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 Paretooptimal 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 Paretooptimal front. Finally, the good performance of RECAS on two watershed simulation model calibration problems indicates its great potential in handling real-world applications.