Related papers: Designing optimal networks for multi-commodity tra…
With the tremendous increase of the Internet traffic, achieving the best performance with limited resources is becoming an extremely urgent problem. In order to address this concern, in this paper, we build an optimization problem which…
An adaptive, adversarial methodology is developed for the optimal transport problem between two distributions $\mu$ and $\nu$, known only through a finite set of independent samples $(x_i)_{i=1..N}$ and $(y_j)_{j=1..M}$. The methodology…
We study the behaviour of various Lyapunov functionals (relative entropies) along the solutions of a family of nonlinear drift-diffusion-reaction equations coming from statistical mechanics and population dynamics. These equations can be…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
An improved fully polynomial-time approximation scheme and a greedy heuristic for the fractional length-bounded maximum multicommodity flow problem with unit edge-lengths are proposed. Computational experiments are carried out on benchmark…
Due to the importance of robustness in many real-world optimization problems, the field of robust optimization has gained a lot of attention over the past decade. We concentrate on maximum flow problems and introduce a novel robust…
Optimality principles in nonequilibrium transport networks are linked to a thermodynamic formalism based on generalized transport potentials endowed with Legendre duality and related contact structure. This allows quantifying the distance…
Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and…
Optimal transportation of raw material from suppliers to customers is an issue arising in logistics that is addressed here with a continuous model relying on optimal transport theory. A physics informed neuralnetwork method is advocated…
This thesis employs statistical learning technique to analyze, predict and solve the fixed charge network flow (FCNF) problem, which is common encountered in many real-world network problems. The cost structure for flows in the FCNF…
Supply chain network is critical to serving customers, so the most common practices are to determine the number, location, and capacity of facilities. But at the same time, uncertainties and risks must be taken into account in order to…
The question of which costs admit unique optimizers in the Monge-Kantorovich problem of optimal transportation between arbitrary probability densities is investigated. For smooth costs and densities on compact manifolds, the only known…
This paper investigates the connections between rectified flows, flow matching, and optimal transport. Flow matching is a recent approach to learning generative models by estimating velocity fields that guide transformations from a source…
Recent developments in modular transport vehicles allow deploying multi-purpose vehicles which can alternately transport different kinds of flows. In this study, we propose a novel variant of the pickup and delivery problem, the…
Following Demidovich's concept and definition of convergent systems, we analyze the optimal nonlinear damping control, recently proposed [1] for the second-order systems. Targeting the problem of output regulation, correspondingly tracking…
We propose a method for providing communication network infrastructure in autonomous multi-agent teams. In particular, we consider a set of communication agents that are placed alongside regular agents from the system in order to improve…
We consider the problem to transport resources/mass while abiding by constraints on the flow through constrictions along their path between specified terminal distributions. Constrictions, conceptualized as toll stations at specified…
In this paper, we present a novel and principled approach to learn the optimal transport between two distributions, from samples. Guided by the optimal transport theory, we learn the optimal Kantorovich potential which induces the optimal…
We introduce a methodology to study the possible matter flows of an ecosystem defined by observational biomass data and realistic biological constraints. The flows belong to a polyhedron in a multi dimensional space making statistical…
We propose a protocol optimization technique that is applicable to both weighted or unweighted graphs. Our aim is to explore by how much a small variation around the Shortest Path or Optimal Path protocols can enhance protocol performance.…