Related papers: Research: Analysis of Transport Model that Approxi…
The Travelling Thief Problem (TTP) is a challenging combinatorial optimization problem that attracts many scholars. The TTP interconnects two well-known NP-hard problems: the Travelling Salesman Problem (TSP) and the 0-1 Knapsack Problem…
Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold. In…
We solve a generalized Kyle model type problem using Monge-Kantorovich duality and backward stochastic partial differential equations. First, we show that the the generalized Kyle model with dynamic information can be recast into a terminal…
In this work we study a modification of the Monge-Kantorovich problem taking into account path dependence and interaction effects between particles. We prove existence of solutions under mild conditions on the data, and after imposing…
We investigate a learning decision support system for vehicle routing, where the routing engine learns implicit preferences that human planners have when manually creating route plans (or routings). The goal is to use these learned…
The goal of this paper is to investigate a decision support system for vehicle routing, where the routing engine learns from the subjective decisions that human planners have made in the past, rather than optimizing a distance-based…
We consider the multidimensional Monge-Kantrovich transport problem in an abstract setting. Our main results state that if a cost function and marginal measures are invariant by a family of transformations, then a solution of the Kantrovich…
Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an…
The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to $c$-conjugates. A new abstract characterization of the optimal plans is obtained in the case where the cost function takes…
In this paper, a novel transport planning model system (TPMS) is formulated which is built on the concepts of supernetworks, multi-modality, integrity and calibration. In the proposed formulation, activity travel pattern (ATP) choice facets…
A measure theoretical approach is presented to study the Monge-Kantorovich optimal mass transport problem. This approach together with Kantorovich duality provide an effective tool to answer a long standing question about the support of…
Decision-making for automated driving remains a challenging task. For their integration into real platforms, these algorithms must guarantee passenger safety and comfort while ensuring interpretability and an appropriate computational time.…
Transporter Net is a recently proposed framework for pick and place that is able to learn good manipulation policies from a very few expert demonstrations. A key reason why Transporter Net is so sample efficient is that the model…
We establish connections between optimal transport theory and the dynamic version of the Kyle model, including new characterizations of informed trading profits via conjugate duality and Monge-Kantorovich duality. We use these connections…
Enabling resilient autonomous motion planning requires robust predictions of surrounding road users' future behavior. In response to this need and the associated challenges, we introduce our model titled MTP-GO. The model encodes the scene…
A probabilistic method for solving the Monge-Kantorovich mass transport problem on $R^d$ is introduced. A system of empirical measures of independent particles is built in such a way that it obeys a doubly indexed large deviation principle…
These notes constitute a sort of Crash Course in Optimal Transport Theory. The different features of the problem of Monge-Kantorovitch are treated, starting from convex duality issues. The main properties of space of probability measures…
This paper aims to develop a learning method for a special class of traveling salesman problems (TSP), namely, the pickup-and-delivery TSP (PDTSP), which finds the shortest tour along a sequence of one-to-one pickup-and-delivery nodes.…
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…
We study online learning of finite Markov decision process (MDP) problems when a side information vector is available. The problem is motivated by applications such as clinical trials, recommendation systems, etc. Such applications have an…