Domination-Based Ordinal Regression for Expensive Multi-Objective Optimization

Xunzhao Yu, Xin Yao, Yan Wang, Ling Zhu, Dimitar P. Filev

Abstract: Most surrogate-assisted evolutionary algorithms save expensive evaluations by approximating fitness functions. However, many real-world applications are high-dimensional multi-objective expensive optimization problems, and it is difficult to approximate their fitness functions accurately using a very limited number of fitness evaluations. This paper proposes a domination-based ordinal regression surrogate, in which a Kriging model is employed to learn the domination relationship values and to approximate the ordinal landscape of fitness functions. Coupling with a hybrid surrogate management strategy, the solutions with higher probabilities to dominate others are selected and evaluated in fitness functions. Our empirical studies on the DTLZ testing functions demonstrate that the proposed algorithm is more efficient when compared with other state-of-the-art expensive multi-objective optimization methods.