Handling Irregular Many-Objective Optimization Problems via Performing Local Searches on External Archives

Adaptive weight-vector adjustment has been explored to compensate for the weakness of the evolutionary many-objective algorithms based on decomposition in solving problems with irregular Pareto-optimal fronts. One essential issue is that the distribution of previously visited solutions likely mismatches the irregular Pareto-optimal front, and the weight vectors are misled towards inappropriate regions. The fact above motivated us to design a novel many-objective evolutionary algorithm by performing local searches on an external archive, namely, LSEA. Specifically, the LSEA contains a new selection mechanism without weight vectors to alleviate the adverse effects of inappropriate weight vectors, progressively improving both the convergence and diversity of the archive. The solutions in the archive also feed back the weight-vector adjustment. Moreover, the LSEA selects a solution with good diversity but relatively poor convergence from the archive and then perturbs the decision variables of the selected solution one by one to search for solutions with better diversity and convergence. At last, the LSEA is compared with five baseline algorithms in the context of 36 widely-used benchmarks with irregular Pareto-optimal fronts. The comparison results demonstrate the competitive performance of the LSEA, as it outperforms the five baselines on 22 benchmarks with respect to metric hypervolume.