A comparative study of standard PSO and adaptive fuzzy PSO for optimization

Abstract

In engineering, complex optimization problems often require efficient and reliable solution methods. An example of a metaheuristic algorithm is particle swarm optimization (PSO), which is widely used for its simplicity and adaptability. However, PSO performance is highly sensitive to parameter settings. To tackle this issue, researchers have developed adaptive variants, such as adaptive fuzzy particle swarm optimization (AF-PSO), that adjust parameters in real time during operation. In this study, standard PSO and AF-PSO are compared using several benchmark functions, Sphere, Rosenbrock, Rastrigin, Ackley, Griewank, and Schwefel, along with the multi-objective test problems ZDT1–3 and DTLZ1–2. Standard PSO was run with fixed parameters values (w=0.729, c₁=c₂=1.494) for the computation. The AF-PSO variant of PSO parameters are adaptively tune with a fuzzy inference concept. Each algorithm is evaluated across multiple independent runs to evaluate performance consistency. Across the test set, AF-PSO achieved superior performance in terms of solution quality and convergence. Among the benchmark functions, Griewank (+74.1%), Ackley (+65.4%), and Sphere (+63.0%) each have performances more than the others. Generally, the findings suggest that adapting parameters during the search improves convergence and solution quality, particularly for complex multimodal optimization problems.