Particle swarm optimization with composite particles in dynamic environments

This article is placed here with the permission of IEEE - Copyright @ 2010 IEEEIn recent years, there has been a growing interest in the study of particle swarm optimization (PSO) in dynamic environments. This paper presents a new PSO model, called PSO with composite particles (PSO-CP), to address dynamic optimization problems. PSO-CP partitions the swarm into a set of composite particles based on their similarity using a "worst first" principle. Inspired by the composite particle phenomenon in physics, the elementary members in each composite particle interact via a velocity-anisotropic reflection scheme to integrate valuable information for effectively and rapidly finding the promising optima in the search space. Each composite particle maintains the diversity by a scattering operator. In addition, an integral movement strategy is introduced to promote the swarm diversity. Experiments on a typical dynamic test benchmark problem provide a guideline for setting the involved parameters and show that PSO-CP is efficient in comparison with several state-of-the-art PSO algorithms for dynamic optimization problems.This work was supported in part by the Key Program of the National Natural Science Foundation (NNSF) of China under Grant 70931001 and 70771021, the Science Fund for Creative Research Group of the NNSF of China under Grant 60821063 and 70721001, the Ph.D. Programs Foundation of the Ministry of education of China under Grant 200801450008, and by the Engineering and Physical Sciences Research Council of U.K. under Grant EP/E060722/1

A clustering particle swarm optimizer for locating and tracking multiple optima in dynamic environments

This article is posted here with permission from the IEEE - Copyright @ 2010 IEEEIn the real world, many optimization problems are dynamic. This requires an optimization algorithm to not only find the global optimal solution under a specific environment but also to track the trajectory of the changing optima over dynamic environments. To address this requirement, this paper investigates a clustering particle swarm optimizer (PSO) for dynamic optimization problems. This algorithm employs a hierarchical clustering method to locate and track multiple peaks. A fast local search method is also introduced to search optimal solutions in a promising subregion found by the clustering method. Experimental study is conducted based on the moving peaks benchmark to test the performance of the clustering PSO in comparison with several state-of-the-art algorithms from the literature. The experimental results show the efficiency of the clustering PSO for locating and tracking multiple optima in dynamic environments in comparison with other particle swarm optimization models based on the multiswarm method.This work was supported by the Engineering and Physical Sciences Research Council of U.K., under Grant EP/E060722/1

A general framework of multi-population methods with clustering in undetectable dynamic environments

Copyright @ 2011 IEEETo solve dynamic optimization problems, multiple population methods are used to enhance the population diversity for an algorithm with the aim of maintaining multiple populations in different sub-areas in the fitness landscape. Many experimental studies have shown that locating and tracking multiple relatively good optima rather than a single global optimum is an effective idea in dynamic environments. However, several challenges need to be addressed when multi-population methods are applied, e.g., how to create multiple populations, how to maintain them in different sub-areas, and how to deal with the situation where changes can not be detected or predicted. To address these issues, this paper investigates a hierarchical clustering method to locate and track multiple optima for dynamic optimization problems. To deal with undetectable dynamic environments, this paper applies the random immigrants method without change detection based on a mechanism that can automatically reduce redundant individuals in the search space throughout the run. These methods are implemented into several research areas, including particle swarm optimization, genetic algorithm, and differential evolution. An experimental study is conducted based on the moving peaks benchmark to test the performance with several other algorithms from the literature. The experimental results show the efficiency of the clustering method for locating and tracking multiple optima in comparison with other algorithms based on multi-population methods on the moving peaks benchmark

Multi-population methods in unconstrained continuous dynamic environments: The challenges

Themulti-populationmethod has been widely used to solve unconstrained continuous dynamic optimization problems with the aim of maintaining multiple populations on different peaks to locate and track multiple changing peaks simultaneously. However, to make this approach efficient, several crucial challenging issues need to be addressed, e.g., how to determine the moment to react to changes, how to adapt the number of populations to changing environments, and how to determine the search area of each population. In addition, several other issues, e.g., communication between populations, overlapping search, the way to create multiple populations, detection of changes, and local search operators, should be also addressed. The lack of attention on these challenging issues within multi-population methods hinders the development of multi-population based algorithms in dynamic environments. In this paper, these challenging issues are comprehensively analyzed by a set of experimental studies from the algorithm design point of view. Experimental studies based on a set of popular algorithms show that the performance of algorithms is significantly affected by these challenging issues on the moving peaks benchmark. Keywords: Multi-population methods, dynamic optimization problems, evolutionary computatio

An adaptive multi-swarm optimizer for dynamic optimization problems

The multi-population method has been widely used to solve dynamic optimization problems (DOPs) with the aim of maintaining multiple populations on different peaks to locate and track multiple changing optima simultaneously. However, to make this approach effective for solving DOPs, two challenging issues need to be addressed. They are how to adapt the number of populations to changes and how to adaptively maintain the population diversity in a situation where changes are complicated or hard to detect or predict. Tracking the changing global optimum in dynamic environments is difficult because we cannot know when and where changes occur and what the characteristics of changes would be. Therefore, it is necessary to take the challenging issues into account to design such adaptive algorithms. To address the issues when multi-population methods are applied for solving DOPs, this paper proposes an adaptive multi-swarm algorithm, where the populations are enabled to be adaptive in dynamic environments without change detection. An experimental study is conducted based on the moving peaks problem to investigate the behavior of the proposed method. The performance of the proposed algorithm is also compared with a set of algorithms that are based on multi-population methods from different research areas in the literature of evolutionary computation

A survey of swarm intelligence for dynamic optimization: algorithms and applications

Swarm intelligence (SI) algorithms, including ant colony optimization, particle swarm optimization, bee-inspired algorithms, bacterial foraging optimization, firefly algorithms, fish swarm optimization and many more, have been proven to be good methods to address difficult optimization problems under stationary environments. Most SI algorithms have been developed to address stationary optimization problems and hence, they can converge on the (near-) optimum solution efficiently. However, many real-world problems have a dynamic environment that changes over time. For such dynamic optimization problems (DOPs), it is difficult for a conventional SI algorithm to track the changing optimum once the algorithm has converged on a solution. In the last two decades, there has been a growing interest of addressing DOPs using SI algorithms due to their adaptation capabilities. This paper presents a broad review on SI dynamic optimization (SIDO) focused on several classes of problems, such as discrete, continuous, constrained, multi-objective and classification problems, and real-world applications. In addition, this paper focuses on the enhancement strategies integrated in SI algorithms to address dynamic changes, the performance measurements and benchmark generators used in SIDO. Finally, some considerations about future directions in the subject are given