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Robust optimization model for uncertain multiobjective linear programs.

Lei Wang1, Min Fang1

  • 1School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan 610074 P.R. China.

Journal of Inequalities and Applications
|February 3, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces robust efficient solutions for multiobjective linear programs with uncertain objective coefficients. These solutions can be found by solving deterministic optimization problems, simplifying complex uncertainty analysis.

Keywords:
multiobjective linear programsrobust efficient solutionsscalarizationuncertainty sets

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Area of Science:

  • Operations Research
  • Optimization Theory

Background:

  • Multiobjective linear programming (MOLP) problems involve optimizing multiple conflicting objectives simultaneously.
  • Real-world applications often face uncertainty in objective function coefficients.

Purpose of the Study:

  • To introduce and define the concept of robust efficient solutions for uncertain multiobjective linear programming (UMOLP) problems.
  • To develop methods for computing these robust efficient solutions.

Main Methods:

  • The study utilizes two scalarization techniques: the weighted sum method and the epsilon-constraint method.
  • These methods are applied to transform the UMOLP problem into deterministic optimization problems.

Main Results:

  • The research establishes that robust efficient solutions for UMOLP with ellipsoidal and general norm uncertainty sets can be computed.
  • The computation relies on solving equivalent deterministic optimization problems.

Conclusions:

  • The proposed approach provides a tractable method for finding robust efficient solutions in the presence of uncertainty.
  • This work contributes to the robust optimization field by offering practical computational strategies for MOLP.