Integer Linear Programs (ILPs) are powerful tools for modeling and solving a large number of combinatorial optimization problems. Recently, it has been shown that Large Neighborhood Search (LNS), as a heuristic algorithm, can find high quality solutions to ILPs faster than Branch and Bound. However, how to find the right heuristics to maximize the performance of LNS remains an open problem. In this paper, we propose a novel approach, CL-LNS, that delivers state-of-the-art anytime performance on several ILP benchmarks measured by metrics including the primal gap, the primal integral, survival rates and the best performing rate. Specifically, CL-LNS collects positive and negative solution samples from an expert heuristic that is slow to compute and learns a new one with a contrastive loss. We use graph attention networks and a richer set of features to further improve its performance.

翻译：整数线性规划是建模和求解大量组合优化问题的强大工具。近期研究表明，大邻域搜索作为一种启发式算法，能比分支定界法更快找到整数线性规划的高质量解。然而，如何找到合适的启发式策略以最大化大邻域搜索的性能仍是开放问题。本文提出一种名为CL-LNS的新方法，在多个整数线性规划基准测试中，通过原始间隙、原始积分、生存率和最优解占比等指标衡量，实现了当前最优的任意时间性能。具体而言，CL-LNS从计算缓慢的专家启发式中收集正负解样本，并利用对比损失函数学习新的启发式策略。我们采用图注意力网络及更丰富的特征集进一步提升其性能。