An Improved Imperialist Competitive Algorithm Based on a New Assimilation Strategy

Meta-heuristic algorithms inspired by the natural processes are part of the optimization algorithms that they have been considered in recent years, such as genetic algorithm, particle swarm optimization, ant colony optimization, firefly algorithm. Recently, a new kind of evolutionary algorithm has been proposed that it is inspired by the human evolution process. This new algorithm has been called Imperialist Competitive Algorithm (ICA). The ICA is a population-based algorithm where the population is represented by countries that are classified as colonies or imperialists. This paper is going to present a modified ICA with high accuracy, referred to here as ICA2. The ICA2 is tested with six well-known benchmark functions. Results show high accuracy and avoidance of local optimum traps to reach the minimum global optimal. Two main operators of the ICA are Assimilation and Revolution. Assimilation policy is the more important than Revolution. This research focuses on an assimilation policy in the ICA to propose a meta-heuristic optimization algorithm for optimizing function with high accuracy and avoiding to trap in local optima rather than using original ICA. Index Terms — evolutionary algorithm, optimization algorithm, imperialist competitive algorithm, assimilation policy. I.INTRODUCTION F the optimal solution is a major challenge in many scientific problems. The heuristic algorithms have widely been used to reach global optimum of different problems. Genetic Algorithm (GA) [2], Particle Swarm Optimization (PSO) [3], Ant Colony Optimization (ACO) [4], Differential Evolution (DE) [5], Gravitation Algorithm (GA) [6] and Firfly Algorithm [7] are some familiar meta-heuristic studies. Recently, inspired by a socio-politically motivated, a metaheuristic algorithm called Imperialist competitive algorithm (ICA) is proposed by Atashpaz and Lucas [8]. The ICA is a multi-agent algorithm with each agent being a country [9]. In ICA, the countries divided into two groups based on their power, colonies and imperialists [8]. But these algorithms have defects to deal with the local optimum trap and the accuracy rate [1]. The local optimum trap is an important shortcoming in optimization. A local optimum is a solution that is optimal within a neighboring set of solutions. This is in contrast to a global optimum, which is the optimal solution among all possible solutions that may occur under different situations [10]. ICA is much more successful than other optimization methods to eradicate these problems [8, 9, and 10]. It has been used to solve different kinds of problems, such as PID controller design [11], initial and boundary-value problems [12] , a new hybrid data-clustering algorithm [13 ,14], economic problems [15,16,17] and many engineering problems [1,9,18,19,20]. The motivation of this study is to present a meta-heuristic algorithm for optimizing with high accuracy and avoiding to trap in local optima, based on the ICA, because of, ICA has successful application in various fields and good 1Department of Computer Engineering, Islamic Azad university, Safashahr Branch, Safashar, IRAN ([email protected],[email protected]) 24 Journal of Advances in Computer Engineering and Technology, 2(2) 2016 performance in comparison to other optimization methods [11]. Various attempts have been made to improve the ICA, include modifications in ICA [10,24,25,26,27] and a hybrid with local search or other optimization techniques [28,29,30,31,32,33]. This study focuses on the assimilation policy because the movement of colonies toward their imperialist has the biggest influence of them all [24]. ICA2 with a new adaptive assimilation strategy avoids from trap of local optimum. Organization of the paper is in order. Section 2 provides a precise description of the basic ICA and reviews the developments on the ICA. Section 3 presents the proposed algorithm. Experimental setup and results are discussed in Section 4. Section 5 includes summary and conclusion. II. IMPERIALIST COMPETITIVE ALGORITHM ICA simulates the social political process of imperialism and imperialistic competition. This algorithm contains a population of agents or countries. The Steps of algorithm are described as below [8]. 1. Initializing ICA starts with an initial population of randomly generated solutions {p1, p2, ..., pN}, where each solution pi is called country and is a 1×n array of variables to be optimized, and N denotes the number of countries. ICA computes the cost of each pi as Ci. Then sort ascending the initial population based on cost values. The most powerful countries are selected as imperialists (equation 1), and the others are divided among imperialists, based on the power of each imperialist (equation 2 ) . That is, PPPPPPPPPPPPiiii = � max 1≤jjjj≤NNNNiiiiiiiiiiii {CCCCjjjj }� − CCCCiiii (1) NNNNNNNNiiii = rrrrrrrrrrrrrrrrrrrr(� PPPPPPPPPPPPiiii ∑ PPPPPPPPPPPPjjjj NNNNiiiiiiiiiiii jjjj=1 � × [NNNN −NNNNiiiiiiiiiiii ])