Force-imitated particle swarm optimization using the near-neighbor effect for locating multiple optima

Copyright @ Elsevier Inc. All rights reserved.Multimodal optimization problems pose a great challenge of locating multiple optima simultaneously in the search space to the particle swarm optimization (PSO) community. In this paper, the motion principle of particles in PSO is extended by using the near-neighbor effect in mechanical theory, which is a universal phenomenon in nature and society. In the proposed near-neighbor effect based force-imitated PSO (NN-FPSO) algorithm, each particle explores the promising regions where it resides under the composite forces produced by the “near-neighbor attractor” and “near-neighbor repeller”, which are selected from the set of memorized personal best positions and the current swarm based on the principles of “superior-and-nearer” and “inferior-and-nearer”, respectively. These two forces pull and push a particle to search for the nearby optimum. Hence, particles can simultaneously locate multiple optima quickly and precisely. Experiments are carried out to investigate the performance of NN-FPSO in comparison with a number of state-of-the-art PSO algorithms for locating multiple optima over a series of multimodal benchmark test functions. The experimental results indicate that the proposed NN-FPSO algorithm can efficiently locate multiple optima in multimodal fitness landscapes.This work was supported in part by the Key Program of National Natural Science Foundation (NNSF) of China under Grant 70931001, Grant 70771021, and Grant 70721001, the National Natural Science Foundation (NNSF) of China for Youth under Grant 61004121, Grant 70771021, the Science Fund for Creative Research Group of NNSF of China under Grant 60821063, the PhD Programs Foundation of Ministry of Education of China under Grant 200801450008, and in part by the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/1 and Grant EP/E060722/2

Particle swarm optimization for multimodal functions: a clustering approach

The particle swarm optimization (PSO) algorithm is designed to find a single optimal solution and needs some modifications to be able to locate multiple optima on a multimodal function. In parallel with evolutionary computation algorithms, these modifications can be grouped in the framework of niching. In this work, we present a new approach to niching in PSO based on clustering particles to identify niches. The neighborhood structure, on which particles rely for communication, is exploited together with the niche information to locate multiple optima in parallel. Our approach was implemented in thek-means-based PSO (kPSO), which employs the standardk-means clustering algorithm, improved with a mechanism to adaptively identify the number of clusters.kPSO proved to be a competitive solution when compared with other existing algorithms, since it showed better performance on a benchmark set of multimodal functions

Adaptive multimodal continuous ant colony optimization

Seeking multiple optima simultaneously, which multimodal optimization aims at, has attracted increasing attention but remains challenging. Taking advantage of ant colony optimization algorithms in preserving high diversity, this paper intends to extend ant colony optimization algorithms to deal with multimodal optimization. First, combined with current niching methods, an adaptive multimodal continuous ant colony optimization algorithm is introduced. In this algorithm, an adaptive parameter adjustment is developed, which takes the difference among niches into consideration. Second, to accelerate convergence, a differential evolution mutation operator is alternatively utilized to build base vectors for ants to construct new solutions. Then, to enhance the exploitation, a local search scheme based on Gaussian distribution is self-adaptively performed around the seeds of niches. Together, the proposed algorithm affords a good balance between exploration and exploitation. Extensive experiments on 20 widely used benchmark multimodal functions are conducted to investigate the influence of each algorithmic component and results are compared with several state-of-the-art multimodal algorithms and winners of competitions on multimodal optimization. These comparisons demonstrate the competitive efficiency and effectiveness of the proposed algorithm, especially in dealing with complex problems with high numbers of local optima

Multimodal estimation of distribution algorithms

Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima

A self-learning particle swarm optimizer for global optimization problems

Copyright @ 2011 IEEE. All Rights Reserved. This article was made available through the Brunel Open Access Publishing Fund.Particle swarm optimization (PSO) has been shown as an effective tool for solving global optimization problems. So far, most PSO algorithms use a single learning pattern for all particles, which means that all particles in a swarm use the same strategy. This monotonic learning pattern may cause the lack of intelligence for a particular particle, which makes it unable to deal with different complex situations. This paper presents a novel algorithm, called self-learning particle swarm optimizer (SLPSO), for global optimization problems. In SLPSO, each particle has a set of four strategies to cope with different situations in the search space. The cooperation of the four strategies is implemented by an adaptive learning framework at the individual level, which can enable a particle to choose the optimal strategy according to its own local fitness landscape. The experimental study on a set of 45 test functions and two real-world problems show that SLPSO has a superior performance in comparison with several other peer algorithms.This work was supported by the Engineering and Physical Sciences Research Council of U.K. under Grants EP/E060722/1 and EP/E060722/2

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

Seeking multiple solutions:an updated survey on niching methods and their applications

Multi-Modal Optimization (MMO) aiming to locate multiple optimal (or near-optimal) solutions in a single simulation run has practical relevance to problem solving across many fields. Population-based meta-heuristics have been shown particularly effective in solving MMO problems, if equipped with specificallydesigned diversity-preserving mechanisms, commonly known as niching methods. This paper provides an updated survey on niching methods. The paper first revisits the fundamental concepts about niching and its most representative schemes, then reviews the most recent development of niching methods, including novel and hybrid methods, performance measures, and benchmarks for their assessment. Furthermore, the paper surveys previous attempts at leveraging the capabilities of niching to facilitate various optimization tasks (e.g., multi-objective and dynamic optimization) and machine learning tasks (e.g., clustering, feature selection, and learning ensembles). A list of successful applications of niching methods to real-world problems is presented to demonstrate the capabilities of niching methods in providing solutions that are difficult for other optimization methods to offer. The significant practical value of niching methods is clearly exemplified through these applications. Finally, the paper poses challenges and research questions on niching that are yet to be appropriately addressed. Providing answers to these questions is crucial before we can bring more fruitful benefits of niching to real-world problem solving

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