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Multiobjective Optimization via Parametric Optimization: Models, Algorithms, and Applications

  • Oleksandr Romanko
  • Alireza Ghaffari-Hadigheh
  • Tamás Terlaky
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 21)

Abstract

In this chapter we highlight the relationships between multiobjective optimization and parametric optimization that is used to solve such problems. Solution of a multiobjective problem is the set of Pareto efficient points, known in the literature as Pareto efficient frontier or Pareto front. Pareto points can be obtained by using either weighting the objectives or by ε-constrained (hierarchical) method for solving multiobjective optimization models. Using those methods we can formulate them as parametric optimization problems and compute their efficient solution set numerically. We present a methodology for conic quadratic optimization that allows tracing the Pareto efficient frontier without discretization of the objective space and without solving the corresponding optimization problem at each discretization point.

Keywords

Pareto Front Multiobjective Optimization Linear Optimization Invariancy Region Optimal Partition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The authors’ research was partially supported by the NSERC Discovery Grant #48923, the Canada Research Chair Program, and MITACS. The third author was also supported by a Start-up Grant of Lehigh University, and the Hungarian National Development Agency and the European Union within the frame of the project TAMOP 4.2.2-08/1-2008-0021 at the Széchenyi István University, entitled “Simulation and Optimization — basic research in numerical mathematics.” We are grateful to Helmut Mausser, Alexander Kreinin, and Ian Iscoe from Algorithmics Incorporated, an IBM Company, for valuable discussions on the practical examples of multiobjective optimization problems in finance. We would like to thank Antoine Deza from McMaster University, Imre Pólik from SAS Institute and Yuri Zinchenko from University of Calgary for their helpful suggestions.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Oleksandr Romanko
    • 1
  • Alireza Ghaffari-Hadigheh
    • 2
  • Tamás Terlaky
    • 3
  1. 1.Department of Computing and SoftwareMcMaster UniversityHamiltonCanada
  2. 2.Department of MathematicsAzarbaijan University of Tarbiat MoallemTabrizIran
  3. 3.Department of Industrial and Systems EngineeringLehigh University, Harold S. Mohler LaboratoryBethlehemUSA

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