Reference Vector Assisted Candidate Search with Aggregated Surrogate for Computationally Expensive Many Objective Optimization Problems

Pareto-optimal sets of multiobjective optimization problems with black-box and computationally expensive objective functions are generally hard to locate within a limited computational budget, and this situation gets even worse when more than three objectives are involved. To this end, we present a novel surrogate-assisted many-objective optimization algorithm RECAS. Unlike most prior studies, the proposed algorithm is a non–evolutionary-based method, and it iteratively determines new points for expensive evaluation via a series of independent reference vector assisted candidate searches. Furthermore, to make the number of surrogates to be maintained independent of the number of objectives, in each candidate search, RECAS constructs a surrogate model in an aggregated manner to approximate the quality assessment indicator of each point rather than a certain objective function. Under some mild assumptions, this study proves that RECAS converges almost surely to the Pareto-optimal front. In the numerical experiments, the effectiveness and reliability of RECAS are examined on both DTLZ and WFG test suites with the number of objectives varying from 2 to 10. Compared with six state-of-the-art many-objective optimization algorithms, RECAS generally performs better in maintaining convergent and well-spread approximation of the Pareto-optimal front. Finally, the good performance of RECAS on two watershed simulation model calibration problems indicates its great potential in handling real-world applications.