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Inverse optimization for multi-objective linear programming.

Mostafa Naghavi1, Ali Asghar Foroughi1, Masoud Zarepisheh2

  • 1Department of Mathematics, University of Qom, Qom, Iran.

Optimization Letters
|June 10, 2022
PubMed
Summary
This summary is machine-generated.

This study extends inverse optimization to multi-objective linear programming, seeking minimal changes to achieve Pareto optimality. The approach tackles a non-convex problem by solving a series of convex subproblems.

Keywords:
EfficiencyInverse optimizationLinear programmingMulti-objective linear programming

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Area of Science:

  • Operations Research
  • Mathematical Optimization
  • Multi-objective Optimization

Background:

  • Inverse optimization typically focuses on single-objective problems.
  • Extending inverse optimization to multi-objective linear programming (MOLP) is a significant challenge.
  • The goal is to find the minimal problem modifications to render a given solution Pareto optimal.

Purpose of the Study:

  • To generalize inverse optimization for multi-objective linear programming.
  • To address the challenge of making a feasible solution weakly Pareto optimal with minimal cost.
  • To develop a method for solving the resulting non-convex optimization problem.

Main Methods:

  • The paper formulates the problem as finding the least modifications to achieve weak Pareto optimality.
  • It identifies special characteristics of this non-convex problem.
  • The non-convex problem is decomposed into a series of convex optimization problems for solution.

Main Results:

  • A method is proposed for inverse optimization in the context of multi-objective linear programming.
  • The generalization successfully replaces single-objective optimality with Pareto optimality.
  • The non-convex nature of the generalized problem is addressed through a series of convex problems.

Conclusions:

  • The proposed method effectively generalizes inverse optimization to multi-objective linear programming.
  • The approach provides a tractable way to solve inverse multi-objective optimization problems.
  • This work offers a new perspective on understanding and modifying multi-objective linear programs.