A novel bee swarm optimization algorithm for numerical function optimization Reza Akbari * , Alireza Mohammadi, Koorush Ziarati Department of Computer Science and Engineering, Shiraz University, Shiraz, Iran article info Article history: Received 12 June 2009 Received in revised form 2 November 2009 Accepted 2 November 2009 Available online 10 November 2009 Keywords: Bee swarm optimization Numerical function optimization Time-varying weights Repulsion factor abstract The optimization algorithms which are inspired from intelligent behavior of honey bees are among the most recently introduced population based techniques. In this paper, a novel algorithm called bee swarm optimization, or BSO, and its two extensions for improving its performance are presented. The BSO is a population based optimization technique which is inspired from foraging behavior of honey bees. The proposed approach provides different patterns which are used by the bees to adjust their flying trajectories. As the first extension, the BSO algorithm introduces different approaches such as repulsion factor and penalizing fitness (RP) to mitigate the stagnation problem. Second, to maintain efficiently the balance between exploration and exploitation, time-varying weights (TVW) are intro- duced into the BSO algorithm. The proposed algorithm (BSO) and its two extensions (BSO– RP and BSO–RPTVW) are compared with existing algorithms which are based on intelligent behavior of honey bees, on a set of well known numerical test functions. The experimental results show that the BSO algorithms are effective and robust; produce excellent results, and outperform other algorithms investigated in this consideration. Ó 2009 Elsevier B.V. All rights reserved. 1. Introduction Optimization has been an active area of research for several decades. As many real-world optimization problems become increasingly complex, better optimization algorithms are always needed. In optimization problems, the objective is to find the minimum or maximum of the function under consideration. So, unconstrained optimization problems can be formulated as a D-dimensional minimization or maximization problem: minðor maxÞ f ð ~ xÞ; ~ x ¼ðx 1 ; x 2 ; ... ; x D Þ ð1Þ where D is the number of the parameters to be optimized. There are many population based optimization techniques avail- able for unconstrained numerical optimization. Genetic algorithms (GA), Particle Swarm Optimization (PSO), and Bee Algo- rithms (BA) are among the most popular optimization algorithms which employ a population of individuals to solve the problem on the hand. The success of a population based method depends on its ability to establish proper balance between exploration and exploitation. A poor balance between exploration and exploitation may result a weak optimization method which may suffer from premature convergence, trapping in a local optima, and stagnation. GA is the most popular evolutionary algorithms, in which a population of individuals evolves according to a set of rules such as selection, crossover and mutation [1]. In such algorithm, exploitation is obtained through selection, where individ- 1007-5704/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cnsns.2009.11.003 * Corresponding author. Tel.: +98 9171003767. E-mail addresses: rakbari@cse.shirazu.ac.ir (R. Akbari), a_mohammadi@cse.shirazu.ac.ir (A. Mohammadi), ziarati@shirazu.ac.ir (K. Ziarati). Commun Nonlinear Sci Numer Simulat 15 (2010) 3142–3155 Contents lists available at ScienceDirect Commun Nonlinear Sci Numer Simulat journal homepage: www.elsevier.com/locate/cnsns