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Faster Hypervolume-Based Search Using Monte Carlo Sampling

In: Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems

Author

Listed:
  • Johannes Bader

    (ETH Zurich)

  • Kalyanmoy Deb
  • Eckart Zitzler

Abstract

In recent years, the hypervolume indicator – a set quality measure considering the dominated portion of the objective space – has gained increasing attention in the context of multiobjective search. This is mainly due to the following feature: whenever one Pareto set approximation completely dominates another approximation, the hypervolume of the former will be greater than the hypervolume of the latter. Unfortunately, the calculation of the hypervolume measure is computationally highly demanding, and current algorithms are exponential in the number of objectives. This paper proposes a methodology based on Monte Carlo sampling to estimate the hypervolume contribution of single solutions regarding a specific Pareto set approximation. It is therefore designed to be used in the environmental selection process of an evolutionary algorithm, and allows substantial speedups in hypervolume-based search as the experimental results demonstrate.

Suggested Citation

  • Johannes Bader & Kalyanmoy Deb & Eckart Zitzler, 2010. "Faster Hypervolume-Based Search Using Monte Carlo Sampling," Lecture Notes in Economics and Mathematical Systems, in: Matthias Ehrgott & Boris Naujoks & Theodor J. Stewart & Jyrki Wallenius (ed.), Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems, pages 313-326, Springer.
    • Handle: RePEc:spr:lnechp:978-3-642-04045-0_27
    DOI: 10.1007/978-3-642-04045-0_27
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    Citations

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    Cited by:

    1. Pilechiha, Peiman & Mahdavinejad, Mohammadjavad & Pour Rahimian, Farzad & Carnemolla, Phillippa & Seyedzadeh, Saleh, 2020. "Multi-objective optimisation framework for designing office windows: quality of view, daylight and energy efficiency," Applied Energy, Elsevier, vol. 261(C).
    2. Olacir R. Castro & Gian Mauricio Fritsche & Aurora Pozo, 2018. "Evaluating selection methods on hyper-heuristic multi-objective particle swarm optimization," Journal of Heuristics, Springer, vol. 24(4), pages 581-616, August.
    3. Ivo Couckuyt & Dirk Deschrijver & Tom Dhaene, 2014. "Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization," Journal of Global Optimization, Springer, vol. 60(3), pages 575-594, November.
    4. Luis Martí & Jesús García & Antonio Berlanga & José M. Molina, 2016. "MONEDA: scalable multi-objective optimization with a neural network-based estimation of distribution algorithm," Journal of Global Optimization, Springer, vol. 66(4), pages 729-768, December.
    5. Nondy, J. & Gogoi, T.K., 2021. "Performance comparison of multi-objective evolutionary algorithms for exergetic and exergoenvironomic optimization of a benchmark combined heat and power system," Energy, Elsevier, vol. 233(C).
    6. Christian Lücken & Benjamín Barán & Carlos Brizuela, 2014. "A survey on multi-objective evolutionary algorithms for many-objective problems," Computational Optimization and Applications, Springer, vol. 58(3), pages 707-756, July.
    7. Garcia-Teruel, Anna & DuPont, Bryony & Forehand, David I.M., 2021. "Hull geometry optimisation of wave energy converters: On the choice of the objective functions and the optimisation formulation," Applied Energy, Elsevier, vol. 298(C).
    8. Joshua Q. Hale & Helin Zhu & Enlu Zhou, 2020. "Domination Measure: A New Metric for Solving Multiobjective Optimization," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 565-581, July.
    9. Eric Bradford & Artur M. Schweidtmann & Alexei Lapkin, 2018. "Efficient multiobjective optimization employing Gaussian processes, spectral sampling and a genetic algorithm," Journal of Global Optimization, Springer, vol. 71(2), pages 407-438, June.

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