A Dual Indicator Ranking Method for Complexly Constrained Multi-Objective Optimization

Addressing multi-objective optimization problems (MOPs) with complex constraints presents a significant challenge due to their diverse nature. While existing algorithms can effectively handle specific types of complex constraints, they often struggle with a variety of such constraints. To address this issue, we propose an innovative evolutionary algorithm for constrained multi-objective optimization. A key feature is the integration of a novel differential operator that generates offspring based on the presence of feasible solutions within the main population. This strategy is particularly effective for handling complex constraints characterised by small feasible spaces and deceptive infeasible regions. Additionally, the algorithm employs a dual-indicator ranking mechanism to evaluate and select individuals from the auxiliary population based on the quality and quantity of feasible solutions generated by the main population. Promising individuals are then migrated back to the main population, thereby enhancing the exploration of the solution space. This approach demonstrates significant superiority in solving MOPs with discontinuous feasible regions or extensive infeasible areas. Empirical comparisons across a range of benchmark problems show that the proposed algorithm outperforms current state-of-the-art methods in evolutionary constrained multi-objective optimization, underscoring its potential as a robust tool for handling MOPs with complex constraints.