A detailed study about CDW-PSO, BWO and GM-CPSO methods on continuous function optimization

Abstract

Gauss map based chaotic particle swarm optimization (GM-CPSO) is a state-of-the-art method involving the necessary chaotic map for PSO and has proved itself in global optimization, hybrid classifier design, etc. GM-CPSO can outperform recent techniques such as chaotic dynamic weight PSO (CDW-PSO), outclassing 20 optimization methods. However, the behavior of GM-CPSO on continuous characterized functions is unknown. As the main aim, this paper comprehensively determines the performance of GM-CPSO specifically on continuous function optimization.

Black widow optimization (BWO) includes a non-stable population size that cannot be fixed. In BWO, the population can increase without any intervention during iterations, which prevents an objective comparison of the method with other methods. Thus, as the second aim, a new viewpoint on BWO population size selection is suggested for an objective comparison of the method.

In various disciplines, stochastic optimization is inevitable to efficiently perform function optimization. Here, the necessary question concerns with which method the best convergence and performance can be achieved. As the third aim, we evaluate three state-of-the-art optimization methods to answer this question.

To realize all of these aims, GM-CPSO is compared with CDW-PSO and BWO methods by using 10 continuous benchmark functions to perform a detailed comparison and reveal which one can achieve reliable scores on low-, middle-, and high-dimensional problems. Fitness-based comparisons, computation time analysis, and convergence-based evaluations are presented to determine the robustness of algorithms. As a result, GM-CPSO arises as the most remarkable method, especially for the middle-and high-dimensional continuous functions.

Subject Classification:

• Primary 65K10
• 65D15
• 46N10

Keywords:

• Benchmark evaluation
• Black widow
• Chaotic behavior
• Gauss map
• Hybrid algorithm
• Optimization