Adaptive knowledge transfer-based particle swarm optimization for constrained multitask optimization

Constrained multitask optimization (CMTO) problems are frequently encountered in practical applications. However, since the feasible regions of different tasks are difficult to match under constraints, it is hard to obtain and transfer effective knowledge among different tasks, resulting in poor convergence performance. To address this issue, a constrained multitask particle swarm optimization algorithm with knowledge transfer-based adaptive penalty function (CMTPSO-APF) is proposed to improve the convergence performance. The main contributions of CMTPSO-APF are three-fold. First, a dynamic particle topology is designed to improve the neighborhood similarity for different tasks with constrained conditions. Then, the particles with similar spatial structures can facilitate the knowledge transfer between different tasks. Second, a covariance matrix learning mechanism is proposed to obtain valid knowledge with constrained conditions. Then, the proposed method can promote the population to move in the direction of the optimal solution. Third, a knowledge transfer-based adaptive penalty function for constrained multitask optimization is designed to achieve the dynamical change of penalty factor according to the evolution state. Then, the adaptive penalty function can promote the transfer of effective knowledge and improve the convergence. Finally, some simulation experiments are carried out on the CMTO benchmark test suites and the practical application of the wastewater treatment process. The results indicate that CMTPSO-APF can improve the convergence performance.