Comparison of hypervolume, IGD and IGD⁺ from the viewpoint of optimal distributions of solutions

Ishibuchi, Hisao1; Imada, Ryo2; Masuyama, Naoki2; Nojima, Yusuke2

10.1007/978-3-030-12598-1_27

2019

16113349

10th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2019

11411 LNCS

332-345

East Lansing, MI, United states

Springer Verlag

Hypervolume (HV) and inverted generational distance (IGD) have been frequently used as performance indicators to evaluate the quality of solution sets obtained by evolutionary multiobjective optimization (EMO) algorithms. They have also been used in indicator-based EMO algorithms. In some studies on many-objective problems, only the IGD indicator was used due to a large computation load of HV calculation. However, the IGD indicator is not Pareto compliant. This means that a better solution set in terms of the Pareto dominance relation can be evaluated as being worse. Recently the IGD plus (IGD⁺) indicator has been proposed as a weakly Pareto compliant version of IGD. In this paper, we compare these three indicators from the viewpoint of optimal distributions of solutions. More specifically, we visually demonstrate similarities and differences among the three indicators by numerically calculating near-optimal distributions of solutions to optimize each indicator for some test problems. Our numerical analysis shows that IGD⁺ is more similar to HV than IGD whereas the formulations of IGD and IGD⁺ are almost the same.
© Springer Nature Switzerland AG 2019.

第一 ; 通讯

EI

National Natural Science Foundation of China[Grant No. 61876075]

20191206656991

Evolutionary algorithms ; Multiobjective optimization

Quality Assurance and Control:913.3 ; Optimization Techniques:921.5

EV Compendex

1.Shenzhen Key Laboratory of Computational Intelligence, University Key Laboratory of Evolving Intelligent Systems of Guangdong Province, Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen; 518055, China
2.Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai; Osaka; 599-8531, Japan

Ishibuchi, Hisao,Imada, Ryo,Masuyama, Naoki,et al. Comparison of hypervolume, IGD and IGD⁺ from the viewpoint of optimal distributions of solutions[C]:Springer Verlag,2019:332-345.