Constrained Evolutionary Bayesian Optimization for Expensive Constrained Optimization Problems With Inequality Constraints

This article proposes a constrained evolutionary Bayesian optimization (CEBO) algorithm to cope with expensive constrained optimization problems with inequality constraints. The uniqueness of CEBO lies in its capability of balancing feasibility and objective improvement under a limited function evaluation budget, which is achieved by designing two strategies to obtain promising solutions. The first strategy prefers feasibility. It tends to obtain a feasible solution by utilizing the predicted value and uncertainty provided by Gaussian process (GP). The second strategy prefers objective improvement. It maintains and evolves the population of evolutionary algorithms, and selects a solution with a good objective function value and violating the constraints not too much based on the predicted value and uncertainty provided by GP at each iteration. The sequential implementation of these two strategies allows CEBO to balance feasibility and objective improvement. The effectiveness of CEBO is verified by 26 test instances and a practical application. The results demonstrate that CEBO is able to find high-quality solutions with 100 FEs.