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Solving discrete multi-objective optimization problems using modified augmented weighted Tchebychev scalarizations

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  • Holzmann, Tim
  • Smith, J.C.

Abstract

In this paper we present the modified augmented weighted Tchebychev norm, which can be used to generate a complete efficient set of solutions to a discrete multi-objective optimization problem. We contribute a generating algorithm that will, without supervision, generate the entire non-dominated set for any number of objectives. To our knowledge, this is the first generating method for general discrete multi-objective problems that uses a variant of the Tchebychev norm. In a computational study, our algorithm’s running times are comparable to previously proposed algorithms.

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  • Holzmann, Tim & Smith, J.C., 2018. "Solving discrete multi-objective optimization problems using modified augmented weighted Tchebychev scalarizations," European Journal of Operational Research, Elsevier, vol. 271(2), pages 436-449.
    • Handle: RePEc:eee:ejores:v:271:y:2018:i:2:p:436-449
    DOI: 10.1016/j.ejor.2018.05.036
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    1. Klamroth, Kathrin & Lacour, Renaud & Vanderpooten, Daniel, 2015. "On the representation of the search region in multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 245(3), pages 767-778.
    2. Laumanns, Marco & Thiele, Lothar & Zitzler, Eckart, 2006. "An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method," European Journal of Operational Research, Elsevier, vol. 169(3), pages 932-942, March.
    3. Ramos, R. M. & Alonso, S. & Sicilia, J. & Gonzalez, C., 1998. "The problem of the optimal biobjective spanning tree," European Journal of Operational Research, Elsevier, vol. 111(3), pages 617-628, December.
    4. Alves, Maria Joao & Climaco, Joao, 2000. "An interactive reference point approach for multiobjective mixed-integer programming using branch-and-bound," European Journal of Operational Research, Elsevier, vol. 124(3), pages 478-494, August.
    5. Melih Ozlen & Benjamin A. Burton & Cameron A. G. MacRae, 2014. "Multi-Objective Integer Programming: An Improved Recursive Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 470-482, February.
    6. Thomas Stidsen & Kim Allan Andersen & Bernd Dammann, 2014. "A Branch and Bound Algorithm for a Class of Biobjective Mixed Integer Programs," Management Science, INFORMS, vol. 60(4), pages 1009-1032, April.
    7. Dächert, Kerstin & Klamroth, Kathrin & Lacour, Renaud & Vanderpooten, Daniel, 2017. "Efficient computation of the search region in multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 260(3), pages 841-855.
    8. Mavrotas, G. & Diakoulaki, D., 1998. "A branch and bound algorithm for mixed zero-one multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 107(3), pages 530-541, June.
    9. Przybylski, Anthony & Gandibleux, Xavier & Ehrgott, Matthias, 2008. "Two phase algorithms for the bi-objective assignment problem," European Journal of Operational Research, Elsevier, vol. 185(2), pages 509-533, March.
    10. Özlen, Melih & Azizoglu, Meral, 2009. "Multi-objective integer programming: A general approach for generating all non-dominated solutions," European Journal of Operational Research, Elsevier, vol. 199(1), pages 25-35, November.
    11. Kirlik, Gokhan & Sayın, Serpil, 2014. "A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems," European Journal of Operational Research, Elsevier, vol. 232(3), pages 479-488.
    12. Banu Lokman & Murat Köksalan, 2013. "Finding all nondominated points of multi-objective integer programs," Journal of Global Optimization, Springer, vol. 57(2), pages 347-365, October.
    13. Klein, Dieter & Hannan, Edward, 1982. "An algorithm for the multiple objective integer linear programming problem," European Journal of Operational Research, Elsevier, vol. 9(4), pages 378-385, April.
    14. Mavrotas, George & Florios, Kostas, 2013. "An improved version of the augmented epsilon-constraint method (AUGMECON2) for finding the exact Pareto set in Multi-Objective Integer Programming problems," MPRA Paper 105034, University Library of Munich, Germany.
    15. Zhang, Weihua & Reimann, Marc, 2014. "A simple augmented ∊-constraint method for multi-objective mathematical integer programming problems," European Journal of Operational Research, Elsevier, vol. 234(1), pages 15-24.
    16. 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.
    17. Sylva, John & Crema, Alejandro, 2004. "A method for finding the set of non-dominated vectors for multiple objective integer linear programs," European Journal of Operational Research, Elsevier, vol. 158(1), pages 46-55, October.
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    4. Tsionas, Mike G., 2019. "Multi-objective optimization using statistical models," European Journal of Operational Research, Elsevier, vol. 276(1), pages 364-378.
    5. Karakaya, G. & Köksalan, M., 2021. "Evaluating solutions and solution sets under multiple objectives," European Journal of Operational Research, Elsevier, vol. 294(1), pages 16-28.
    6. Bashir Bashir & Özlem Karsu, 2022. "Solution approaches for equitable multiobjective integer programming problems," Annals of Operations Research, Springer, vol. 311(2), pages 967-995, April.
    7. Tim Holzmann & J. Cole Smith, 2019. "Shortest path interdiction problem with arc improvement recourse: A multiobjective approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(3), pages 230-252, April.
    8. Stephan Helfrich & Tyler Perini & Pascal Halffmann & Natashia Boland & Stefan Ruzika, 2023. "Analysis of the weighted Tchebycheff weight set decomposition for multiobjective discrete optimization problems," Journal of Global Optimization, Springer, vol. 86(2), pages 417-440, June.
    9. Argyris, Nikolaos & Karsu, Özlem & Yavuz, Mirel, 2022. "Fair resource allocation: Using welfare-based dominance constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 560-578.
    10. Salo, Ahti & Andelmin, Juho & Oliveira, Fabricio, 2022. "Decision programming for mixed-integer multi-stage optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 299(2), pages 550-565.
    11. Zhang, Xingmin & Zhang, Shuai, 2021. "Optimal time-varying tail risk network with a rolling window approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).

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