Adaptive Grouping Brain Storm Optimization for Multimodal Optimization Problems

Introduction

For solving an optimal problem, the principal purpose is finding the single optimal solution. However, in engineering application, the ideal optimal solutions may not have a good effect due to physical or other constraints. For example, in the field of industrial design, the fittest solutions may not be realized, or for the convenience of assembly and maintenance, or for higher reliability (Sheng & Li, 2012). Therefore, we want to locate less fittest solutions for providing more alternatives. Multimodal optimization problem is a type of problem, whose objective functions lead to multimodal domains. There exists multiple global optimal solutions and many local optimal solutions in the restricted solution vector space. The purpose of the design of optimization algorithms for solving these problems is finding as many multiple global optimal and local optimal solutions as possible on the premise of ensuring global optimal precision.

Swarm intelligence algorithm is a kind of heuristic random algorithm, which regards optimization problems as searching for optimal value in solution space, and guides the searching process by heuristic information (Kennedy, Eberhart, &Shi, 2001). There have been many researches in swarm intelligence algorithm for solving multimodal optimization problems. Particle swarm optimization (PSO) is widely used to solve multimodal optimization problems. PSO mimics the behavior of birds flocking (Kennedy & Eberhart, 1995). It has strong convergence, which is valuable for searching global optimal solutions quickly. However, the strong convergence is not friendly for searching local optimal solutions. Artificial bee colony algorithm (ABC) mimics the foraging behavior of bees, which is proposed by Karaboga and Basturk (2007). The colony of artificial bees is divided into three groups, one for random reaching, one for deciding, and one for going to the food source. The position of a food source represents a possible solution of the optimization. Election campaign algorithm (ECA) simulates the behavior that election candidates chase the highest support in election campaign (Lv, Xie, Liu, Zhang, Luo & Cheng, 2010). The effects from candidates to voters depend on the distances between the candidates and voters, which helps converging to a local optimal solution faster and more stably. However, there are many parameters involved in the algorithm. It results in the difficulty in adjusting the parameters for different multimodal problems. Brain storm optimization (BSO) mimics the behavior of human discussion (Shi, 2011). It contains grouping operation, which is widely used in the idea of niche. So BSO has its unique advantage in solving multimodal optimization problems.