A computational approach to pivot selection in the LP relaxationof set problems

F.Djannaty; B.Rostamy

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A computational approach to pivot selection in the LP relaxationof set problems

机译：集问题LP松弛中枢轴选择的一种计算方法

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It has long been known to the researchers that choosing a variable having the most negative reduced cost as the entering variable is not the best choice in the simplex method as shown by Harris (1975). Thus, suitable modifications in the pivot selection criteria may enhance the algorithm. Previous efforts such as that by Dantzig and steepest-edge rules for pivot selection are based on finding a unified strategy for entering variable in all linear programming problems. In the present work, a number of strategies for pivot selection in the LP relaxation of the set problems are proposed which consider the specific knowledge of the problem. A significant reduction in the number of iterations is achieved for a set of randomly generated test problems.

机译：研究人员早就知道，选择成本最大的负降低变量作为输入变量并不是单纯形方法的最佳选择，正如Harris（1975）所示。因此，对枢轴选择标准的适当修改可以增强算法。以前的工作（例如Dantzig所做的努力和用于枢轴选择的最陡边规则）都是基于在所有线性编程问题中找到用于输入变量的统一策略。在当前的工作中，提出了一些在LP放松所设置问题中进行枢轴选择的策略，这些策略考虑了该问题的具体知识。对于一组随机生成的测试问题，可以大大减少迭代次数。

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《Advances in decision sciences》 |2006年第4期|共11页
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F.Djannaty; B.Rostamy;
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A computational approach to pivot selection in the LP relaxationof set problems

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