Novel Particle Swarm Optimization Algorithm for Multimodal Optimization Problems by Enhancing the Robustness and Diversity

Abstract

Particle Swarm Optimization (PSO) is a Swarm Intelligence (SI) based algorithm developed by Kennedy and Eberhart in 1995. PSO was initially designed for locating single peak and became popular for solving global optimization problems as well. In spite of its simplicity, PSO has several limitations, which prevent it from achieving efficient solution. However, the two main limitations are its slow convergence rate and the local trapping dilemma. In order to tackle this situation, researchers have tried to avoid the premature convergence by performing some extra computations and have improved the convergence speed by introducing new parameters in PSO. Furthermore, in many cases, instead of the single best solution, we need to know about all possible solutions as well. In this regard, different multimodal techniques have been proposed to handle multimodal optimization problem, including crowding, deterministic crowding, fitness sharing, derating, restrict tournament selection, clearing, clustering, and speciation. However, among these solutions some techniques find only all global optima, whereas in many cases all possible optima are required. But, locating all global optimum solution for the PSO and other evolutionary algorithms has its own issues. Furthermore, these issues become more challenging when we are intended to locate all possible solutions of multimodal optimization problems. In literature, various evolutionary multimodal optimization techniques have been proposed. The objectives of these algorithms are to tackle some general issues like how to locate multiple global as well as local optimal solutions?; How to retain the located optima until the end of the search?; How to locate multiple optima parallel with less number of function evaluations?; and how to avoid premature convergence by maintaining or increasing population diversity?. Among the number of existing multimodal optimization algorithms, species-based PSO (SPSO) algorithms are very common to locate multiple optima parallel. Due to its intrinsic nature of multiple species, it implicitly resolves many issues that have been occurring in single population as well as sequential evolutionary multimodal optimization algorithms. The species-based PSO is one of the SI-based multimodal optimization algorithms that can locate multiple peaks in parallel. Species-based PSO algorithms still have two main issues, which are the random initialization issue and the exploitation capability. In presence of random initialization, some promising area may remain unexplored and species are not formed around that area which ultimately misses some optima in the solution space. To the best of our knowledge, random initialization issue in species-based PSO has not been well addressed. Another issue with speciation, best of our knowledge that has not been addressed is its exploitation capability. As the species are formed in each iteration step around the seed particle and each particle learn locally. Therefore, the particles cooperate and interact with a few particles in a specific area and cannot move across the species boundaries. This dissertation is an effort to solve the above mentioned problems. In order to enhance the performance of PSO, for locating the global optima in complex multimodal problems, we have proposed an accelerated convergent PSO (ACPSO) by introducing a new velocity update equation. Further, we proposed a robust species-based PSO, called exploration strategy inspired species-based PSO VIII (ESPSO), to enhance the exploitation capability of SPSO by introducing an explorer swarm that resolve the random initialization as well as exploitation issues of SPSO. The extensive experimentation has proved the effectiveness of both solutions as compared to the existing state-of-the-art when compared with the standard benchmark test problems.