Scalable Approaches to Selecting Key Entities in Large Networked Infrastructure Systems

This work aims at bringing advances in discrete optimization algorithms to solving practical engineering problems at scale. Often times, in many engineering design problems, there is a need to select a small set of influential or representative elements from a large ground set of entities in an optimal fashion. Submodular optimization provides for a formal way to solve such problems. Common examples with infrastructure systems involve sensor placement and identification of key entities with certain objectives. However, scaling these approaches to large infrastructure systems can be challenging because of the high computational complexity of the overall framework that include the optimization algorithms as well as high-complexity compute-oracles that provide the necessary objective function values. In this work, we explore a well-studied and widely-applicable paradigm, namely leader-selection in a multi-agent networked setting in the context of scalable methodologies. We demonstrate novel frameworks that utilize variations of accelerated submodular optimization algorithms along with linear-algebraic methods that can help accelerate the oracle computations. We further explore this combination in conjunction with graph partitioning paradigms to take advantage of the accelerated algorithms in a distributed setting. Finally we demonstrate the key findings on a practical problem in an operational setting. For this, we leverage an example road network with approximately 18k nodes and 27k edges in a traffic control application, where we seek a limited number of k = 200 key intersections. This problem can be solved in a serial setting in just under 5 hours providing more than 2 orders of magnitude speed-up over methods that do not consider acceleration techniques.