A Supervised Learning and Control Method to Improve Particle Swarm Optimization Algorithms

This paper presents an adaptive particle swarm optimization with supervised learning and control (APSO-SLC) for the parameter settings and diversity maintenance of particle swarm optimization (PSO) to adaptively choose parameters, while improving its exploration competence. Although PSO is a powerful optimization method, it faces such issues as difficult parameter setting and premature convergence. Inspired by supervised learning and predictive control strategies from machine learning and control fields, we propose APSO-SLC that employs several strategies to address these issues. First, we treat PSO with its optimization problem as a system to be controlled and model it as a dynamic quadratic programming model with box constraints. Its parameters are estimated by the recursive least squares with a dynamic forgetting factor to enhance better parameter setting and weaken worse ones. Its optimal parameters are calculated by this model to feed back to PSO. Second, a progress vector is proposed to monitor the progress rate for judging whether premature convergence happens. By studying the reason of premature convergence, this work proposes the strategies of back diffusion and new attractor learning to extend swam diversity, and speed up the convergence. Experiments are performed on many benchmark functions to compare APSO-SLC with the state-of-the-art PSOs. The results show that it is simple to program and understand, and can provide excellent and consistent performance.