In this paper we compare two new binary linear formulations to a standard quadratic binary program for the gray pattern problem and solved all three by the Gurobi solver. One formulation performed significantly better and obtained seven optimal solutions that were not proven optimal before. It is interesting that the formulation that performed best is based on significantly more variables and constraints.

中文翻译：

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为几种灰度模式实例找到最佳解决方案

在本文中，我们将两个新的二进制线性公式与一个用于灰色图案问题的标准二次二进制程序进行了比较，并通过Gurobi求解器解决了所有这三个问题。一种配方的性能要好得多，并获得了七个以前从未被证明是最佳的最佳解决方案。有趣的是，表现最佳的配方是基于明显更多的变量和约束条件。