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A numerical method for nonconvex multi-objective optimal control problems

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  • C. Kaya
  • Helmut Maurer

Abstract

A numerical method is proposed for constructing an approximation of the Pareto front of nonconvex multi-objective optimal control problems. First, a suitable scalarization technique is employed for the multi-objective optimal control problem. Then by using a grid of scalarization parameter values, i.e., a grid of weights, a sequence of single-objective optimal control problems are solved to obtain points which are spread over the Pareto front. The technique is illustrated on problems involving tumor anti-angiogenesis and a fed-batch bioreactor, which exhibit bang–bang, singular and boundary types of optimal control. We illustrate that the Bolza form, the traditional scalarization in optimal control, fails to represent all the compromise, i.e., Pareto optimal, solutions. Copyright Springer Science+Business Media New York 2014

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  • C. Kaya & Helmut Maurer, 2014. "A numerical method for nonconvex multi-objective optimal control problems," Computational Optimization and Applications, Springer, vol. 57(3), pages 685-702, April.
    • Handle: RePEc:spr:coopap:v:57:y:2014:i:3:p:685-702
    DOI: 10.1007/s10589-013-9603-2
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    References listed on IDEAS

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    1. L. Grosset & B. Viscolani, 2006. "Reciprocal Optimal Control Problems and the Associated Pareto Frontier," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 113-123, July.
    2. Nahid Banihashemi & C. Yalçın Kaya, 2013. "Inexact Restoration for Euler Discretization of Box-Constrained Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 726-760, March.
    3. Henri Bonnel & C. Yalçın Kaya, 2010. "Optimization Over the Efficient Set of Multi-objective Convex Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 93-112, October.
    4. C.Y. Kaya & J.L. Noakes, 2003. "Computational Method for Time-Optimal Switching Control," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 69-92, April.
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    Cited by:

    1. Nguyen Thi Toan & Le Quang Thuy, 2023. "S-Derivative of the Extremum Multifunction to a Multi-objective Parametric Discrete Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 240-265, January.
    2. C. Yalçın Kaya, 2019. "Markov–Dubins interpolating curves," Computational Optimization and Applications, Springer, vol. 73(2), pages 647-677, June.
    3. Andreas Lichtenberger & Joao Paulo Braga & Willi Semmler, 2022. "Green Bonds for the Transition to a Low-Carbon Economy," SCEPA working paper series. 2022-02, Schwartz Center for Economic Policy Analysis (SCEPA), The New School.
    4. Stephan Dempe & Gabriele Eichfelder & Jörg Fliege, 2015. "On the effects of combining objectives in multi-objective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(1), pages 1-18, August.
    5. C. Yalçın Kaya, 2020. "Optimal Control of the Double Integrator with Minimum Total Variation," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 966-981, June.
    6. Bui Trong Kien & Trinh Duy Binh, 2023. "On the second-order optimality conditions for multi-objective optimal control problems with mixed pointwise constraints," Journal of Global Optimization, Springer, vol. 85(1), pages 155-183, January.
    7. Cui, Yunfei & Geng, Zhiqiang & Zhu, Qunxiong & Han, Yongming, 2017. "Review: Multi-objective optimization methods and application in energy saving," Energy, Elsevier, vol. 125(C), pages 681-704.
    8. C. Yalçın Kaya, 2017. "Markov–Dubins path via optimal control theory," Computational Optimization and Applications, Springer, vol. 68(3), pages 719-747, December.
    9. Owen Davis & Siavash Radpour, 2022. "Older Workers’ Wages Are Growing—But Not Fast Enough," SCEPA publication series. 2022-02, Schwartz Center for Economic Policy Analysis (SCEPA), The New School.
    10. Nguyen Thi Toan & Le Quang Thuy & Nguyen Tuyen & Yi-Bin Xiao, 2021. "Second-order KKT optimality conditions for multiobjective discrete optimal control problems," Journal of Global Optimization, Springer, vol. 79(1), pages 203-231, January.
    11. Andreas Lichtenberger & Joao Paulo Braga & Willi Semmler, 2022. "Green Bonds for the Transition to a Low-Carbon Economy," Econometrics, MDPI, vol. 10(1), pages 1-31, March.
    12. Regina S. Burachik & Alexander C. Kalloniatis & C. Yalçın Kaya, 2021. "Sparse Network Optimization for Synchronization," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 229-251, October.

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