Graph Reduction with Unsupervised Learning in Column Generation: A Routing Application

Column Generation (CG) is a popular method dedicated to enhancing computational efficiency in large scale Combinatorial Optimization (CO) problems. It reduces the number of decision variables in a problem by solving a pricing problem. For many CO problems, the pricing problem is an Elementary Shortest Path Problem with Resource Constraints (ESPPRC). Large ESPPRC instances are difficult to solve to near-optimality. Consequently, we use a Graph neural Network (GNN) to reduces the size of the ESPPRC such that it becomes computationally tractable with standard solving techniques. Our GNN is trained by Unsupervised Learning and outputs a distribution for the arcs to be retained in the reduced PP. The reduced PP is solved by a local search that finds columns with large reduced costs and speeds up convergence. We apply our method on a set of Capacitated Vehicle Routing Problems with Time Windows and show significant improvements in convergence compared to simple reduction techniques from the literature. For a fixed computational budget, we improve the objective values by over 9\% for larger instances. We also analyze the performance of our CG algorithm and test the generalization of our method to different classes of instances than the training data.

Digital Twin Applications in Urban Logistics: An Overview

Urban traffic attributed to commercial and industrial transportation is observed to largely affect living standards in cities due to external effects pertaining to pollution and congestion. In order to counter this, smart cities deploy technological tools to achieve sustainability. Such tools include Digital Twins (DT)s which are virtual replicas of real-life physical systems. Research suggests that DTs can be very beneficial in how they control a physical system by constantly optimizing its performance. The concept has been extensively studied in other technology-driven industries like manufacturing. However, little work has been done with regards to their application in urban logistics. In this paper, we seek to provide a framework by which DTs could be easily adapted to urban logistics networks. To do this, we provide a characterization of key factors in urban logistics for dynamic decision-making. We also survey previous research on DT applications in urban logistics as we found that a holistic overview is lacking. Using this knowledge in combination with the characterization, we produce a conceptual model that describes the ontology, learning capabilities and optimization prowess of an urban logistics digital twin through its quantitative models. We finish off with a discussion on potential research benefits and limitations based on previous research and our practical experience.