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

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

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

Static and Dynamic Multimodal Optimization by Improved Covariance Matrix Self-Adaptation Evolution Strategy with Repelling Subpopulations

The covariance matrix self-adaptation evolution strategy with repelling subpopulations (RS-CMSA-ES) is one of the most successful multimodal optimization (MMO) methods currently available. However, some of its components may become inefficient in certain situations. This study introduces the second variant of this method, called RS-CMSA-ESII. It improves the adaptation schemes for the normalized taboo distances of the archived solutions and the covariance matrix of the subpopulation, the termination criteria for the subpopulations, and the way in which the infeasible solutions are treated. It also improves the time complexity of RS-CMSA-ES by updating the initialization procedure of a subpopulation and developing a more accurate metric for determining critical taboo regions. The effects of these modifications are illustrated by designing controlled numerical simulations. RS-CMSA-ESII is then compared with the most successful and recent niching methods for MMO on a widely adopted test suite. The results obtained reveal the superiority of RS-CMSA-ESII over these methods, including the winners of the competition on niching methods for MMO in previous years. Besides, this study extends RS-CMSA-ESII to dynamic MMO and compares it with a few recently proposed methods on the modified moving peak benchmark functions

Region-based memetic algorithm with archive for multimodal optimisation.

In this paper we propose a specially designed memetic algorithm for multimodal optimisation problems. The proposal uses a niching strategy, called region-based niching strategy, that divides the search space in predefined and indexable hypercubes with decreasing size, called regions. This niching technique allows our proposal to keep high diversity in the population, and to keep the most promising regions in an external archive. The most promising solutions are improved with a local search method and also stored in the archive. The archive is used as an index to effiently prevent further exploration of these areas with the evolutionary algorithm. The resulting algorithm, called Region-based Memetic Algorithm with Archive, is tested on the benchmark proposed in the special session and competition on niching methods for multimodal function optimisation of the Congress on Evolutionary Computation in 2013. The results obtained show that the region-based niching strategy is more efficient than the classical niching strategy called clearing and that the use of the archive as restrictive index significantly improves the exploration efficiency of the algorithm. The proposal achieves better exploration and accuracy than other existing techniques

Bio-inspired computation: where we stand and what's next

In recent years, the research community has witnessed an explosion of literature dealing with the adaptation of behavioral patterns and social phenomena observed in nature towards efficiently solving complex computational tasks. This trend has been especially dramatic in what relates to optimization problems, mainly due to the unprecedented complexity of problem instances, arising from a diverse spectrum of domains such as transportation, logistics, energy, climate, social networks, health and industry 4.0, among many others. Notwithstanding this upsurge of activity, research in this vibrant topic should be steered towards certain areas that, despite their eventual value and impact on the field of bio-inspired computation, still remain insufficiently explored to date. The main purpose of this paper is to outline the state of the art and to identify open challenges concerning the most relevant areas within bio-inspired optimization. An analysis and discussion are also carried out over the general trajectory followed in recent years by the community working in this field, thereby highlighting the need for reaching a consensus and joining forces towards achieving valuable insights into the understanding of this family of optimization techniques

A multi-angle hierarchical differential evolution approach for multimodal optimization problems

Multimodal optimization problem (MMOP) is one of the most common problems in engineering practices that requires multiple optimal solutions to be located simultaneously. An efficient algorithm for solving MMOPs should balance the diversity and convergence of the population, so that the global optimal solutions can be located as many as possible. However, most of existing algorithms are easy to be trapped into local peaks and cannot provide high-quality solutions. To better deal with MMOPs, considerations on the solution quality angle and the evolution stage angle are both taken into account in this paper and a multi-angle hierarchical differential evolution (MaHDE) algorithm is proposed. Firstly, a fitness hierarchical mutation (FHM) strategy is designed to balance the exploration and exploitation ability of different individuals. In the FHM strategy, the individuals are divided into two levels (i.e., low/high-level) according to their solution quality in the current niche. Then, the low/high-level individuals are applied to different guiding strategies. Secondly, a directed global search (DGS) strategy is introduced for the low-level individuals in the late evolution stage, which can improve the population diversity and provide these low-level individuals with the opportunity to re-search the global peaks. Thirdly, an elite local search (ELS) strategy is designed for the high-level individuals in the late evolution stage to refine their solution accuracy. Extensive experiments are developed to verify the performance of MaHDE on the widely used MMOPs test functions i.e., CEC’2013. Experimental results show that MaHDE generally outperforms the compared state-of-the-art multimodal algorithms

Bio-inspired computation: where we stand and what's next

In recent years, the research community has witnessed an explosion of literature dealing with the adaptation of behavioral patterns and social phenomena observed in nature towards efficiently solving complex computational tasks. This trend has been especially dramatic in what relates to optimization problems, mainly due to the unprecedented complexity of problem instances, arising from a diverse spectrum of domains such as transportation, logistics, energy, climate, social networks, health and industry 4.0, among many others. Notwithstanding this upsurge of activity, research in this vibrant topic should be steered towards certain areas that, despite their eventual value and impact on the field of bio-inspired computation, still remain insufficiently explored to date. The main purpose of this paper is to outline the state of the art and to identify open challenges concerning the most relevant areas within bio-inspired optimization. An analysis and discussion are also carried out over the general trajectory followed in recent years by the community working in this field, thereby highlighting the need for reaching a consensus and joining forces towards achieving valuable insights into the understanding of this family of optimization techniques

A close neighbor mobility method using particle swarm optimizer for solving multimodal optimization problems

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Niching is an important technique for multimodal optimization. Most existing niching methods require specification of certain niching parameters in order to perform well. But these parameters are usually difficult to set because they depend on the problem. The particle swarm optimization algorithm using the ring neighborhood topology does not require any niche parameters, but the determination of the particle neighborhood in this method is based on the subscript of the particle, and the result fails to achieve the best performance. For better performance, in this paper, a particle swarm optimization algorithm based on the ring neighborhood topology of Euclidean distance between particles is proposed, which is called the close neighbor mobility optimization algorithm. The algorithm mainly includes the following three strategies: elite selection mechanism, close neighbor mobility strategy and modified DE strategy. It mainly uses the Euclidean distance between particles. Each particle forms its own unique niche, evolves in a local scope, and finally locates multiple global optimal solutions with high precision. The algorithm greatly improves the accuracy of the particle. The experimental results show that the close neighbor mobility optimization algorithm has better performance than most single-objective multi-modal algorithms