Data-Driven Approaches for Large-Scale Optimization

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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.**