A Kriging-Assisted Evolutionary Algorithm With Dual Perspectives and Dual Indicators for Expensive Robust Multiobjective Optimization

Balancing optimality and robustness is the key to solving expensive robust multiobjective optimization problems (ExRMOPs) by evolutionary algorithms. However, existing studies usually design algorithms based on either the average perspective or the worst perspective, overlooking the complementarity of these two perspectives-the former prefers optimality, whereas the latter prefers robustness. Therefore, this article proposes a Kriging-assisted evolutionary algorithm with dual perspectives and dual indicators (called KPI) to solve ExRMOPs. In KPI, we develop a dual-perspective aggregation function (DPAF) as the replaced objective to guide the evolutionary search. Specifically, in terms of each original objective, DPAF of each solution is defined as the weighted sum of the performance evaluated from the average perspective and the worst perspective. The weight used in DPAF is related to the stability level of the current population, enabling DPAF to adaptively balance optimality and robustness. In addition, we design a dual-indicator candidate selection strategy to identify high-quality candidates from the final population of the evolutionary search for expensive function evaluations. In this strategy, we first eliminate solutions with poor robust optimality by the proposed robust optimality indicator. Subsequently, based on the robust optimality indicator and a common diversity indicator, several solutions with good robust optimality and diversity are selected as candidates from the remaining solutions. Extensive experiments on two test suites and a real-world application verify the superiority of KPI.