Symmetry in integer programming causes redundant search and is often handled with symmetry breaking constraints that remove as many equivalent solutions as possible. We propose an algebraic method which allows to generate a random family of polynomial inequalities which can be used as symmetry breakers. The method requires as input an arbitrary base polynomial and a group of permutations which is specific to the integer program. The computations can be easily carried out in any major symbolic computation software. In order to test our approach, we describe a case study on near half-capacity 0-1 bin packing instances which exhibit substantial symmetries. We statically generate random quadratic breakers and add them to a baseline integer programming problem which we then solve with Gurobi. It turns out that simple symmetry breakers, especially combining few variables and permutations, most consistently reduce work time.

翻译：整数规划中的对称性会导致冗余搜索，通常通过对称性破缺约束来处理，以尽可能消除等价解。我们提出一种代数方法，能够生成随机多项式不等式族作为对称性破缺器。该方法以任意基多项式及特定于整数规划的置换群作为输入，计算过程可在任何主流符号计算软件中轻松实现。为验证该方法，我们以具有显著对称性的近半容量0-1装箱问题实例为案例进行研究。通过静态生成随机二次破缺器，将其加入基线整数规划问题后使用Gurobi求解。结果表明，简单的对称性破缺器（特别是结合少量变量与置换的破缺器）能最稳定地减少求解时间。