Enhanced Multi-Strategy Particle Swarm Optimization for Constrained Problems with an Evolutionary-Strategies-Based Unfeasible Local Search Operator

Abstract

Nowadays, optimization problems are solved through meta-heuristic algorithms based on stochastic search approaches borrowed from mimicking natural phenomena. Notwithstanding their successful capability to handle complex problems, the No-Free Lunch Theorem by Wolpert and Macready (1997) states that there is no ideal algorithm to deal with any kind of problem. This issue arises because of the nature of these algorithms that are not properly mathematics-based, and the convergence is not ensured. In the present study, a variant of the well-known swarm-based algorithm, the Particle Swarm Optimization (PSO), is developed to solve constrained problems with a different approach to the classical penalty function technique. State-of-art improvements and suggestions are also adopted in the current implementation (inertia weight, neighbourhood). Furthermore, a new local search operator has been implemented to help localize the feasible region in challenging optimization problems. This operator is based on hybridization with another milestone meta-heuristic algorithm, the Evolutionary Strategy (ES). The self-adaptive variant has been adopted because of its advantage of not requiring any other arbitrary parameter to be tuned. This approach automatically determines the parameters’ values that govern the Evolutionary Strategy simultaneously during the optimization process. This enhanced multi-strategy PSO is eventually tested on some benchmark constrained numerical problems from the literature. The obtained results are compared in terms of the optimal solutions with two other PSO implementations, which rely on a classic penalty function approach as a constraint-handling method.

Constraint handling techniques for metaheuristics: a state-of-the-art review and new variants

“…While recently, Rosso et al (2022) a variant of the well-known swarm-based algorithm, the Particle Swarm Optimization (PSO), is developed to solve constrained problems with a different approach to the classical penalty function technique. Stateof-art improvements and suggestions are also adopted in the current implementation (inertia weight, neighbourhood).…”

A two-stage adaptive penalty method based on co-evolution for constrained evolutionary optimization

“…In general, there are four cases in CHTs, namely those based on penalty function [6,14], separation of constraints and objective function [15][16][17], multiobjective optimization [18][19][20], and hybrid methods [21,22], respectively. Additionaly, some researchers have designed non-penalty-based CHTs by using supervised learning technology [23] or special operators [24]. In [23], the non-penalty-based CHT for the particle swarm optimization (PSO) was implemented by adopting the support vector machine (SVM).…”

“…After a training phase on the current positions of the swarm, the new trial positions were labeled as feasible or unfeasible positions using the trained predictive model. In [24], a variant of the PSO was developed for COPs. And a new local search operator was implemented to help localize the feasible region in challenging optimization problems.…”

A Modified Reptile Search Algorithm for Numerical Optimization Problems

“…Genetic algorithms provide solutions through the concept of crossover and mutation of species in nature. In addition, other evolutionary-based algorithms have been proposed, including DE [ 26 ], evolutionary programming [ 27 ], and evolutionary strategies [ 28 ]. The second category is physics-based algorithms, which originate from natural physics laws.…”