For several decades the dominant techniques for integer linear programming have been branching and cutting planes. Recently, several authors have developed core point methods for solving symmetric integer linear programs (ILPs). An integer point is called a core point if its orbit polytope is lattice-free. It has been shown that for symmetric ILPs, optimizing over the set of core points gives the same answer as considering the entire space. Existing core point techniques rely on the number of core points (or equivalence classes) being finite, which requires special symmetry groups. In this paper we develop some new methods for solving symmetric ILPs (based on outer approximations of core points) that do not depend on finiteness but are more efficient if the group has large disjoint cycles in its set of generators.

翻译：几十年来，整数线性规划的主流技术一直是分支定界法与割平面法。近年来，多位学者提出了求解对称整数线性规划（ILP）的核心点方法。若一个整数点的轨道多面体无格点，则称该点为核心点。研究表明，对于对称ILP，在核心点集上优化与在全空间上优化结果相同。现有核心点技术依赖于核心点（或等价类）的有限性，这需要特殊的对称群结构。本文提出了若干基于核心点外部逼近的新方法用于求解对称ILP，这些方法不依赖有限性条件，但若群生成元集合中存在大型不相交循环，其效率更高。