arXiv:2412.09444cs.LG2024-12AAAI被引 6

用遗传编程自动生成高效分支定界搜索策略,速度快且性能更优。

Search Strategy Generation for Branch and Bound Using Genetic Programming

  • 用遗传编程自动演化节点评估函数,生成智能搜索策略。
  • 在多种难题上平均提速11.3%,仅比最优基线慢2%。
  • 适合需要快速、自适应搜索策略的优化求解场景。

分支定界(B&B)是整数规划中的精确方法,通过递归分割搜索空间形成树结构。确定树中下一步探索的子问题——即搜索策略——至关重要。传统手工设计的启发式方法对所有问题类别效果有限,而基于神经网络的方法虽更智能但计算开销大。本文提出GP2S(遗传编程生成搜索策略),一种自动构建B&B搜索策略启发式的新机器学习方法,旨在实现智能决策的同时保持轻量计算。我们将策略定义为一个函数,结合节点与问题特征评估节点质量,再基于此进行最佳优先搜索。利用遗传编程算法探索策略空间,选取在训练集上表现最佳的策略。实验对比了SCIP标准方法、基于图神经网络的近期方法及手工启发式。首次评估涵盖三类原始难题,在与训练集相似及更大规模实例上测试。本方法最慢仅比最优基线慢2%,且始终优于SCIP,平均提速11.3%。此外,在MIPLIB 2017数据集上,从不同实例子集生成多个启发式,其在15倍更多实例、15倍时间限制下,7/10情况下超越SCIP平均表现,部分方法在可行解数量或最优性间隙方面领先多数实验。

原文摘要 · Abstract (English)

Branch-and-Bound (B\&B) is an exact method in integer programming that recursively divides the search space into a tree. During the resolution process, determining the next subproblem to explore within the tree-known as the search strategy-is crucial. Hand-crafted heuristics are commonly used, but none are effective over all problem classes. Recent approaches utilizing neural networks claim to make more intelligent decisions but are computationally expensive. In this paper, we introduce GP2S (Genetic Programming for Search Strategy), a novel machine learning approach that automatically generates a B\&B search strategy heuristic, aiming to make intelligent decisions while being computationally lightweight. We define a policy as a function that evaluates the quality of a B\&B node by combining features from the node and the problem; the search strategy policy is then defined by a best-first search based on this node ranking. The policy space is explored using a genetic programming algorithm, and the policy that achieves the best performance on a training set is selected. We compare our approach with the standard method of the SCIP solver, a recent graph neural network-based method, and handcrafted heuristics. Our first evaluation includes three types of primal hard problems, tested on instances similar to the training set and on larger instances. Our method is at most 2\% slower than the best baseline and consistently outperforms SCIP, achieving an average speedup of 11.3\%. Additionally, GP2S is tested on the MIPLIB 2017 dataset, generating multiple heuristics from different subsets of instances. It exceeds SCIP's average performance in 7 out of 10 cases across 15 times more instances and under a time limit 15 times longer, with some GP2S methods leading on most experiments in terms of the number of feasible solutions or optimality gap.

分支定界遗传编程优化求解启发式搜索

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