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Optimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton-Jacobi-Bellman equations. Building on recent machine learning inspired approaches towards high-dimensional PDEs, we investigate the…

Optimization and Control · Mathematics 2023-01-31 Nikolas Nüsken , Lorenz Richter

Multi-agent pathfinding (MAPF) is the problem of finding a set of conflict-free paths for a set of agents. Typically, the agents' moves are limited to a pre-defined graph of possible locations and allowed transitions between them, e.g. a…

Artificial Intelligence · Computer Science 2024-09-02 Konstantin Yakovlev , Anton Andreychuk , Roni Stern

Multi-Agent Path Finding (MAPF) requires collision-free trajectories for multiple agents on a shared graph, often with the objective of minimizing the sum-of-costs (SOC). Many optimal and bounded-suboptimal solvers rely on time-expanded…

Multiagent Systems · Computer Science 2026-04-08 Fernando Salanova , Eduardo Montijano , Cristian Mahulea

The objective of designing a control system is to steer a dynamical system with a control signal, guiding it to exhibit the desired behavior. The Hamilton-Jacobi-Bellman (HJB) partial differential equation offers a framework for optimal…

Machine Learning · Computer Science 2025-10-22 Jostein Barry-Straume , Adwait D. Verulkar , Arash Sarshar , Andrey A. Popov , Adrian Sandu

Many high-level multi-agent planning problems, including multi-robot navigation and path planning, can be effectively modeled using deterministic actions and observations. In this work, we focus on such domains and introduce the class of…

Artificial Intelligence · Computer Science 2025-09-01 Yang You , Alex Schutz , Zhikun Li , Bruno Lacerda , Robert Skilton , Nick Hawes

Large-scale multi-agent pathfinding (MAPF) presents significant challenges in several areas. As systems grow in complexity with a multitude of autonomous agents operating simultaneously, efficient and collision-free coordination becomes…

Multiagent Systems · Computer Science 2024-02-27 Huijie Tang , Federico Berto , Zihan Ma , Chuanbo Hua , Kyuree Ahn , Jinkyoo Park

Complex scheduling problems require a large amount computation power and innovative solution methods. The objective of this paper is the conception and implementation of a multi-agent system that is applicable in various problem domains.…

Multiagent Systems · Computer Science 2020-04-21 Peter Hillmann , Tobias Uhlig , Gabi Dreo Rodosek , Oliver Rose

Multi-agent path finding (MAPF) is the problem of finding collision-free paths for a team of agents to reach their goal locations. State-of-the-art classical MAPF solvers typically employ heuristic search to find solutions for hundreds of…

Multiagent Systems · Computer Science 2024-04-01 Rishi Veerapaneni , Qian Wang , Kevin Ren , Arthur Jakobsson , Jiaoyang Li , Maxim Likhachev

In a previous work (Akian, Fodjo, 2016), we introduced a lower complexity probabilistic max-plus numerical method for solving fully nonlinear Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite…

Optimization and Control · Mathematics 2018-02-08 Marianne Akian , Eric Fodjo

We formalize Multi-Agent Path Finding with Deadlines (MAPF-DL). The objective is to maximize the number of agents that can reach their given goal vertices from their given start vertices within the deadline, without colliding with each…

Artificial Intelligence · Computer Science 2018-06-13 Hang Ma , Glenn Wagner , Ariel Felner , Jiaoyang Li , T. K. Satish Kumar , Sven Koenig

Conflict-Based Search is one of the most popular methods for multi-agent path finding. Though it is complete and optimal, it does not scale well. Recent works have been proposed to accelerate it by introducing various heuristics. However,…

Artificial Intelligence · Computer Science 2023-01-23 Chenning Yu , Qingbiao Li , Sicun Gao , Amanda Prorok

This paper addresses a continuous-time continuous-space chance-constrained stochastic optimal control (SOC) problem via a Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). Through Lagrangian relaxation, we convert the…

Optimization and Control · Mathematics 2022-05-03 Apurva Patil , Alfredo Duarte , Aislinn Smith , Takashi Tanaka , Fabrizio Bisetti

Multi-robot path finding in dynamic environments is a highly challenging classic problem. In the movement process, robots need to avoid collisions with other moving robots while minimizing their travel distance. Previous methods for this…

Artificial Intelligence · Computer Science 2025-12-12 Shaoming Peng

The goal of Multi-Agent Path Finding (MAPF) is to find a set of paths for a fleet of agents moving in a shared environment such that the agents reach their goals without colliding with each other. In practice, some of the robots executing…

Multiagent Systems · Computer Science 2025-09-15 David Zahrádka , Denisa Mužíková , David Woller , Miroslav Kulich , Jiří Švancara , Roman Barták

We consider the problem of computing safety regions, modeled as nonconvex backward reachable sets, for a nonlinear car collision avoidance model with time-dependent obstacles. The Hamilton-Jacobi-Bellman framework is used. A new formulation…

Optimization and Control · Mathematics 2019-11-28 Ilaria Xausa , Robert Baier , Olivier Bokanowski , Matthias Gerdts

This paper proposes FMAP (Forward Multi-Agent Planning), a fully-distributed multi-agent planning method that integrates planning and coordination. Although FMAP is specifically aimed at solving problems that require cooperation among…

Artificial Intelligence · Computer Science 2015-01-30 Alejandro Torreño , Eva Onaindia , Óscar Sapena

This article proposes a numerical scheme for computing the evolution of vehicular traffic on a road network over a finite time horizon. The traffic dynamics on each link is modeled by the Hamilton-Jacobi (HJ) partial differential equation…

Physics and Society · Physics 2017-02-14 Yanning Li , Christian G. Claudel , Benedetto Piccoli , Daniel B. Work

This paper proposes an actor-critic algorithm for controlling the temperature of a battery pack using a cooling fluid. This is modeled by a coupled 1D partial differential equation (PDE) with a controlled advection term that determines the…

Machine Learning · Computer Science 2023-05-19 Amartya Mukherjee , Jun Liu

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…

Optimization and Control · Mathematics 2026-03-10 Yacine Mokhtari

Large language model (LLM)-based agents have demonstrated remarkable capabilities in decision-making tasks, but struggle significantly with complex, long-horizon planning scenarios. This arises from their lack of macroscopic guidance,…

Computation and Language · Computer Science 2025-08-27 Ziyue Li , Yuan Chang , Gaihong Yu , Xiaoqiu Le