A Dynamic Dimensionality Expansion-Based Evolutionary Algorithm for Constrained Many-Objective Optimization

When searching for the Pareto fronts of constrained many-objective optimization problems (CMaOPs), two main challenges arise. One is the constraint obstacles posed by infeasible regions, and the other is the curse of dimensionality arising from the high-dimensional objective space. Substantial efforts have been dedicated to overcoming the constraint obstacles, yielding significant success. However, few studies have focused on the curse of dimensionality in CMaOPs, leading to a lack of effective mechanisms in this area. To address this issue, this paper proposes a dynamic dimensionality expansion mechanism. Therein, the CMaOP is transformed into a dynamic problem with few to many objectives. It enables the rapid discovery of high-quality feasible solutions with good convergence and then prunes large regions of the objective space that do not contain feasible optimal solutions. Incorporating the dynamic dimensionality expansion mechanism with a multi-directional search-based update mechanism, which combines various constraint handling techniques, and an independent-integrated regeneration strategy, which is for generating high-quality offspring, this paper suggests a dynamic dimensionality expansion-based evolutionary algorithm for solving CMaOPs. Numerical experiments on several benchmark test series show that the proposed algorithm outperforms CMOCSO, CCMO, DSPCMDE, ICMA, and MTCMO in handling different CMaOPs. Moreover, further investigation also shows that the proposed dynamic dimensionality expansion mechanism significantly improves the performance of the existing algorithms.