Knowledge-guided global optimization for expensive and black-box constrained multi-objective engineering design problems

Constrained multi-objective optimization problems (CMOPs) involving expensive and black-box objectives and constraints pose significant challenges in engineering design problems (EDPs). This paper introduces a novel knowledge-guided evolutionary multitasking (EMT)-based global optimization algorithm (SA-EMCMO) specifically designed to address such computationally expensive and black-box CMOPs. SA-EMCMO approach models the optimization of an expensive CMOP as two interrelated tasks: the main task, which focuses on solving the original expensive CMOP, and the auxiliary task, which aims to optimize the objectives while neglecting the constraints. A surrogate-assisted constrained multi-objective evolutionary algorithm (SA-CMOEA) is designed to address the main task, while the auxiliary task continuously provides valuable knowledge to guide the main task's optimization. Notably, the genetic information carried by both parent and offspring individuals is dynamically regarded as useful knowledge due to the complementary nature of the two tasks. This knowledge is transferred between the tasks to enhance their overall performance. Additionally, a dynamic sampling strategy is proposed to efficiently select final solutions from the main or auxiliary tasks for real function evaluations within a limited number of function evaluations. The effectiveness of SA-EMCMO algorithm is demonstrated through comprehensive comparison with state-of-the-art methods on 132 benchmark mathematical problems and its application to six EDPs, confirming its superior performance in solving complex EDPs.