The optimization computation is an essential transversal branch of operations research which is primordial in many technical fields: transport, finance, networks, energy, learning, etc. In fact, it aims to minimize the resource consumption and maximize the generated profits. This work provides a new method for cost optimization which can be applied either on path optimization for graphs or on binary constraint reduction for Constraint Satisfaction Problem (CSP). It is about the computing of the “transitive closure of a given binary relation with respect to a property.” Thus, this paper introduces the mathematical background for the transitive closure of binary relations. Then, it gives the algorithms for computing the closure of a binary relation according to another one. The elaborated algorithms are shown to be polynomial. Since this technique is of great interest, we show its applications in some important industrial fields.

中文翻译：

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使用高级关系传递闭包将多式联运中的成本旅行减到最少

优化计算是运筹学中必不可少的横向分支，在运输，金融，网络，能源，学习等许多技术领域都是原始的。事实上，它的目的是最大程度地减少资源消耗并最大化产生的利润。这项工作为成本优化提供了一种新方法，该方法可以应用于图的路径优化或约束满足问题（CSP）的二元约束减少。它是关于“给定二进制关系相对于属性的传递闭包”的计算。因此，本文介绍了二元关系的传递闭合的数学背景。然后，给出了用于根据另一关系计算二元关系的闭合的算法。详细的算法显示为多项式。