Exact solution of network flow models with strong relaxations

TL;DR

This paper presents an exact solution framework for MILP models with strong relaxations using network-flow characterization, column generation, and advanced branching, solving many previously open instances.

Contribution

It introduces a novel framework combining network-flow-based column generation and asymmetric branching for solving complex MILP models efficiently.

Findings

Solved numerous open instances to proven optimality

Demonstrated the framework's efficiency through extensive experiments

Achieved significant improvements over existing methods

Abstract

We address the solution of Mixed Integer Linear Programming (MILP) models with strong relaxations that are derived from Dantzig-Wolfe decompositions and allow a pseudo-polynomial pricing algorithm. We exploit their network-flow characterization and provide a framework based on column generation, reduced-cost variable-fixing, and a highly asymmetric branching scheme that allows us to take advantage of the potential of the current MILP solvers. We apply our framework to a variety of cutting and packing problems from the literature. The efficiency of the framework is proved by extensive computational experiments, in which a significant number of open instances could be solved to proven optimality for the first time.