Multitask Particle Swarm Optimization With Dynamic Transformation

Multitask optimization (MTO) mainly utilizes knowledge transfer among tasks to address multiple optimization problems in parallel. However, the decision space dimensions of different tasks often differ, which leads to the failure of knowledge transfer. Therefore, it is a challenging problem to transfer knowledge among tasks with different dimensions to achieve parallel optimization of multiple tasks. To address this problem, multitask particle swarm optimization with a dynamic transformation strategy (MTPSO-DTS) is proposed to improve the performance of MTO. First, an intertask similarity index based on gradient information and location information is designed to dynamically assess the degree of similarity among different tasks. Then, the intertask similarity is determined to assist the transformation of dimensions. Second, a dynamic transformation strategy based on intertask similarity is developed to achieve a uniform representation of different dimension knowledge, including dimension supplementation and dimension reduction. Then, the MTPSO-DTS algorithm, which takes advantage of the search characteristics of particle swarm optimization, can facilitate knowledge transfer among tasks with different dimensions. Third, the convergence of the MTPSO-DTS algorithm is analyzed to verify the validity theoretically. Finally, numerical comparison experiments on benchmark problems and a practical application are carried out to demonstrate the effectiveness of the MTPSO-DTS algorithm. The results indicate that the proposed MTPSO-DTS algorithm can facilitate knowledge transfer among tasks of different dimensions to promote parallel optimization of multiple tasks.