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Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances,…
Utilities face the challenge of responding to power outages due to storms and ice damage, but most power grids are not equipped with sensors to pinpoint the precise location of the faults causing the outage. Instead, utilities have to…
We consider a multi-robot setting, where we have a fleet of multi-capacity autonomous robots that must service spatially distributed pickup-and-delivery requests with fixed maximum wait times. Requests can be either scheduled ahead of time…
In this paper, we consider a distributionally robust resource planning model inspired by a real-world service industry problem. In this problem, there is a mixture of known demand and uncertain future demand. Prior to having full knowledge…
Mobility-on-demand systems are transforming the way we think about the transportation of people and goods. Most research effort has been placed on scalability issues for systems with a large number of agents and simple pick-up/drop-off…
We propose a hierarchical splitting approach to differential equations that provides a design principle for constructing splitting methods for $N$-split systems by iteratively applying splitting methods for two-split systems. We analyze the…
This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…
We develop a fluid-flow model for routing problems, where fluid consists of different size particles and the task is to route the incoming fluid to $n$ parallel servers using the size information in order to minimize the mean latency. The…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
The Dial-a-Ride Problem (DARP) is an optimization problem that involves determining optimal routes and schedules for several vehicles to pick up and deliver items at minimum cost. Motivated by real-world carpooling and crowdshipping…
In this paper, we consider a large-scale instance of the classical Pickup-and-Delivery Vehicle Routing Problem (PDVRP) that must be solved by a network of mobile cooperating robots. Robots must self-coordinate and self-allocate a set of…
In the unsplittable capacitated vehicle routing problem, we are given a metric space with a vertex called depot and a set of vertices called terminals. Each terminal is associated with a positive demand between 0 and 1. The goal is to find…
Truck platooning, a linking technology of trucks on the highway, has gained enormous attention in recent years due to its benefits in energy and operation cost savings. However, most existing studies on truck platooning limit their focus on…
The problem of fair division known as "cake cutting" has been the focus of multiple papers spanning several decades. The most prominent problem in this line of work has been to bound the query complexity of computing an envy-free outcome in…
We study real-time routing policies in smart transit systems, where the platform has a combination of cars and high-capacity vehicles (e.g., buses or shuttles) and seeks to serve a set of incoming trip requests. The platform can use its…
This paper considers max-min fair rate allocation and routing in energy harvesting networks where fairness is required among both the nodes and the time slots. Unlike most previous work on fairness, we focus on multihop topologies and…
Expanders are powerful algorithmic structures with two key properties: they are a) routable: for any multi-commodity flow unit demand, there exists a routing with low congestion over short paths, where a demand is unit if the amount of…
In this paper, we propose a catalog of iterative methods for solving the Split Feasibility Problem in the non-convex setting. We study four different optimization formulations of the problem, where each model has advantageous in different…
We present a hierarchical computation approach for solving finite-time optimal control problems using operator splitting methods. The first split is performed over the time index and leads to as many subproblems as the length of the…
We study a new variant of the well-studied Vehicle Routing Problem with Time Windows (VRPTW), called the fragility-constrained VRPTW, which assumes that 1) the capacity of a vehicle is organized in multiple identical stacks; 2) all items…