A Hybrid Regressor and Classifier-Assisted Evolutionary Algorithm for Expensive Optimization With Incomplete Constraint Information

Abstract

Surrogate-assisted evolutionary algorithms (SAEAs) have become a popular tool to solve expensive optimization problems and have been gradually used to deal with expensive constraints. To handle inequality expensive constraints, existing SAEAs need both the information of constraint violation and satisfaction to construct surrogate models for constraints. However, many problems only feedback whether the candidate solution is feasible or how much degree it violates constraints. There is no detailed information of how much degree the candidate satisfies constraints. The performance of most existing SAEAs decreases a lot in solving expensive constrained optimization problems (ECOPs) with such incomplete constraint information. To solve the problem, this article proposes a hybrid regressor and classifier-assisted evolutionary algorithm (HRCEA). HRCEA adopts a radial basis function regression model to approximate the degree of constraint violation. In order to make a more credible prediction, a logistic regression classifier (LRC) is constructed for the offspring rectification. The classifier works in cooperation with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha$</tex-math> </inline-formula> -cut strategy, in which the high confidence level can significantly improve the prediction reliability. Besides, the LRC is built based on the boundary training data selection strategy, which is devised to select samples around feasible boundaries. This strategy is helpful for the LRC to fit the local feasibility structure. Extensive experiments on commonly used benchmark functions in CEC2006 and CEC 2010 demonstrate that HRCEA has satisfactory performance in found results and execution efficiency when solving ECOPs with incomplete constraint information. Furthermore, HRCEA is utilized to solve ceramic formula design optimization problem, which shows its promising application in real-world optimization problems.