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A novel approach based on preference-based index for interval bilevel linear programming problem.

Aihong Ren1, Yuping Wang2, Xingsi Xue3

  • 1Department of Mathematics, Baoji University of Arts and Sciences, Baoji, 721013 China.

Journal of Inequalities and Applications
|June 6, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for interval bilevel linear programming problems with interval coefficients. The approach handles uncertainty and decision-maker preferences to find preference-based optimal solutions.

Keywords:
bilevel programmingestimation of distribution algorithminterval numberpreference-based index

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Area of Science:

  • Operations Research
  • Optimization Theory

Background:

  • Bilevel linear programming problems with interval coefficients present significant challenges due to inherent uncertainty.
  • Existing methods may not adequately address the preferences of decision-makers in interval environments.

Purpose of the Study:

  • To develop a novel methodology for solving interval bilevel linear programming problems with interval coefficients in objective functions and constraints.
  • To incorporate decision-maker preferences into the optimization process for interval programming.

Main Methods:

  • Conversion of the original problem to an interval bilevel programming problem with interval coefficients in objective functions using normal variation and chance-constrained programming.
  • Definition of preference level based on a preference-based index to quantify decision-maker preferences for interval objective functions.
  • Construction of a deterministic bilevel programming problem using preference levels and order relations.
  • Introduction of the concept of a preference δ-optimal solution.
  • Solving the deterministic nonlinear bilevel problem using an estimation of distribution algorithm.

Main Results:

  • The proposed methodology effectively handles the uncertainty associated with interval numbers in bilevel linear programming.
  • A preference-based deterministic model is successfully constructed, allowing for the incorporation of diverse decision-maker preferences.
  • The estimation of distribution algorithm proves effective in solving the resulting complex nonlinear bilevel problem.
  • Numerical examples validate the effectiveness and practical applicability of the developed approach.

Conclusions:

  • The presented method offers a robust framework for addressing interval bilevel linear programming problems with interval coefficients.
  • The incorporation of preference levels provides a more nuanced and realistic approach to decision-making in uncertain environments.
  • The study demonstrates a viable computational strategy for solving these complex optimization problems.