A dynamic multi-objective evolutionary algorithm based on geometric prediction and vector–scalar transformation strategy

Abstract

Dynamic multi-objective evolutionary algorithms (DMOEAs) have attracted significant attention from scholars due to their strong robustness and wide range of applications across various fields. A current research focus is on how to quickly track the changing Pareto Set (PS) and Pareto Front (PF); however, the distribution of optimal individuals on the PF is often overlooked. To address this issue, we propose a dynamic multi-objective evolutionary algorithm based on geometric prediction and vector–scalar transformation strategy (GPVS). By combining memory and diversity strategies, we propose a zoom-in and zoom-out prediction strategy for population range estimation based on a geometric center point. The mirror adjustment strategy is introduced as a prediction adjustment mechanism to accelerate the algorithm’s convergence. The vector–scalar transformation strategy optimizes the distribution of the evolved population following geometric prediction, ensuring that individuals carry the maximum possible evolutionary information. This strategy provides valuable population information for the next evolution. We evaluated the performance of the proposed algorithm through experimental comparisons with classical algorithms on 22 test functions, demonstrating its effectiveness and robustness in solving dynamic multi-objective optimization problems (DMOPs).