We propose an optimization framework which integrates decision diagrams (DDs) and integer linear programming (ILP) to solve combinatorial optimization problems. The hybrid DD-ILP approach explores the solution space based on a recursive compilation of relaxed DDs and incorporates ILP calls to solve subproblems associated with DD nodes. The selection of DD nodes to be explored by ILP technology is a significant component of the approach. We show how supervised machine learning can be useful to detect, on-the-fly, a subproblem structure for ILP technology. We use the maximum independent set problem as a case study. Computational experiments show that, in presence of suitable problem structure, the integrated DD-ILP approach can exploit complementary strengths and improve upon the performance of both a stand-alone DD solver and an ILP solver in terms of solution time and number of solved instances.

中文翻译：

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集成整数规划和决策图搜索树及其在最大独立集问题中的应用

我们提出了一个优化框架，该框架集成了决策图（DDs）和整数线性规划（ILP）以解决组合优化问题。混合DD-ILP方法基于递归DD的递归编译来探索解决方案空间，并结合ILP调用来解决与DD节点关联的子问题。ILP技术要探索的DD节点的选择是该方法的重要组成部分。我们展示了有监督的机器学习如何对即时检测ILP技术的子问题结构有用。我们使用最大独立集问题作为案例研究。计算实验表明，在存在适当问题结构的情况下，