arXiv subjects

Ted Ralphs

Publications and source records attributed to Ted Ralphs.

3 recordsLinked to original sources

arXiv2025

Parametric Disjunctive Cuts for Sequences of Mixed Integer Linear Optimization Problems

Many applications require solving sequences of related mixed-integer linear programs. We introduce a class of parametric disjunctive inequalities (PDIs), obtained by reusing the disjunctive proofs of optimality from prior solves to construct cuts valid for perturbed instances. We describe several methods of generating such cuts that navigate the tradeoff between computational expense and strength. We provide sufficient conditions under which PDIs support the disjunctive hull and a tightening step that guarantees support when needed. On perturbed instances from MIPLIB 2017, augmenting branch-and-cut with PDIs substantially improves performance, reducing total solve times on the majority of challenging cases.

math.OC↗

arXiv2025

Counterfactual Explanations for Integer Optimization Problems

Counterfactual explanations (CEs) offer a human-understandable way to explain decisions by identifying specific changes to the input parameters of a base or present model that would lead to a desired change in the outcome. For optimization models, CEs have primarily been studied in limited contexts and little research has been done on CEs for general integer optimization problems. In this work, we address this gap. We first show that the general problem of constructing a CE is $\Sigma_2^p$-complete even for binary integer programs with just a single mutable constraint. Second, we propose solution algorithms for several of the most tractable special cases: (i) mutable objective parameters, (ii) a single mutable constraint, (iii) mutable right-hand-side, and (iv) all input parameters can be modified. We evaluate our approach using classical knapsack problem instances, focusing on cases with mutable constraint parameters. Additionally, we present experiments on the resource constrained shortest path problem.

math.OC↗

arXiv2018

Exploring the Numerics of Branch-and-Cut for Mixed Integer Linear Optimization

We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the numerical conditioning of the LP relaxations resulting from the branching and cutting operations can be effectively predicted and whether such predictions can be used to make better algorithmic choices. In a first step towards this goal, we discuss here the numerical behavior of an existing solver in order to determine whether our intuitive understanding of this behavior is correct.

math.OC↗