On the Use of Dynamic Reference Points in HypE

  • Jingda Deng
  • Qingfu Zhang
  • Hui Li
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10593)


In evolutionary multiobjective optimization, hypervolume indicator is one of the most commonly-used performance metrics. To reduce its high computational costs in many objective optimization, Monte Carlo method is used in HypE (Hypervolume Estimation algorithm for multi-objective optimization) for approximating hypervolume values. However, the diversity preservation of HypE can be poor under inappropriate settings of the reference point. In this paper, the influence of the reference point on HypE is discussed and two variants of HypE algorithm with dynamic reference points are proposed to improve the performance of HypE. Our experimental results suggest that the new algorithms outperform HypE with fixed reference points on a set of multiobjective test instances with different shapes of Pareto fronts.


Multiobjective optimization Evolutionary computation Hypervolume Reference point 



The work described in this paper was supported by the National Science Foundation of China under Grant 61473241, and a grant from ANR/RCC Joint Research Scheme sponsored by the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. A-CityU101/16) and France National Research Agency (ANR-16-CE23-0013-01).


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceCity University of Hong KongHong KongHong Kong
  2. 2.City University of Hong Kong Shenzhen Research InstituteShenzhenChina
  3. 3.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anChina

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