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We consider maps $T$ solving the optimal transport problem with a cost $c(x-y)$ modeled on the $p$-cost. For H\"older continuous marginals, we prove a $C^{1,\alpha}$-partial regularity result for $T $in the set $\{|T(x)-x|>0\}$.
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 propose a new polynomial-time deterministic algorithm that produces an approximated solution for the traveling salesperson problem. The proposed algorithm ranks cities based on their priorities calculated using a power function of means…
We consider the problem of routing for logistics purposes, in a contested environment where an adversary attempts to disrupt the vehicle along the chosen route. We construct a game-theoretic model that captures the problem of optimal…
Jerk-constrained trajectories offer a wide range of advantages that collectively improve the performance of robotic systems, including increased energy efficiency, durability, and safety. In this paper, we present a novel approach to…
We analyze simulated annealing (SA) for simple randomized instances of the Traveling Salesperson Problem. Our analysis shows that the theoretically optimal cooling schedule of Hajek explores members of the solution set which are in…
Digital simulation of quantum dynamics by evaluating the time evolution of a Hamiltonian is the initially proposed application of quantum computing. The large number of quantum gates required for emulating the complete second quantization…
The ``Heatmap + Monte Carlo Tree Search (MCTS)'' paradigm has recently emerged as a prominent framework for solving the Travelling Salesman Problem (TSP). While considerable effort has been devoted to enhancing heatmap sophistication…
The Traveling Salesman Problem (TSP) is one of the classic and hard problems in combinatorial optimization. We develop a new heuristic that uses a connection between Minimum Cost Flow Problems and the TSP to improve on a given suboptimal…
In robotic planetary surface exploration, strategic mobility planning is an important task that involves finding candidate long-distance routes on orbital maps and identifying segments with uncertain traversability. Then, expert human…
This paper proposes a hybrid genetic algorithm for solving the Multiple Traveling Salesman Problem (mTSP) to minimize the length of the longest tour. The genetic algorithm utilizes a TSP sequence as the representation of each individual,…
In this paper, using variational approaches, we investigate the first order planning problem arising in the theory of mean field games. We show the existence and uniqueness of weak solutions of the problem in the case of a large class of…
We study the synthesis of a policy in a Markov decision process (MDP) following which an agent reaches a target state in the MDP while minimizing its total discounted cost. The problem combines a reachability criterion with a discounted…
Paper provides a method for solving the reverse Monge-Kantorovich transport problem (TP). It allows to accumulate positive decision-taking experience made by decision-taker in situations that can be presented in the form of TP. The initial…
In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost $c_{ij}$ of traveling from city $i$ to city $j$, which is the same in either direction for the Symmetric TSP. The objective…
Tournament solutions are frequently used to select winners from a set of alternatives based on pairwise comparisons between alternatives. Prior work has shown that several common tournament solutions tend to select large winner sets and…
This article presents a mathematical model for identifying the safest travel routes during a pandemic by minimizing disease contraction risks, such as COVID-19. We formulate this as the LEAST INFECTION PROBABILITY PATH (LIPP) problem, which…
In Group Trip Planning (GTP) Query Problem, we are given a city road network where a number of Points of Interest (PoI) have been marked with their respective categories (e.g., Cafeteria, Park, Movie Theater, etc.). A group of agents want…
Given a set of basic areas, the territory design problem asks to create a predefined number of territories, each containing at least one basic area, such that an objective function is optimized. Desired properties of territories often…
A novel algorithm is proposed to solve the sample-based optimal transport problem. An adversarial formulation of the push-forward condition uses a test function built as a convolution between an adaptive kernel and an evolving probability…