Inverse Mixed Integer Optimization: Polyhedral Insights and Trust Region Methods

TL;DR

This paper advances inverse optimization for mixed integer linear problems by providing new theoretical insights and algorithms, significantly improving solution capabilities for large and complex instances.

Contribution

It introduces a general characterization of optimality conditions and develops cutting plane algorithms tailored for inverse mixed integer linear optimization problems.

Findings

Algorithms outperform existing methods on large, difficult instances

New optimality conditions enable more efficient inverse problem solving

Substantial computational improvements demonstrated in experiments

Abstract

Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision-making. In this paper, we present a new set of theoretical insights and algorithms for the general class of inverse mixed integer linear optimization problems. Specifically, a general characterization of optimality conditions is established and leveraged to design new cutting plane solution algorithms. Through an extensive set of computational experiments, we show that our methods provide substantial improvements over existing methods in solving the largest and most difficult instances to date.