HypE

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/


References in zbMATH (referenced in 46 articles )

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  1. Guerreiro, Andreia P.; Fonseca, Carlos M.: An analysis of the hypervolume Sharpe-ratio indicator (2020)
  2. Rojas-Gonzalez, Sebastian; van Nieuwenhuyse, Inneke: A survey on kriging-based infill algorithms for multiobjective simulation optimization (2020)
  3. Chabane, Brahim; Basseur, Matthieu; Hao, Jin-Kao: Lorenz dominance based algorithms to solve a practical multiobjective problem (2019)
  4. Ermis, Gülcin; Akkan, Can: Search algorithms for improving the Pareto front in a timetabling problem with a solution network-based robustness measure (2019)
  5. Li, Hao-ran; He, Fa-zhi; Yan, Xiao-hu: IBEA-SVM: an indicator-based evolutionary algorithm based on pre-selection with classification guided by SVM (2019)
  6. Zhou, Yuren; He, Xiaoyu; Xiang, Yi; Cai, Shaowei: A set of new multi- and many-objective test problems for continuous optimization and a comprehensive experimental evaluation (2019)
  7. Gomes, Ricardo J.; Guerreiro, Andreia P.; Kuhn, Tobias; Paquete, Luís: Implicit enumeration strategies for the hypervolume subset selection problem (2018)
  8. Luo, Naili; Li, Xia; Lin, Qiuzhen: Objective reduction for many-objective optimization problems using objective subspace extraction (2018)
  9. Feliot, Paul; Bect, Julien; Vazquez, Emmanuel: A Bayesian approach to constrained single- and multi-objective optimization (2017)
  10. Greiner, David; Periaux, Jacques; Emperador, Jose M.; Galván, Blas; Winter, Gabriel: Game theory based evolutionary algorithms: a review with Nash applications in structural engineering optimization problems (2017)
  11. Liu, Chao; Yan, Bai; Gao, Yang: A new hypervolume-based differential evolution algorithm for many-objective optimization (2017)
  12. Steponavičė, Ingrida; Hyndman, Rob J.; Smith-Miles, Kate; Villanova, Laura: Dynamic algorithm selection for Pareto optimal set approximation (2017)
  13. Wang, Chun; Ji, Zhicheng; Wang, Yan: A novel memetic algorithm based on decomposition for multiobjective flexible job shop scheduling problem (2017)
  14. Ye Tian, Ran Cheng, Xingyi Zhang, Yaochu Jin: PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization (2017) arXiv
  15. Zuo, Cili; Wu, Lianghong; Zeng, Zhao-Fu; Wei, Hua-Liang: Stochastic fractal based multiobjective fruit fly optimization (2017)
  16. Cubukcuoglu, Cemre; Chatzikonstantinou, Ioannis; Tasgetiren, Mehmet Fatih; Sariyildiz, I. Sevil; Pan, Quan-Ke: A multi-objective harmony search algorithm for sustainable design of floating settlements (2016)
  17. Lei, Hongtao; Wang, Rui; Laporte, Gilbert: Solving a multi-objective dynamic stochastic districting and routing problem with a co-evolutionary algorithm (2016)
  18. Martí, Luis; García, Jesús; Berlanga, Antonio; Molina, José M.: MONEDA: scalable multi-objective optimization with a neural network-based estimation of distribution algorithm (2016)
  19. Zhang, Xingyi; Tian, Ye; Jin, Yaochu: Approximate non-dominated sorting for evolutionary many-objective optimization (2016)
  20. Cao, Yongtao; Smucker, Byran J.; Robinson, Timothy J.: On using the hypervolume indicator to compare Pareto fronts: applications to multi-criteria optimal experimental design (2015)

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