A computational study of cutting-plane methods for multi-stage stochastic integer programs

TL;DR

This paper conducts a computational analysis of cutting-plane algorithms for multi-stage stochastic mixed-integer programming, comparing Benders', Integer L-shaped, and Lagrangian cuts, and proposing an enhancement strategy for efficiency.

Contribution

It reveals the relationship between Integer L-shaped cuts and Lagrangian dual solutions and introduces an alternating evaluation strategy to improve computational efficiency.

Findings

Integer L-shaped cuts are optimal solutions of the Lagrangian dual.

The proposed enhancement reduces the computational time of cut generation.

Preliminary results show improved performance on real-world problems.

Abstract

We report a computational study of cutting plane algorithms for multi-stage stochastic mixed-integer programming models with the following cuts: (i) Benders', (ii) Integer L-shaped, and (iii) Lagrangian cuts. We first show that Integer L-shaped cuts correspond to one of the optimal solutions of the Lagrangian dual problem, and, therefore, belong to the class of Lagrangian cuts. To efficiently generate these cuts, we present an enhancement strategy to reduce time-consuming exact evaluations of integer subproblems by alternating between cuts derived from the relaxed and exact computation. Exact evaluations are only employed when Benders' cut from the relaxation fails to cut off the incumbent solution. Our preliminary computational results show the merit of this approach on multiple classes of real-world problems.