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A New Scalarization Technique to Approximate Pareto Fronts of Problems with Disconnected Feasible Sets

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  • R. S. Burachik

    (University of South Australia)

  • C. Y. Kaya

    (University of South Australia)

  • M. M. Rizvi

    (University of South Australia)

Abstract

We introduce and analyze a novel scalarization technique and an associated algorithm for generating an approximation of the Pareto front (i.e., the efficient set) of nonlinear multiobjective optimization problems. Our approach is applicable to nonconvex problems, in particular to those with disconnected Pareto fronts and disconnected domains (i.e., disconnected feasible sets). We establish the theoretical properties of our new scalarization technique and present an algorithm for its implementation. By means of test problems, we illustrate the strengths and advantages of our approach over existing scalarization techniques such as those derived from the Pascoletti–Serafini method, as well as the popular weighted-sum method.

Suggested Citation

  • R. S. Burachik & C. Y. Kaya & M. M. Rizvi, 2014. "A New Scalarization Technique to Approximate Pareto Fronts of Problems with Disconnected Feasible Sets," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 428-446, August.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:2:d:10.1007_s10957-013-0346-0
    DOI: 10.1007/s10957-013-0346-0
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    References listed on IDEAS

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    1. Liu, Y. & Teo, K. L. & Yang, X. Q., 1999. "Approximation methods for non-convex curves," European Journal of Operational Research, Elsevier, vol. 117(1), pages 125-135, August.
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    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. Gabriele Eichfelder, 2009. "Scalarizations for adaptively solving multi-objective optimization problems," Computational Optimization and Applications, Springer, vol. 44(2), pages 249-273, November.
    5. M. Ehrgott & S. Ruzika, 2008. "Improved ε-Constraint Method for Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 375-396, September.
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    Cited by:

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    2. G. Bento & J. Cruz Neto & G. López & Antoine Soubeyran & J. Souza, 2018. "The Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization with Application to the Compromise Problem," Post-Print hal-01985333, HAL.
    3. Tong Shu & Xiaoqin Gao & Shou Chen & Shouyang Wang & Kin Keung Lai & Lu Gan, 2016. "Weighing Efficiency-Robustness in Supply Chain Disruption by Multi-Objective Firefly Algorithm," Sustainability, MDPI, vol. 8(3), pages 1-27, March.
    4. Brian Dandurand & Margaret M. Wiecek, 2016. "Quadratic scalarization for decomposed multiobjective optimization," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 1071-1096, October.
    5. Li, Mingxin & Jiang, Xiaoli & Carroll, James & Negenborn, Rudy R., 2022. "A multi-objective maintenance strategy optimization framework for offshore wind farms considering uncertainty," Applied Energy, Elsevier, vol. 321(C).
    6. Fereshteh Akbari & Mehrdad Ghaznavi & Esmaile Khorram, 2018. "A Revised Pascoletti–Serafini Scalarization Method for Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 560-590, August.

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