Local Branching Relaxation Heuristics for Integer Linear Programs
This work addresses a bottleneck in combinatorial optimization for practitioners, though it is incremental as it builds on existing Local Branching methods.
The paper tackled the problem of slow neighborhood selection in Large Neighborhood Search for integer linear programs by proposing LB-RELAX heuristics that use linear programming relaxation, achieving state-of-the-art anytime performance on benchmarks with faster runtime while maintaining effectiveness.
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.