Benders Decomposition Using Graph Modeling and Multi-Parametric Programming
Parth Brahmbhatt, David L. Cole, Victor M. Zavala, Styliani Avraamidou
TL;DR
This paper introduces a new framework for accelerating Benders decomposition using graph modeling and multiparametric programming surrogates to improve performance and interpretability in solving complex optimization problems.
Contribution
The novel framework combines graph-theoretic modeling with multiparametric programming surrogates to replace subproblem solves with fast evaluations in Benders decomposition.
Findings
Using mp surrogates achieves substantial speedups in subproblem solve time while preserving convergence guarantees.
The framework enables solution analysis and interpretability through mp critical region tracking.
The approach overcomes scalability issues of mp and supports heterogeneous subproblems with a unified structure.
Abstract
Benders decomposition is a widely used method for solving large and structured optimization problems, but its performance is affected by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating Benders decomposition. Specifically, we express the problem structure by using a graph-theoretic modeling abstraction in which nodes represent optimization subproblems and edges represent connectivity between subproblems. A key innovation of our approach is that we embed multiparametric programming (mp) surrogates for node subproblems, which maps the exact analytical map of the subproblem solution space. The use of mp surrogates allows us to replace subproblem solves with fast look-ups and function evaluations for primal and dual variables during the iterative Benders process. We formally show the equivalence between classical Benders cuts and…
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Taxonomy
TopicsAdvanced Multi-Objective Optimization Algorithms · Constraint Satisfaction and Optimization · Risk and Portfolio Optimization