A new R2 indicator for better hypervolume approximation

Shang，Ke1; Zhang，Min Ling2; Ishibuchi，Hisao1; Liu，Yiping3

10.1145/3205455.3205543

2018-07-02

GECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference

745-752

Kyoto, Japan

Association for Computing Machinery, Inc

In this paper, a new R2 indicator is proposed for better hypervolume approximation. First the fact that the original R2 indicator is not a good approximation for the hypervolume is illustrated by examples. Then the new R2 indicator is derived based on the Divergence theorem and Riemann sum approximation. The difference between the original R2 and the new R2 is only the added exponential in the new R2 where the exponential is the same as the dimensionality of the objective space (i.e., the number of objectives). The new R2, the original R2 and some other R2 variants are compared through comprehensive numerical studies on different solution sets under different scenarios. The results show the superiority of the proposed new R2 indicator over other R2 variants for the hypervolume approximation, where the new R2 indicator achieves the best linear relation with the true hypervolume.

Divergence theorem Hypervolume approximation R2 indicator Riemann sum

第一

英语

EI ; CPCI-S

Shenzhen Graduate School, Peking University[ZDSYS201703031748 284]

20183105630530

Computer science ; Evolutionary algorithms

Computer Theory, Includes Formal Logic, Automata Theory, Switching Theory, Programming Theory:721.1

2-s2.0-85050600405

Scopus

1.Shenzhen Key Laboratory of Computational Intelligence, Department of Computer Science and Engineering, Southern University of Science and Technology, ,Shenzhen,China
2.School of Computer Science and Engineering, Southeast University Nanjing, ,China
3.Department of Computer Science and Intelligent Systems, Osaka Prefecture University, ,Osaka,Japan

Shang，Ke,Zhang，Min Ling,Ishibuchi，Hisao,et al. A new R2 indicator for better hypervolume approximation[C]:Association for Computing Machinery, Inc,2018:745-752.