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Global Sensitivity Analysis via a Statistical Tolerance Approach.

Stewart Curry1, Ilbin Lee2, Simin Ma1

  • 1H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, 755 Ferst Dr. NW Atlanta, GA 30332.

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|October 2, 2023
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Summary
This summary is machine-generated.

This study introduces a tolerance approach for optimization modeling with uncertain parameters. It develops methods to analyze how simultaneous input variations affect optimal solutions, enhancing sensitivity analysis.

Keywords:
Linear ProgrammingParametric ProgrammingRobustness and Sensitivity AnalysisSensitivity AnalysisTolerance Sensitivity

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Area of Science:

  • Optimization Theory
  • Mathematical Modeling
  • Computational Mathematics

Background:

  • Sensitivity analysis and multiparametric programming are crucial for understanding optimization model behavior under parameter uncertainty.
  • Existing methods often struggle with simultaneous variations in multiple input parameters, especially when these parameters are described by multivariate probability distributions.

Purpose of the Study:

  • To develop a robust framework for sensitivity analysis in optimization when objective and constraint parameters (RIM parameters) vary jointly.
  • To introduce a tolerance approach using principal component analysis for defining confidence sets for random input parameters.
  • To extend the tolerance approach to handle cases with multiple optimal bases within the tolerance region.

Main Methods:

  • Introduction of a tolerance approach based on principal component analysis to define distribution-suited tolerance regions.
  • Extension of the tolerance approach to address multiple optimal bases by studying critical regions.
  • Development of a computational algorithm to identify critical regions within the RIM parameter space that cover a given tolerance region.

Main Results:

  • A novel tolerance approach is proposed for analyzing simultaneous variations in optimization model inputs.
  • Theoretical insights into the geometric properties of critical regions are provided, enhancing the understanding of joint parameter variations.
  • A computational algorithm is presented for finding critical regions relevant to sensitivity analysis.

Conclusions:

  • The proposed framework offers a deeper geometric understanding of critical regions in parametric programming with jointly varying parameters.
  • The developed methods are evaluated through experiments in sensitivity analysis, inventory management model predictive control, and large-scale optimization problems.
  • This work advances the theory and computational methods for sensitivity analysis in optimization under multivariate parameter uncertainty.