Comparison of Firefly, Cultural and the Artificial Bee Colony Algorithms for Optimization Vaishali R. Kulkarni1, Veena Desai2, Raghavendra V. Kulkarni1 1Faculty of Engineering and Technology, M. S. Ramaiah University of Applied Sciences, Bengaluru 560058 2Department of Electronics and Communication Engineering, KLS Gogte Institute of Technology, Belagavi 590008 *Contact Author E-mail: [email protected] Abstract Global optimization refers to the technique for finding the best element in the given domain by satisfying certain constraints. Optimization algorithms are classified as deterministic and heuristic. Deterministic algorithms provide guaranteed solutions but with high computational demand. Heuristic and metaheuristic algorithms have been successfully used in optimization problems. They provide a solution close to the optimum with a better speed and less complexity. In this paper three metaheuristic algorithms namely firefly , cultural and the artificial bee colony, algorithm have been investigated over benchmark function optimization. The results and numeric simulation include comparison of the algorithms in terms of minimization of the objective function. Results of Matlab implementation show that the firefly algorithm performs the optimization in the most accurate manner. Cultural algorithm is inferior to firefly and the ABC algorithm shows the poorest performance among the three. Keywords: Metaheuristic Algorithms, ABC Algorithm, Firefly Algorithm, Cultural Algorithm, Global Optimization solved using metaheuristics than problem- specific 1. INTRODUCTION heuristic algorithms There are two categories of optimization algorithms: Many researchers use metaheuristic and heuristic deterministic or exact algorithms and heuristics. definition interchangeably, as a concrete definition has Deterministic algorithms find the guaranteed optimal been elusive. These algorithms have been categorized solution in a finite amount of time. However, for from Evolutionary Computation (EC), Swarm complex optimization problems for eg: global or NP- Intelligence (SI) and other paradigms of Computational hard optimization problems, the amount of time may Intelligence. They are referred as nature inspired or bio- increase exponentially with respect to the dimensions of inspired algorithms. Recent metaheuristic algorithms the problem. On the other hand, heuristics do not have preserve search experience embodied in some form of guarantee of solution but they usually find good enough memory for better solutions. Metaheuristic algorithms solutions in a reasonable amount of time. The found have been used in solving NP-hard optimization solution may not be the best of all actual solutions to the problems such as machine learning, traveling salesman given problem, but it may be the approximate and still problem, scheduling, maximum clique problem, p- be useful as it does not require long time. The median problem, search problems, feature selection etc. justification of heuristic algorithms is based on The metaheuristic algorithms based on SI have been arguments of plausibility, rather than mathematical applied for benchmark function optimization n this proof. It is possible that, heuristic algorithm may paper. These algorithms are: Firefly Algorithm (FA), conclude that no solution exists. Heuristic methods are Cultural Algorithm (CA) and the Artificial Bee Colony usually designed to fit a specific problem type rather Algorithm (ABC). than a variety of applications. This drawback is overcome with metaheuristic algorithms. Metaheuristic FA simulates the behavior of fireflies searching for algorithms can be applied to broader range of problems. brightness [1]. CA is based on EC and it is also called as Metaheuristic algorithms include a high-level problem- a meta-evolutionary algorithm. CA includes of the independent algorithmic frame-work that provides a set culture that comprises of the parameters such as habits, of guidelines or strategies to develop heuristic beliefs, knowledge and customs of the society. CA uses optimization algorithms. In comparison with heuristics, culture to interact with the environmental condition and metaheuristics are powerful and robust, they can revive works upon improvement of convergence to obtain from any situation, irrespective of initial solutions. The optimal solution [2]. The ABC algorithm is based on the key ideas of metaheuristics are [1]: food foraging behavior of honeybees [3]. Generally an optimization problem can be considered as a 1. Search process is using the information gathered to minimization or maximization problem. In the move towards the global optimum based on optimization process, the absolutely best decision that guidelines corresponds to the minimum or maximum of a suitable 2. Metaheuristic can escape from getting trapped in objective function must be taken. The decision should be local minima by generating new solutions. New taken in the presence of the collection of feasible solution is a combination of two or more good constraints. An objective function also known as fitness solutions function expresses the main aim of the model which is 3. Metaheuristic algorithms explore neighborhood either to be minimized or maximized. A set of unknowns structure that avoids trying similar solutions or variables control the value of the objective function in 4. A very good solution can be found in a relatively given constraints. The performance of the system such as quick speed. Large complicated problems can be physical limitations, utility, design, loss, error etc. can be modelled by an objective function. The constraints on RUAS-SASTech Journal 22 Vol. 16, Issue 2 objective function may be due to technical, economical dimensions, population size and number of iteration. or some other considerations. A set of standard Several factors decide the benchmark functions benchmark functions can be used to validate classification. These factors are: optimization problem. Benchmark functions can be unimodal or multimodal. Unimodal are with single local 1. Dimensionality: As the dimension increase, there is optima and multimodal functions are with more than one increase in search space. It is a challenge for local optima. The exploration and exploitation process of optimization problem to handle high dimensions in an algorithm can be tested using these functions. The nonlinear problems metaheuristic algorithms can be tested in an unbiased 2. Modality: The number of peaks in the function way by applying on the benchmark functions. In this landscape define modality. The search process of paper, the FA, CA and the ABC algorithm have been algorithm might get stuck in one of the peaks and applied on benchmark functions to test the efficiency of this will mislead the search process, taking it away algorithm in terms of accuracy. The remainder of this from the optimal solution paper has been organized as follows: Previous research 3. Basins: This refers to the plateau in optimization in optimization with SI and EC has been surveyed in problem. Basin can hamper the search process as it Section 2. An overview of the benchmark functions has can get attracted towards such regions. This will get been presented in Section 3. A brief overview of an obstacle in the exploration of solutions algorithms used have been outlined in Section 4. Details 4. Separability: It is a measure of difficulty of of the results obtained have been presented in Section 5. different benchmark functions. Separable functions Finally, concluding remarks and future scope for future are easy to solve in comparison with un-separable research have been given in Section 6. or dependent functions The performance of metaheuristic algorithms can tested in an effective manner using these features of benchmark 2. RELATED WORK function. Some of the popular benchmark functions have been used for in this work are listed below. The algorithms used in this work are inspired by SI and EC paradigms of CI. SI is defined as the emergent 1. Rastrigin Function collective intelligence of groups of simple agents, 2. Rosenbrock Function commonly referred as population. SI algorithms works 3. Schewefel Function in a distributed and self-organized manner. SI is based on 4. Sphere Function the behavior of swarms for example: social insects, flock of birds, colonies of ants etc. These colonies work on the 4. ALGORITHMS principle of division of labor and have been successful in exploring the search space for optimal solutions. EC is SI is defined as the emergent collective intelligence of inspired by the theory of biological evolution. EC has groups of simple agents that work in a distributed and been successfully used to create optimization self-organized manner. These colonies work on the procedures. Evolution is seen as a process leading to the principle of division of labor and have been successful in survival of the population and reproduce in specific exploring the search space for optimal solutions. The environment. CA has been used in many constrained ABC algorithm has been used in many science and applications as presented in article [4]. A self-adaptive engineering applications. The variants and applications CA with fuzzy controller has been presented in article of the ABC algorithm has been expressed in article [9]. [5]. The evolution process in fuzzy controller has been Comprehensive study of FA has been presented in article controlled by using CA in this work. Several research has [10]. CA is derived from cultural evolution models in been done in the FA- and ABC-based