A study on the effectiveness of constraint handling schemes within Efficient Global Optimization framework

摘要

Efficient Global Optimization (EGO) is a well established iterative approach originally introduced to solve computationally expensive unconstrained optimization problems. EGO relies on an underlying Gaussian Process (GP) model and identifies an infill location for sampling that maximizes the expected improvement (EI) function. The infill point is evaluated which in turn is used to update the GP model, and this cycle continues until the termination condition is satisfied. In order to deal with constrained optimization problems, several modifications have been suggested in the literature over the years. While the approaches are novel and often complex, the performance is assessed using a small set of test cases (typically two or three). It is thus difficult to judge if they indeed offer significant benefits over simple constrained EGO formulations. In this paper we introduce a simple constrained EGO formulation, where the algorithm attempts to locate infill locations that maximize the probability of feasibility (until a feasible solution is identified) and then switches to maximize the penalized EI function (EI is penalized using the probability of feasibility). The performance of the proposed approach is compared with others using a suite of 10 well studied problems. The results obtained using the proposed approach are competitive and often better than previously reported results for the problems. We hope this study will prompt more interest in the development of efficient constraint handling schemes that can be used within EGO.