Local Branching Relaxation Heuristics for Integer Linear Programs

TL;DR

This paper introduces LB-RELAX heuristics that leverage LP relaxations to efficiently select neighborhoods in Local Branching for ILPs, achieving faster solutions with state-of-the-art performance.

Contribution

It proposes LB-RELAX heuristics that improve the efficiency of Local Branching in ILP by using LP relaxations for neighborhood selection.

Findings

LB-RELAX achieves similar effectiveness as LB but faster.

LB-RELAX provides state-of-the-art anytime performance on ILP benchmarks.

The heuristics are applicable to a wide range of combinatorial optimization problems.

Abstract

Large Neighborhood Search (LNS) is a popular heuristic algorithm for solving combinatorial optimization problems (COP). It starts with an initial solution to the problem and iteratively improves it by searching a large neighborhood around the current best solution. LNS relies on heuristics to select neighborhoods to search in. In this paper, we focus on designing effective and efficient heuristics in LNS for integer linear programs (ILP) since a wide range of COPs can be represented as ILPs. Local Branching (LB) is a heuristic that selects the neighborhood that leads to the largest improvement over the current solution in each iteration of LNS. LB is often slow since it needs to solve an ILP of the same size as input. Our proposed heuristics, LB-RELAX and its variants, use the linear programming relaxation of LB to select neighborhoods. Empirically, LB-RELAX and its variants compute as effective neighborhoods as LB but run faster. They achieve state-of-the-art anytime performance on several ILP benchmarks.