论文标题

MILP的启发式增强分支机构求解器的设计和实施

Design and Implementation of an Heuristic-Enhanced Branch-and-Bound Solver for MILP

论文作者

Silva, Warley Almeida, Bobbio, Federico, Caye, Flore, Liu, Defeng, Pepin, Justine, Perreault-Lafleur, Carl, St-Arnaud, William

论文摘要

我们提出了为2022年MIP竞争开发的混合整数程序(MIP)的求解器。鉴于竞争规则确定的计算时间限制了10分钟,我们的方法着重于找到可行的解决方案,并通过分支和结合的算法改进它。竞争的另一个规则允许最多使用8个线程。每个线程都有不同的原始启发式,该启发式是由超参数调整的,以找到可行的解决方案。在每个线程中,一旦找到了可行的解决方案,我们就会停止,然后使用嵌入本地搜索启发式的分支和结合方法来改善现有解决方案。我们实施的潜水启发式方法的三种变体设法为培训数据集的10个实例找到了可行的解决方案。这些启发式方法是我们实施的启发式方法中表现最好的。我们的分支机构和结合算法在培训数据集的一小部分中有效,并且它设法为实例找到了可行的解决方案,我们无法通过潜水启发式方法解决。总体而言,当用广泛的计算能力实施时,我们的组合方法可以在时间限制内解决训练数据集的19个问题中的11个。我们对MIP竞赛的提交被授予了“杰出的学生提交”荣誉奖。

We present a solver for Mixed Integer Programs (MIP) developed for the MIP competition 2022. Given the 10 minutes bound on the computational time established by the rules of the competition, our method focuses on finding a feasible solution and improves it through a Branch-and-Bound algorithm. Another rule of the competition allows the use of up to 8 threads. Each thread is given a different primal heuristic, which has been tuned by hyper-parameters, to find a feasible solution. In every thread, once a feasible solution is found, we stop and we use a Branch-and-Bound method, embedded with local search heuristics, to ameliorate the incumbent solution. The three variants of the Diving heuristic that we implemented manage to find a feasible solution for 10 instances of the training data set. These heuristics are the best performing among the heuristics that we implemented. Our Branch-and-Bound algorithm is effective on a small portion of the training data set, and it manages to find an incumbent feasible solution for an instance that we could not solve with the Diving heuristics. Overall, our combined methods, when implemented with extensive computational power, can solve 11 of the 19 problems of the training data set within the time limit. Our submission to the MIP competition was awarded the "Outstanding Student Submission" honorable mention.

扫码加入交流群

加入微信交流群

微信交流群二维码

扫码加入学术交流群,获取更多资源