Local Branching Relaxation Heuristics for Integer Linear Programs

Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learning

“…Adaptive Neighborhood Size Adaptive methods are commonly used to set the neighborhood size k t in previous work (Sonnerat et al, 2021;Huang et al, 2022a). The initial neighborhood size k 0 is set to a constant or a fraction of the number of variables.…”

“…The initial neighborhood size k 0 is set to a constant or a fraction of the number of variables. In this paper, we consider the following adaptive method (Huang et al, 2022a): in iteration t, if LNS finds an improved solution, we let k t+1 = k t , otherwise k t+1 = min{γ • k t , β • n} where γ > 1 is a constant and we upper bound k t to a constant fraction β < 1 of the number of variables to make sure the sub-ILP is not too large (thus, too difficult) to solve. Adaptively setting k t helps LNS escape local minima by expanding the search neighborhood when it fails to improve the solution.…”

“…Liu et al (2022) use ML to tune the runtime limit and neighborhood sizes for LB. Huang et al (2022a) propose LB-RELAX to select variables by solving the LP relaxation of LB.…”

“…(3) LB-RELAX (Huang et al, 2022a): LNS which selects the neighborhood with the LB-RELAX heuristics; (4) IL-LNS (Sonnerat et al, 2021); (5) RL-LNS (Wu et al, 2021). We compare with two more baselines in Appendix.…”

“…On the other hand, Large Neighborhood Search (LNS) has recently been shown to find high quality solutions much faster than BnB for large ILP instances (Song et al, 2020;Wu et al, 2021;Sonnerat et al, 2021;Huang et al, 2022a). LNS starts from an initial solution (i.e., a feasible assignment of values to variables) and then improves the current best solution by iteratively picking a subset of variables to reoptimize while leaving others fixed.…”