Abstract In this paper, we consider symmetric binary programs that contain set packing, partitioning, or covering inequalities. To handle symmetries as well as set packing, partitioning, or covering constraints simultaneously, we introduce constrained symresacks which are the convex hulls of all binary points that are lexicographically not smaller than their image w.r.t. a coordinate permutation and which fulfill packing, partitioning, or covering constraints. We show that linear optimization problems over constrained symresacks can be solved in cubic time. Furthermore, we derive complete linear descriptions of constrained symresacks for particular classes of symmetries. These inequalities can then be used as strong symmetry handling cutting planes in a branch-and-bound procedure. Numerical experiments show that we can benefit from incorporating set packing, partitioning, or covering constraints into symmetry handling inequalities.

中文翻译：

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包装、分隔和覆盖symresacks

摘要 在本文中，我们考虑包含集合打包、分区或覆盖不等式的对称二进制程序。为了同时处理对称性以及设置打包、分区或覆盖约束，我们引入了受约束的 symresacks，它是所有二进制点的凸包，这些二进制点在字典上不小于它们的图像 wrt 坐标排列，并满足打包、分区或覆盖约束。我们表明可以在三次时间内解决受约束的 symresacks 上的线性优化问题。此外，我们推导出了特定对称类的约束对称袋的完整线性描述。然后，这些不等式可以用作分支定界过程中的强对称处理切割平面。