Solution Stability Judgment Mechanism Based on a Dynamic Grid System for Multi-Objective Optimization Algorithms

In decomposition-based evolutionary multi-objective optimization algorithms (MOEA/Ds) with adaptive strategies for weight vectors, the vectors are updated periodically. Their updates' timing and frequency significantly influence optimization outcomes. Better results are promising to be obtained when weight vectors are updated at the time that the population reaches stability. Therefore, this work proposes a solution stability judgment mechanism based on a dynamic grid system to analyze whether the solutions in objective space have reached a state of stable convergence. To verify the effectiveness of our proposed mechanism, we add it to three MOEA/Ds with adaptive weight vector strategies and conduct experiments on 11 benchmarks compared with these algorithms' original forms. The results demonstrate that the proposed mechanism can significantly enhance the optimization performance of these algorithms. It can find better weight update times, which helps to result in better solutions in limited iterations with a faster speed.