HypE: an algorithm for fast hypervolume-based many-objective optimization. In the field of evolutionary multi-criterion optimization, the hypervolume indicator is the only single set quality measure that is known to be strictly monotonic with regard to Pareto dominance: whenever a Pareto set approximation entirely dominates another one, then the indicator value of the dominant set will also be better. This property is of high interest and relevance for problems involving a large number of objective functions. However, the high computational effort required for hypervolume calculation has so far prevented the full exploitation of this indicator’s potential; current hypervolume-based search algorithms are limited to problems with only a few objectives. This paper addresses this issue and proposes a fast search algorithm that uses Monte Carlo simulation to approximate the exact hypervolume values. The main idea is not that the actual indicator values are important, but rather that the rankings of solutions induced by the hypervolume indicator. In detail, we present HypE, a hypervolume estimation algorithm for multi-objective optimization, by which the accuracy of the estimates and the available computing resources can be traded off; thereby, not only do many-objective problems become feasible with hypervolume-based search, but also the runtime can be flexibly adapted. Moreover, we show how the same principle can be used to statistically compare the outcomes of different multi-objective optimizers with respect to the hypervolume—so far, statistical testing has been restricted to scenarios with few objectives. The experimental results indicate that HypE is highly effective for many-objective problems in comparison to existing multi-objective evolutionary algorithms. HypE is available for download at http://www.tik.ee.ethz.ch/sop/download/supplementary/hype/

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  1. Binois, Mickael; Picheny, Victor; Taillandier, Patrick; Habbal, Abderrahmane: The Kalai-Smorodinsky solution for many-objective Bayesian optimization (2020)
  2. Chen, Huangke; Cheng, Ran; Wen, Jinming; Li, Haifeng; Weng, Jian: Solving large-scale many-objective optimization problems by covariance matrix adaptation evolution strategy with scalable small subpopulations (2020)
  3. Dong, Zhiming; Wang, Xianpeng; Tang, Lixin: MOEA/D with a self-adaptive weight vector adjustment strategy based on chain segmentation (2020)
  4. Guerreiro, Andreia P.; Fonseca, Carlos M.: An analysis of the hypervolume Sharpe-ratio indicator (2020)
  5. Hale, Joshua Q.; Zhu, Helin; Zhou, Enlu: Domination measure: a new metric for solving multiobjective optimization (2020)
  6. Han, Ding; Zheng, Jianrong: A Kriging model-based expensive multiobjective optimization algorithm using R2 indicator of expectation improvement (2020)
  7. Liang, Liang: A fusion multiobjective empire split algorithm (2020)
  8. Liu, Yuan; Zhu, Ningbo; Li, Kenli; Li, Miqing; Zheng, Jinhua; Li, Keqin: An angle dominance criterion for evolutionary many-objective optimization (2020)
  9. Liu, Zhi-Zhong; Wang, Yong; Huang, Pei-Qiu: AnD: a many-objective evolutionary algorithm with angle-based selection and shift-based density estimation (2020)
  10. Li, Wenhua; Wang, Rui; Zhang, Tao; Ming, Mengjun; Li, Kaiwen: Reinvestigation of evolutionary many-objective optimization: focus on the Pareto knee front (2020)
  11. Luo, Jianping; Huang, Xiongwen; Yang, Yun; Li, Xia; Wang, Zhenkun; Feng, Jiqiang: A many-objective particle swarm optimizer based on indicator and direction vectors for many-objective optimization (2020)
  12. Qi, Yutao; Liu, Dazhuang; Li, Xiaodong; Lei, Jiaojiao; Xu, Xiaoying; Miao, Qiguang: An adaptive penalty-based boundary intersection method for many-objective optimization problem (2020)
  13. Rojas-Gonzalez, Sebastian; van Nieuwenhuyse, Inneke: A survey on kriging-based infill algorithms for multiobjective simulation optimization (2020)
  14. Tang, Weisen; Liu, Hai-Lin; Chen, Lei; Tan, Kay Chen; Cheung, Yiu-ming: Fast hypervolume approximation scheme based on a segmentation strategy (2020)
  15. Zhang, XuWei; Liu, Hao; Tu, LiangPing; Zhao, Jian: An efficient multi-objective optimization algorithm based on level swarm optimizer (2020)
  16. Zhang, Zhechen; Liu, Sanyang; Gao, Weifeng; Xu, Jingwei; Zhu, Shengqi: An enhanced multi-objective evolutionary optimization algorithm with inverse model (2020)
  17. Zheng, Wei; Wu, Jianyu; Zhang, Chenghu; Sun, Jianyong: A clustering-based multiobjective evolutionary algorithm for balancing exploration and exploitation (2020)
  18. Bai, Hui; Zheng, Jinhua; Yu, Guo; Yang, Shengxiang; Zou, Juan: A Pareto-based many-objective evolutionary algorithm using space partitioning selection and angle-based truncation (2019)
  19. Bao, Chunteng; Xu, Lihong; Goodman, Erik D.: A novel two-archive matching-based algorithm for multi- and many-objective optimization (2019)
  20. Chabane, Brahim; Basseur, Matthieu; Hao, Jin-Kao: Lorenz dominance based algorithms to solve a practical multiobjective problem (2019)

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