论文标题
使用激活处理程序处理整数编程中的子对称性
Handling Sub-symmetry in Integer Programming using Activation Handlers
论文作者
论文摘要
可以利用整数程序(IP)中的对称性(IPS)以减少解决时间。通常只处理原始IP的对称性,但是在分支结合的树的某些节点上可能会出现新的对称性。虽然可以轻松地使用对称处理不平等(SHIS)来处理原始对称性,但处理后来引起的亚对称性更为复杂。为了处理亚符号,最近已提出添加由辅助变量激活的shis。但是,这可能会大大增加IP的大小,因为所有子符号都需要明确建模。作为替代方案,我们提出了一个新的框架,用于普遍激活SHIS,所谓的激活处理程序。该框架允许直接实现检查活动子对称的例程,从而消除了对辅助变量的需求。特别是,激活处理程序可以激活比SHIS更强大的对称处理技术。我们表明我们的方法是灵活的,并在多重门单位,单位承诺和图形着色问题中进行了应用。数值结果表明,现有的亚对称处理方法的性能有了很大的改善。
Symmetry in integer programs (IPs) can be exploited in order to reduce solving times. Usually only symmetries of the original IP are handled, but new symmetries may arise at some nodes of the branch-and-bound tree. While symmetry-handling inequalities (SHIs) can easily be used to handle original symmetries, handling sub-symmetries arising later on is more intricate. To handle sub-symmetries, it has recently been proposed to add SHIs that are activated by auxiliary variables. This, however, may increase the size of the IP substantially as all sub-symmetries need to be modeled explicitly. As an alternative, we propose a new framework for generically activating SHIs, so-called activation handlers. This framework allows for a direct implementation of routines that check for active sub-symmetries, eliminating the need for auxiliary variables. In particular, activation handlers can activate symmetry-handling techniques that are more powerful than SHIs. We show that our approach is flexible, with applications in the multiple-knapsack, unit commitment, and graph coloring problems. Numerical results show a substantial performance improvement on the existing sub-symmetry-handling methods.