We present an approach to couple the resolution of Combinatorial Optimization problems with methods from Machine Learning. Specifically, our study is framed in the context where a reference discrete optimization problem is given and there exist data for many variations of such reference problem (historical or simulated) along with their optimal solution. Those variations can be originated by disruption but this is not necessarily the case. We study how one can exploit these to make predictions about an unseen new variation of the reference instance.

The methodology is composed by two steps. We demonstrate how a classifier can be built from these data to determine whether the solution to the reference problem still applies to a perturbed instance. In case the reference solution is only partially applicable, we build a regressor indicating the magnitude of the expected change, and conversely how much of it can be kept for the perturbed instance. This insight, derived from a priori information, is expressed via an additional constraint in the original mathematical programming formulation.

We present the methodology through an application to the classical facility location problem and we provide an empirical evaluation and discuss the benefits, drawbacks and perspectives of such an approach.

Although it cannot be used in a black-box manner, i.e., it has to be adapted to the specific application at hand, we believe that the approach developed here is general and explores a new perspective on the exploitation of past experience in Combinatorial Optimization.

我们提出了一种将组合优化问题的解决方案与机器学习方法相结合的方法。具体而言，我们的研究是在给定参考离散优化问题的情况下进行的，并且存在有关该参考问题（历史或模拟）的许多变体以及它们的最优解的数据。这些变化可能是由中断引起的，但不一定是这种情况。我们研究了如何利用这些来对参考实例的未知新变化做出预测。

该方法由两个步骤组成。我们演示了如何从这些数据构建分类器，以确定对参考问题的解决方案是否仍然适用于受干扰的实例。在参考解决方案仅部分适用的情况下，我们将建立一个回归器来指示预期变化的幅度，反之则可以为受干扰的实例保留多少变化。从先验信息中得出的这种见解是通过原始数学编程公式中的附加约束来表达的。

我们通过对经典设施选址问题的应用介绍了该方法，并提供了实证评估并讨论了这种方法的优点，缺点和观点。

尽管不能以黑匣子的方式使用它，即必须使其适应当前的特定应用，但我们认为此处开发的方法是通用的，并探索了利用组合优化中过去经验的新观点。