使用并行回火求解整数线性规划
Solving Integer Linear Programming with Parallel Tempering
AI总结：
提出一种无求解器、基于采样的整数线性规划优化框架，利用局部平衡提议和并行回火技术直接探索离散可行区域，在多个基准上优于或匹敌经典求解器。
摘要：
整数线性规划（ILP）作为建模广泛组合优化问题的通用框架，通常由复杂的精确求解器或启发式方法求解。虽然基于学习的方法最近显示出有效性，但它们存在对分布外实例泛化能力差以及对外部求解器的固有依赖。在这项工作中，我们提出了一种无求解器、基于采样的ILP优化框架，无需训练或外部求解器即可直接探索离散可行区域。利用ILP的线性结构，我们采用局部平衡提议构建转移核，从而避免梯度近似。为了克服ILP能量景观的高度多模态性，我们集成了并行回火。除了标准的温度回火，我们还引入了惩罚回火，它在保持可行解目标景观的同时调节约束障碍。实验上，我们的方法在所有四个基准上持续优于SCIP，在200秒预算内匹配或超过Gurobi在四个任务中的两个，并且比基于学习的方法对分布偏移具有更强的鲁棒性。此外，在MIPLIB 2017实例上，我们的框架无需任何问题特定调优即可与经典求解器保持竞争力。
英文摘要：
Integer Linear Programming (ILP) serves as a versatile framework for modeling a wide range of combinatorial optimization problems, typically addressed by sophisticated exact solvers or heuristics. While learning-based approaches have recently shown their effectiveness, they suffer from poor generalization to out-of-distribution instances and inherent dependence on external solvers. In this work, we propose a solver-free, sampling-based optimization framework for ILP that directly explores discrete feasible regions without training or external solvers. Exploiting the linear structure of ILP, we employ a Locally-Balanced Proposal to construct a transition kernel, thereby avoiding the gradient approximation. To overcome the highly multimodal nature of ILP energy landscapes, we integrate Parallel Tempering. In addition to standard temperature tempering, we introduce penalty tempering, which modulates constraint barriers while preserving the objective landscape over feasible solutions. Empirically, our method consistently outperforms SCIP across all four benchmarks, matches or exceeds Gurobi on two of four tasks within a 200-second budget, and is substantially more robust to distribution shift than learning-based methods. Furthermore, on MIPLIB 2017 instances, our framework remains competitive with classical solvers without any problem-specific tuning.
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