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  3. Benders Decomposition Using Graph Modeling And Multi-parametric Programming.

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Benders Decomposition Using Graph Modeling and Multi-Parametric Programming.

Parth Brahmbhatt1, David L Cole1, Victor M Zavala1,2

  • 1Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States.

Industrial & Engineering Chemistry Research
|November 17, 2025

View abstract on PubMed

Summary
This summary is machine-generated.

We introduce a new framework to accelerate Benders decomposition using graph modeling and multiparametric programming (mp) surrogates. This approach significantly speeds up subproblem solving while maintaining solution accuracy for optimization problems.

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Area of Science:

  • Operations Research
  • Computational Optimization

Background:

  • Benders decomposition is effective for large optimization problems but hindered by repeated subproblem solves.
  • Existing methods struggle with scalability and interpretability.

Purpose of the Study:

  • To develop a flexible and modular framework for accelerating Benders decomposition.
  • To enhance the efficiency and interpretability of solving structured optimization problems.

Main Methods:

  • Employed a graph-theoretic abstraction to model problem structure, representing subproblems as nodes and connections as edges.
  • Integrated multiparametric programming (mp) surrogates for subproblems to replace iterative solves with fast look-ups.
  • Demonstrated equivalence between classical Benders cuts and mp-derived cuts.
  • Implemented the framework in the open-source PlasmoBenders.jl package.

    • Main Results:

    • Achieved substantial speedups in subproblem solve times using mp surrogates.
    • Preserved the convergence guarantees of Benders decomposition.
    • Enabled enhanced solution analysis and interpretability through mp critical region tracking.
    • Successfully applied to a two-stage stochastic programming problem for capacity expansion decisions.

    Conclusions:

    • Combining surrogate modeling with graph modeling provides an extensible foundation for structure-exploiting decomposition.
    • The proposed approach overcomes scalability issues associated with multiparametric programming.
    • MP surrogates offer a unifying framework for representing heterogeneous subproblems with a homogeneous structure.