Adaptive large neighborhood search for mixed integer programming

Abstract

Large Neighborhood Search (LNS) heuristics are among the most powerful but also most expensive heuristics for mixed integer programs (MIP). Ideally, a solver adaptively concentrates its limited computational budget by learning which LNS heuristics work best for the MIP problem at hand. To this end, this work introduces Adaptive Large Neighborhood Search (ALNS) for MIP, a primal heuristic that acts as a framework for eight popular LNS heuristics such as Local Branching and Relaxation Induced Neighborhood Search (RINS). We distinguish the available LNS heuristics by their individual search spaces, which we call auxiliary problems. The decision which auxiliary problem should be executed is guided by selection strategies for the multi armed bandit problem, a related optimization problem during which suitable actions have to be chosen to maximize a reward function. In this paper, we propose an LNS-specific reward function to learn to distinguish between the available auxiliary problems based on successful calls and failures. A second, algorithmic enhancement is a generic variable fixing prioritization, which ALNS employs to adjust the subproblem complexity as needed. This is particularly useful for some LNS problems which do not fix variables by themselves. The proposed primal heuristic has been implemented within the MIP solver SCIP. An extensive computational study is conducted to compare different LNS strategies within our ALNS framework on a large set of publicly available MIP instances from the MIPLIB and Coral benchmark sets. The results of this simulation are used to calibrate the parameters of the bandit selection strategies. A second computational experiment shows the computational benefits of the proposed ALNS framework within the MIP solver SCIP.

UAV-based Receding Horizon Control for 3D Inspection Planning

“…Nevertheless, for some of the configurations of the parameters the proposed approach shows potential for real-time execution, considering that these results have been obtained on a 2GHz laptop computer. It is also worth noting that additional computational savings can be obtained through various heuristics and approximations [39]- [41] which can provide adequate near-optimal MIP solutions in real-time. A more thorough investigation of the real-time performance of the proposed approach and its real-world implemetation will be investigated in future works.…”

Adaptive Anytime Multi-Agent Path Finding Using Bandit-Based Large Neighborhood Search

“…In recent years, MABs have been used as adaptive metacontrollers to tune learning and optimization algorithms on the fly (Schaul et al 2019;Badia et al 2020;Hendel 2022). Besides roulette wheel selection, UCB1 and ϵ-greedy are commonly used for destroy heuristic selection in LNS in the context of mixed integer programming, vehicle routing, and scheduling problems with fixed neighborhood sizes (Chen et al 2016;Chen and Bai 2018;Chmiela et al 2023).…”

Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learning

“…Recently, an adaptive LNS primal heuristic (Hendel, 2022) has been proposed to combine the power of these heuristics, where it essentially solves a multi armed bandit problem to choose which heuristic to apply.…”