Analysis of statistical model-based optimization enhancements in Generalized Self-Adapting Particle Swarm Optimization framework

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Abstract This paper presents characteristics of model-based optimization methods utilized within the Generalized Self-Adapting Particle Swarm Optimization (GA– PSO) – a hybrid global optimization framework proposed by the authors. GAPSO has been designed as a generalization of a Particle Swarm Optimization (PSO) algorithm on the foundations of a large degree of independence of individual particles. GAPSO serves as a platform for studying optimization algorithms in the context of the following research hypothesis: (1) it is possible to improve the performance of an optimization algorithm through utilization of more function samples than standard PSO sample-based memory, (2) combining specialized sampling methods (i.e. PSO, Differential Evolution, model-based optimization) will result in a better algorithm performance than using each of them separately. The inclusion of model-based enhancements resulted in the necessity of extending the GAPSO framework by means of an external samples memory - this enhanced model is referred to as M-GAPSO in the paper. We investigate the features of two model-based optimizers: one utilizing a quadratic function and the other one utilizing a polynomial function. We analyze the conditions under which those model-based approaches provide an effective sampling strategy. Proposed model-based optimizers are evaluated on the functions from the COCO BBOB benchmark set.