An improved multi-objective artificial physics optimization algorithm based on R2 indicator and its application

Artificial Physics Optimization (APO) algorithms in solving constrained multi-objective problems often encounter challenges such as uneven population distribution and imbalances between global and local search capabilities. To address these issues, we propose the Constrained Rank Multi-Objective Artificial Physical Optimization based on the R2 indicator (R2-ICRMOAPO) algorithm. This algorithm integrates non-dominated sorting with the R2 indicator and updates the external storage set using the contribution value derived from the R2 indicator formula, ensuring both set distribution and convergence. It also dynamically adjusts inertia weights and gravitational factors to enhance its global and local search capabilities. To evaluate the performance of the R2-ICRMOAPO algorithm, we compared it with four other multi-objective optimization algorithms using standard test functions. The results indicate that it demonstrates superior distribution and optimization performance. Furthermore, we applied it to optimize the parameters of a hydro-pneumatic suspension system. The experimental results show that it can reduce the root mean square value of car body vertical acceleration by approximately 21.4% and the root mean square value of dynamic tire load by about 19.6%. This reduction effectively enhances vehicle smoothness within a reasonable range. Consequently, these results confirm the feasibility of the R2-ICRMOAPO algorithm to solve practical problems.