Maintaining Diversity by Clustering in Dynamic Environments Changhe Li School of Computer Science China University of Geosciences Wuhan, China 430074 Email: changhe.lw@gmail.com Shengxiang Yang Department of Information Systems and Computing, Brunel University Uxbridge, Middlesex UB8 3PH, U. K. Email: shengxiang.yang@brunel.ac.uk Ming Yang School of Computer Science China University of Geosciences Wuhan, China 430074 Email: yangming0702@gmail.com Abstract—Maintaining population diversity is a crucial issue for the performance of evolutionary algorithms (EAs) in dynamic environments. In the literature of EAs for dynamic optimization problems (DOPs), many studies have been done to address this issue based on change detection techniques. However, many changes are hard or impractical to be detected in real-world applications. Although, some research has been done by means of maintaining diversity without change detection. These methods are not effective because the continuous focus on diversity slows down the optimization process. This paper presents a maintaining diversity method without change detection based on a clustering technique. The method was implemented through particle swarm optimization (PSO), which was named CPSOR. The performance of the CPSOR algorithm was evaluated on the GDBG benchmark. A comparison study with another algorithm based on change detection has shown the effectiveness of the CPSOR algorithm for tracking and locating the global optimum in dynamic environments. I. I NTRODUCTION Generally speaking, maintaining population diversity is an important issue for algorithms to effectively track and lo- cate the global optimum in dynamic environments, where changes occur over time. Recently, investigating evolutionary algorithms (EAs) for dynamic optimization problems (DOPs) has attracted many researchers because EAs are intrinsically inspired from natural or biological evolution, which is always subject to an ever-changing environment, and hence EAs, with proper enhancements, have a potential to be good optimizers for DOPs. Over the years, several approaches have been developed to address DOPs, including diversity increasing and maintaining schemes [5], [6], [8], memory schemes [2], multi- population schemes [3], [13], adaptive schemes [19], multi- objective optimization methods [4], hybrid approaches [11], change prediction methods [15], and problem change detection approaches [14]. In dynamic environments, the aim should be to locate and track a set of optima rather than a single global optimum. And many experimental studies have also shown that this is an effective idea to solve DOPs [1], [18]. To locate and track multiple optima, the multi-population method seems an ideal tool to fulfill the task. From the literature for DOPs, many algorithms have been proposed to address DOPs using the multi-population method [1], [7], [8], [18], with the idea of maintaining diversity by dividing the whole search space into different sub-spaces and then separately searching within these sub-spaces. However, one challenging issue of using the multi- population method is that of how to create an appropriate number of sub-populations with an appropriate number of individuals to cover different sub-areas in the fitness landscape. In order to answer this question, a clustering particle swarm optimizer (CPSO) was proposed in [7], [18]. In CPSO, a hierarchical clustering method is employed to automatically create a proper number of sub-populations in different sub- areas. Another challenge for EAs in dynamic environments is how to handle the dynamism when a change occurs. So far, most algorithms proposed for DOPs are informed when a change occurs or use some techniques to detect changes. However, it is difficult or impossible to detect changes in some cases. For example, it will be very hard to detect changes if only some random local sub-areas change over time in the entire search space. In this case, we can not always successfully detect the changes or predict the changes because we do not know when or where the changes occur in the search space. To address this issue, a updated version of CPSO algorithm, called CPSOR [8], was proposed to solve DOPs without change detection. In the studies on the moving peaks problem [2], the CPSOR algorithm has shown an superior performance against several state-of-the-art algorithms. This paper applies the CPSOR algorithm to solve the GDBG benchmark [9]. The paper discusses some challenges when applying EAs using multi-population methods to solve DOPs. The key components of the CPSOR algorithm are also described in this paper. In order to find out a general setup of the parameters of the CPSOR algorithm for the GDBG benchmark, we also carried out a parameter sensitivity study. The effectiveness of the CPSOR algorithm is also shown through the performance comparison of the CPSOR algorihm and the CPSO algorithm. The rest of this paper is organized as follows. Section II reviews the relevant work that has been done using multi-population methods to maintain the population diversity in dynamic environments . The challenges of using multi- population methods to maintain diversity are also discussed in Section II. Section III describes the fundamental ideas of the 978-1-4673-1509-8/12/$31.00 ©2012 IEEE WCCI 2012 IEEE World Congress on Computational Intelligence June, 10-15, 2012 - Brisbane, Australia IEEE CEC