A Steady-State Algorithm for Solving Expensive Multiobjective Optimization Problems With Nonparallelizable Evaluations

Expensive multiobjective optimization problems (EMOPs) refer to those wherein evaluation of each candidate solution incurs a significant cost. To solve such problems within a limited number of solution evaluations, surrogate-assisted evolutionary algorithms (SAEAs) are often used. However, existing SAEAs typically operate in a generational framework wherein multiple solutions are identified for evaluation in each generation. There exist relatively few proposals in steady-state framework, wherein only a single solution is evaluated in each iteration. The development of such algorithms is crucial to efficiently solve EMOPs for which the evaluation of candidate designs cannot be parallelized. Furthermore, regardless of the framework used, the performance of current SAEAs tends to degrade when the Pareto front (PF) of the problem has irregularities, such as extremely concave/convex segments, even for 2/3-objective problems. To contextualize the motivation of this study, the performance of a few state-of-the-art SAEAs is first demonstrated on some such selected problems. Then, to address the above research gaps, we propose a surrogate-assisted steady-state EA (SASSEA), which incorporates a number of novel elements, including: 1) effective use of model uncertainty information to aid the search, including the use of the probabilistic dominance and Mahalanobis distance; 2) two-step infill identification using nondominance (ND) and distance-based selection; and 3) a shadow ND mechanism to avoid repeated selection and evaluation of dominated solutions. The efficacy of the proposed approach is demonstrated through extensive benchmarking on a range of test problems. It shows competitive performance relative to many state-of-the-art SAEAs, including both steady-state and generational approaches.