Preference-Based Nonlinear Normalization for Multiobjective Optimization

He，Linjun1,2; Nan，Yang1; Ishibuchi，Hisao1; Srinivasan，Dipti2

10.1007/978-3-031-27250-9_40

2023

0302-9743

1611-3349

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

13970 LNCS

563-577

Normalization is commonly used in multiobjective evolutionary algorithms (MOEAs) in order to handle multiobjective optimization problems with differently-scaled objectives. The goal of normalization is to obtain uniformly-distributed solutions over the entire Pareto front. However, in practice, such a uniform solution set may not be a well-distributed solution set for decision making when the desired distribution of solutions is not uniform. To obtain a well-distributed solution set that meets the desired distribution, in this paper, we propose a preference-based nonlinear normalization method that transforms the objective space based on the probability integral transform theorem. As a result, the use of a standard MOEA to search for uniformly-distributed solutions in the transformed objective space leads to a desired well-distributed solution set. The proposed method is incorporated in three different MOEAs (i.e., a Pareto dominance-based MOEA, a decomposition-based MOEA, and an indicator-based MOEA). Experimental results demonstrate the flexibility and effectiveness of the proposed method. Our code is available at https://github.com/linjunhe/moea-pn.

Decision making Evolutionary multiobjective optimization (EMO) Normalization Preference incorporation

第一 ; 通讯

英语

EI

20231313822004

Computation theory ; Evolutionary algorithms ; Integral equations ; Multiobjective optimization ; Probability distributions

Computer Theory, Includes Formal Logic, Automata Theory, Switching Theory, Programming Theory:721.1 ; Management:912.2 ; Calculus:921.2 ; Optimization Techniques:921.5 ; Probability Theory:922.1

2-s2.0-85151052620

Scopus

1.Department of Computer Science and Engineering,Southern University of Science and Technology (SUSTech),Shenzhen,China
2.Department of Electrical and Computer Engineering,National University of Singapore,Singapore,Singapore

He，Linjun,Nan，Yang,Ishibuchi，Hisao,et al. Preference-Based Nonlinear Normalization for Multiobjective Optimization[C],2023:563-577.