Find robust solutions over time by two-layer multi-objective optimization method

Robust optimization over time is a practical dynamic optimization method, which provides two detailed computable metrics to get the possible robust solutions for dynamic scalar optimization problems. However, the robust solutions fit for more time-varying moments or approximate the optimum more because only one metric is considered as the optimization objective. To find the true robust solution set satisfying maximum both survival time and average fitness simultaneously during all dynamic environments, a novel two-layer multi-objective optimization method is proposed. In the first layer, considering both metrics, the acceptable optimal solutions for each changing environment is found. Subsequently, they are composed of the practical robust solution set in the second layer. Taking the average fitness and the length of the robust solution set as two objectives, the optimal combinations for the whole time-varying environments are explored. The experimental results for the modified moving peaks benchmark shows that the robust solution sets considering both metrics are superior to the robust solutions gotten by ROOT. As the key parameters, the fitness threshold has the more obvious impact on the performances of MROOT than the time window, whereas ROOT is more sensitive to both of them.