Data-Driven Approaches for Large-Scale Optimization

面对十多年来收集的海量数据，交通和电信等不同行业的公司都在寻求将这些数据转换为信息，以创造竞争优势。最重要的是，他们希望使用它来评估、优化和验证其运营、流程和业务模型。随着数据的可用性和计算能力的提高，有机会构建直接利用数据的优化模型。 然而，合并海量数据会带来大量的优化挑战，这是当前方法无法处理的。启发式方法可以解决这些问题，但不能保证。数据挖掘技术可用于突出可用于构建良好解决方案的数据的特定方面。Data Analytics提供了各种快速、高效的技术来实现这一目的。它们中的一些可以通过软件库(如R或Python)轻松访问，并在实践中表现良好。 目前的提案利用这些技术的效率来设计解决方案，并对解决方案提供质量保证。例如，优化物流网络的设计将涉及对配送中心的位置和需求分配的决定。通过挖掘随时间推移的需求数据，可以确定最有可能成为配送中心最佳位置的需求集群。通过这样做，我们解决了物流网络设计的第一部分问题。第二部分，将个人需求分配给配送中心，可以基于启发式方法或通过解决更容易的优化问题来完成。最后，给出了一个可行的网络设计方案。剩下的问题是，它是否是最好的。这一步骤涉及使用高级优化技术，如逆优化，以设计出与解进行比较的下限。如果发现它远不是最优的，则执行另一次迭代。同样的方法将适用于基于呼叫数据的电信网络、应急响应系统或呼叫中心的设计。 预计该提议将开启解决大规模和超大规模优化问题的新的研究方向，并为解决一些极具挑战性的实际问题打开大门。如果挖掘得当，数据将揭示这些特征。 我们用这种方法解决仓储行业混合情况下的码垛问题的经验非常有希望。问题的实质是如何根据客户需求以最佳方式形成托盘。我们挖掘数据以揭示具有共同特征的框，这些框可以组合在一起形成层。然后将各层堆叠起来，形成托盘。

Faced with massive amounts of data that has been collected for over a decade, companies from a variety of industries, such as transportation and telecommunication, are looking to transform this data to information in order to create competitive advantage. Most importantly, they are hoping to use it to assess, optimize, and validate their operations, processes, and business models. With data availability and the improvements in computational power, there is an opportunity to build optimization models that make direct use of the data. Incorporating massive data, however, introduces substantial optimization challenges that cannot be handled by current methods. Heuristics can tackle these problems, but come with no guarantee. Data mining techniques can be used to highlight specific aspects of the data that can be used to construct good solutions. Data Analytics offer a variety of quick and efficient techniques that can serve this purpose. Some of them are easily accessible through software libraries such as R or Python, and perform well in practice. The current proposal exploits the efficiency of these techniques to devise solutions that come with a quality guarantee on the solution. For example, optimizing the design of a logistics network will involve decisions on the location of distribution centres and the assignment of demand to them. By mining demand data over time, it could be possible to identify demand clusters that would most probably be the optimal location for distribution centres. By doing so, we have solved the first part of the logistics network design problem. The second part, the assignment of individual demand to the distribution centres, can be done based on a heuristic or by solving an easier optimization problem. At the end, a feasible network design is achieved. What remains is whether it is the best. This step involves the use of advanced optimization techniques such as inverse optimization to devise a lower bound against which the solution is compared. If it is revealed that it is far from being optimal, an other iteration is performed. This same approach would apply to the design of a telecommunication network, an emergency response system, or a call center based on call data. The proposal is expected to initiate a new research direction in the solution of large and very large-scale optimization problems and to open the door towards solving some of the very challenging practical problems. Data, if mined properly, would reveal these characteristics. Our experience with this approach for the solution of mixed-case palletization problems in the warehousing industry is very promising. The problem is essentially that of optimally forming pallets based on customer demand. We mine data to reveal boxes with common characteristics that could be grouped together to form layers. Layers are then stacked to form pallets.