学习处理组合优化中的参数扰动:在设施选址中的应用

IF 2.1 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE EURO Journal on Transportation and Logistics Pub Date : 2020-12-01 DOI:10.1016/j.ejtl.2020.100023
Andrea Lodi , Luca Mossina , Emmanuel Rachelson
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引用次数: 21

摘要

我们提出了一种将组合优化问题的解决与机器学习方法相结合的方法。具体来说,我们的研究是在给定参考离散优化问题的背景下进行的,并且存在此类参考问题(历史或模拟)的许多变化及其最优解的数据。这些变化可能源于颠覆,但事实并非如此。我们研究如何利用这些来预测参考实例的一个看不见的新变化。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,以确定引用问题的解决方案是否仍然适用于受干扰的实例。如果参考解决方案仅部分适用,我们建立一个回归量,指示预期变化的大小,反过来,对于受干扰的实例,它可以保留多少。这种从先验信息中获得的洞察力,通过原始数学规划公式中的附加约束来表达。我们将该方法应用于经典的设施选址问题,并提供了一个实证评估,并讨论了这种方法的优点、缺点和前景。虽然它不能以黑盒方式使用,也就是说,它必须适应手头的特定应用程序,但我们相信这里开发的方法是通用的,并且在利用组合优化中的过去经验方面探索了一个新的视角。
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Learning to handle parameter perturbations in Combinatorial Optimization: An application to facility location

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.

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来源期刊
CiteScore
4.60
自引率
0.00%
发文量
24
审稿时长
129 days
期刊介绍: The EURO Journal on Transportation and Logistics promotes the use of mathematics in general, and operations research in particular, in the context of transportation and logistics. It is a forum for the presentation of original mathematical models, methodologies and computational results, focussing on advanced applications in transportation and logistics. The journal publishes two types of document: (i) research articles and (ii) tutorials. A research article presents original methodological contributions to the field (e.g. new mathematical models, new algorithms, new simulation techniques). A tutorial provides an introduction to an advanced topic, designed to ease the use of the relevant methodology by researchers and practitioners.
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