide maximum disjoint covers potential directions for future work. to enhance the coverage area and network life. There is room for improving the throughput by extending the GAs from single cell to multi-cell optimization, with inter-channel noise REFERENCES cancellation [121]. [1] F. Hillier and G. Lieberman, “Introduction to operations research,” McGraw Hill, New York, 2001. D. GAs, Complexity Theory, and Wireless Networks [2] M. Ridley, Evolution. 3rd Edition. Blackwell, 2004. [3] M. Mitchell, An introduction to genetic algorithms. 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