This paper presents a variant of particle swarm optimizers (PSOs) that we call the comprehensive learning particle swarm optimizer (CLPSO), which uses a novel learning strategy whereby all other particles' historical best information is used to update a particle's velocity. This strategy enables the diversity of the swarm to be preserved to discourage premature convergence. Experiments were conducted (using codes available from http://www.ntu.edu.sg/home/epnsugan) on multimodal test functions such as Rosenbrock, Griewank, Rastrigin, Ackley, and Schwefel and composition functions both with and without coordinate rotation. The results demonstrate good performance of the CLPSO in solving multimodal problems when compared with eight other recent variants of the PSO.

Comprehensive learning particle swarm optimizer for global optimization of multimodal functions

This paper introduces a novel parameter automation strategy for the particle swarm algorithm and two further extensions to improve its performance after a predefined number of generations. Initially, to efficiently control the local search and convergence to the global optimum solution, time-varying acceleration coefficients (TVAC) are introduced in addition to the time-varying inertia weight factor in particle swarm optimization (PSO). From the basis of TVAC, two new strategies are discussed to improve the performance of the PSO. First, the concept of "mutation" is introduced to the particle swarm optimization along with TVAC (MPSO-TVAC), by adding a small perturbation to a randomly selected modulus of the velocity vector of a random particle by predefined probability. Second, we introduce a novel particle swarm concept "self-organizing hierarchical particle swarm optimizer with TVAC (HPSO-TVAC)". Under this method, only the "social" part and the "cognitive" part of the particle swarm strategy are considered to estimate the new velocity of each particle and particles are reinitialized whenever they are stagnated in the search space. In addition, to overcome the difficulties of selecting an appropriate mutation step size for different problems, a time-varying mutation step size was introduced. Further, for most of the benchmarks, mutation probability is found to be insensitive to the performance of MPSO-TVAC method. On the other hand, the effect of reinitialization velocity on the performance of HPSO-TVAC method is also observed. Time-varying reinitialization step size is found to be an efficient parameter optimization strategy for HPSO-TVAC method. The HPSO-TVAC strategy outperformed all the methods considered in this investigation for most of the functions. Furthermore, it has also been observed that both the MPSO and HPSO strategies perform poorly when the acceleration coefficients are fixed at two.

Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients

A unified view of metaheuristics This book provides a complete background on metaheuristics and shows readers how to design and implement efficient algorithms to solve complex optimization problems across a diverse range of applications, from networking and bioinformatics to engineering design, routing, and scheduling. It presents the main design questions for all families of metaheuristics and clearly illustrates how to implement the algorithms under a software framework to reuse both the design and code. Throughout the book, the key search components of metaheuristics are considered as a toolbox for: Designing efficient metaheuristics (e.g. local search, tabu search, simulated annealing, evolutionary algorithms, particle swarm optimization, scatter search, ant colonies, bee colonies, artificial immune systems) for optimization problems Designing efficient metaheuristics for multi-objective optimization problems Designing hybrid, parallel, and distributed metaheuristics Implementing metaheuristics on sequential and parallel machines Using many case studies and treating design and implementation independently, this book gives readers the skills necessary to solve large-scale optimization problems quickly and efficiently. It is a valuable reference for practicing engineers and researchers from diverse areas dealing with optimization or machine learning; and graduate students in computer science, operations research, control, engineering, business and management, and applied mathematics.

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Metaheuristics: From Design to Implementation

The particle swarm optimization algorithm: convergence analysis and parameter selection

The particle swarm optimization (PSO), new to the electromagnetics community, is a robust stochastic evolutionary computation technique based on the movement and intelligence of swarms. This paper introduces a conceptual overview and detailed explanation of the PSO algorithm, as well as how it can be used for electromagnetic optimizations. This paper also presents several results illustrating the swarm behavior in a PSO algorithm developed by the authors at UCLA specifically for engineering optimizations (UCLA-PSO). Also discussed is recent progress in the development of the PSO and the special considerations needed for engineering implementation including suggestions for the selection of parameter values. Additionally, a study of boundary conditions is presented indicating the invisible wall technique outperforms absorbing and reflecting wall techniques. These concepts are then integrated into a representative example of optimization of a profiled corrugated horn antenna.

Particle swarm optimization in electromagnetics

The particle swarm is an algorithm for finding optimal regions of complex search spaces through the interaction of individuals in a population of particles. This paper analyzes a particle's trajectory as it moves in discrete time (the algebraic view), then progresses to the view of it in continuous time (the analytical view). A five-dimensional depiction is developed, which describes the system completely. These analyses lead to a generalized model of the algorithm, containing a set of coefficients to control the system's convergence tendencies. Some results of the particle swarm optimizer, implementing modifications derived from the analysis, suggest methods for altering the original algorithm in ways that eliminate problems and increase the ability of the particle swarm to find optima of some well-studied test functions.

The particle swarm - explosion, stability, and convergence in a multidimensional complex space

Many metaheuristic approaches are inherently stochastic. In order to compare such methods, statistical tests are needed. However, choosing an appropriate test is not trivial, given that each test has some assumptions about the distribution of the underlying data that must be true before it can be used. Permutation tests (P-Tests) are statistical tests with minimal number of assumptions. These tests are simple, intuitive and nonparametric. In this paper, we argue researchers in the field of metaheuristics to adopt P-Tests to compare their algorithms. We define two statistic tests and then present an algorithm that uses them to compute the p-value. The proposed process is used to compare 5 metaheuristic algorithms on 10 benchmark functions. The resulting p-values are compared with the p-values of two widely used statistical tests. The results show that the proposed P-test is generally consistent with the classical tests, but more conservative in few cases.

https://www.mdpi.com/2227-7390/10/13/2219/pdf?version=1656582896

M. Clerc

Papers

The particle swarm - explosion, stability, and convergence in a multidimensional complex space

Permutation Tests for Metaheuristic Algorithms

Laplace’s rule of succession: a simple and efficient way to compare metaheuristics