Related papers: Tree-based formulation for the multi-commodity flo…
The traditional multi-commodity flow problem assumes a given flow network in which multiple commodities are to be maximally routed in response to given demands. This paper considers the multi-commodity flow network-design problem: given a…
The purpose of this work is to develop an algorithmic optimization approach for a capacitated Multi-Commodity flow problem, where the objective is to minimize the total link costs, where the cost of each arc increases convexly with its…
Mode-based model-reduction is used to reduce the degrees of freedom of high dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and…
A common objective in the analysis of tabular data is estimating the conditional distribution (in contrast to only producing predictions) of a set of "outcome" variables given a set of "covariates", which is sometimes referred to as the…
The Multi-Commodity Pickup and Delivery Vehicle Routing Problem aims to optimize the pickup and delivery of multiple unique commodities using a fleet of several agents with limited payload capacities. This paper addresses the challenge of…
When the underlying physical network layer in optimal network flow problems is a large graph, the associated optimization problem has a large set of decision variables. In this paper, we discuss how the cycle basis from graph theory can be…
This paper presents centralized and distributed Alternating Direction Method of Multipliers (ADMM) frameworks for solving large-scale nonconvex optimization problems with binary decision variables subject to spanning tree or rooted…
We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper…
In this paper, we generalize the minimum flow decomposition problem (MFD) to incorporate uncertain edge capacities and tackle it from the perspective of robust optimization. In the classical flow decomposition problem, a network flow is…
In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…
To address the challenge of conflicting traffic flows that complete on opposing cycle times in a specific phase of the traffic light, we proposed a novel decentralized traffic light control methodology based on the identification of the…
While normalizing flows for continuous data have been extensively researched, flows for discrete data have only recently been explored. These prior models, however, suffer from limitations that are distinct from those of continuous flows.…
Designing and optimizing different flows in networks is a relevant problem in many contexts. While a number of methods have been proposed in the physics and optimal transport literature for the one-commodity case, we lack similar results…
We introduce the concept of low-step multi-commodity flow emulators for any undirected, capacitated graph. At a high level, these emulators contain approximate multi-commodity flows whose paths contain a small number of edges, shattering…
Decision trees are highly interpretable models for solving classification problems in machine learning (ML). The standard ML algorithms for training decision trees are fast but generate suboptimal trees in terms of accuracy. Other discrete…
The tree-based ensembles are known for their outstanding performance in classification and regression problems characterized by feature vectors represented by mixed-type variables from various ranges and domains. However, considering…
We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in…
In transmission networks power flows and network topology are deeply intertwined due to power flow physics. Recent literature shows that specific network substructures named bridge-blocks prevent line failures from propagating globally. A…
Telecommunication networks frequently face technological advancements and need to upgrade their infrastructure. Adapting legacy networks to the latest technology requires synchronized technicians responsible for migrating the equipment. The…
In light of the need for design and analysis of intermodal transportation systems, we propose an algorithmic framework to determine the system optimum of an intermodal transportation system. To this end, we model an intermodal…