A complete expected improvement criterion for Gaussian process assisted highly constrained expensive optimization

Expected improvement (EI) is a popular infill criterion in Gaussian process assisted optimization of expensive problems for determining which candidate solution is to be assessed using the expensive evaluation method. An EI criterion for constrained expensive optimization (constrained EI) has also been suggested, which requires that feasible solutions exist in the candidate solutions. However, the constrained EI criterion will fail to work in case there are no feasible solutions. To address the above issue, this paper proposes a new EI criterion for highly constrained optimization that can work properly even when no feasible solution is available in the current population. The proposed constrained EI criterion can not only exploit local feasible regions, but also explore infeasible yet promising regions, making it a complete constrained EI criterion. The complete constrained EI is theoretically validated and empirically verified. Simulation results demonstrate that the proposed complete constrained EI is better than or comparable to five existing infill criteria.