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The cross-entropy method in multi-objective optimisation: An assessment

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  • Bekker, James
  • Aldrich, Chris

Abstract

Solving multi-objective problems requires the evaluation of two or more conflicting objective functions, which often demands a high amount of computational power. This demand increases rapidly when estimating values for objective functions of dynamic, stochastic problems, since a number of observations are needed for each evaluation set, of which there could be many. Computer simulation applications of real-world optimisations often suffer due to this phenomenon. Evolutionary algorithms are often applied to multi-objective problems. In this article, the cross-entropy method is proposed as an alternative, since it has been proven to converge quickly in the case of single-objective optimisation problems. We adapted the basic cross-entropy method for multi-objective optimisation and applied the proposed algorithm to known test problems. This was followed by an application to a dynamic, stochastic problem where a computer simulation model provides the objective function set. The results show that acceptable results can be obtained while doing relatively few evaluations.

Suggested Citation

  • Bekker, James & Aldrich, Chris, 2011. "The cross-entropy method in multi-objective optimisation: An assessment," European Journal of Operational Research, Elsevier, vol. 211(1), pages 112-121, May.
  • Handle: RePEc:eee:ejores:v:211:y:2011:i:1:p:112-121
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    1. Rubinstein, Reuven Y., 1997. "Optimization of computer simulation models with rare events," European Journal of Operational Research, Elsevier, vol. 99(1), pages 89-112, May.
    2. Bettonvil, Bert & del Castillo, Enrique & Kleijnen, Jack P.C., 2009. "Statistical testing of optimality conditions in multiresponse simulation-based optimization," European Journal of Operational Research, Elsevier, vol. 199(2), pages 448-458, December.
    3. Shukla, Pradyumn Kumar & Deb, Kalyanmoy, 2007. "On finding multiple Pareto-optimal solutions using classical and evolutionary generating methods," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1630-1652, September.
    4. Sridhar Bashyam & Michael C. Fu, 1998. "Optimization of (s, S) Inventory Systems with Random Lead Times and a Service Level Constraint," Management Science, INFORMS, vol. 44(12-Part-2), pages 243-256, December.
    5. Beausoleil, Ricardo P., 2006. ""MOSS" multiobjective scatter search applied to non-linear multiple criteria optimization," European Journal of Operational Research, Elsevier, vol. 169(2), pages 426-449, March.
    6. Tsou, Ching-Shih, 2009. "Evolutionary Pareto optimizers for continuous review stochastic inventory systems," European Journal of Operational Research, Elsevier, vol. 195(2), pages 364-371, June.
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    Cited by:

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    2. Fahimnia, Behnam & Sarkis, Joseph & Eshragh, Ali, 2015. "A tradeoff model for green supply chain planning:A leanness-versus-greenness analysis," Omega, Elsevier, vol. 54(C), pages 173-190.
    3. Nguyen, Hoa T.M. & Chow, Andy H.F. & Ying, Cheng-shuo, 2021. "Pareto routing and scheduling of dynamic urban rail transit services with multi-objective cross entropy method," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 156(C).
    4. Shi, Jie & Wang, Luhao & Lee, Wei-Jen & Cheng, Xingong & Zong, Xiju, 2019. "Hybrid Energy Storage System (HESS) optimization enabling very short-term wind power generation scheduling based on output feature extraction," Applied Energy, Elsevier, vol. 256(C).
    5. Qun Niu & Ming You & Zhile Yang & Yang Zhang, 2021. "Economic Emission Dispatch Considering Renewable Energy Resources—A Multi-Objective Cross Entropy Optimization Approach," Sustainability, MDPI, vol. 13(10), pages 1-33, May.
    6. 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.
    7. Caballero, Rafael & Hernández-Díaz, Alfredo G. & Laguna, Manuel & Molina, Julián, 2015. "Cross entropy for multiobjective combinatorial optimization problems with linear relaxations," European Journal of Operational Research, Elsevier, vol. 243(2), pages 362-368.
    8. Wang, Luhao & Li, Qiqiang & Ding, Ran & Sun, Mingshun & Wang, Guirong, 2017. "Integrated scheduling of energy supply and demand in microgrids under uncertainty: A robust multi-objective optimization approach," Energy, Elsevier, vol. 130(C), pages 1-14.

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