Prediction of Pareto Dominance Using an Attribute Tendency Model for Expensive Multi-Objective Optimization

Abstract

This paper proposes a novel surrogate-assisted multi-objective evolutionary algorithm, MOEA-ATCM, to solve expensive or black-box multi-objective problems with small evaluation budgets. The proposed approach encompasses a state-of-the-art MOEA based on a nondominated sorting genetic algorithm assisted by multi-fidelity optimization methods. A high-fidelity attribute tendency (AT) surrogate model was used to construct a linear decision space by introducing the knowledge of the objective space. A coarse model (CM) based on the AT model and correlation analyses of the objective functions and decision attributes were used to predict the Pareto dominance for candidates in the new decision space constructed by the AT model. Two major roles of MOEA-ATCM were identified: (1) the development of a new multi-fidelity surrogate-model-based method to predict Pareto dominance in a decision space that was then applied to MOEA, which does not need to dynamically update surrogate models in the optimization process and (2) the development of a Pareto dominance prediction method to obtain good nondominated solutions of expensive or black box problems with relatively few objective function evaluations. The advantages of MOEA-ATCM were verified by mathematical benchmark problems and a real-world multi-objective parameter optimization problem.