Large Neighborhood Search for Multi-Agent Task Assignment and Path Finding with Precedence Constraints

TL;DR

This paper introduces a large neighborhood search method for joint task assignment and path finding with precedence constraints in multi-robot systems, significantly improving solution quality over fixed assignments.

Contribution

It extends MAPF-PC to TAPF-PC, enabling simultaneous optimization of task assignment, precedence satisfaction, and routing cost using a novel large neighborhood search approach.

Findings

Achieves 89.1% improvement over fixed-assignment solutions.

Effectively captures gains from flexible reassignment under precedence constraints.

Demonstrates scalability across multiple benchmark families.

Abstract

Many multi-robot applications require tasks to be completed efficiently and in the correct order, so that downstream operations can proceed at the right time. Multi-agent path finding with precedence constraints (MAPF-PC) is a well-studied framework for computing collision-free plans that satisfy ordering relations when task sequences are fixed in advance. In many applications, however, solution quality depends not only on how agents move, but also on which agent performs which task. This motivates the lifted problem of task assignment and path finding with precedence constraints (TAPF-PC), which extends MAPF-PC by jointly optimizing assignment, precedence satisfaction, and routing cost. To address the resulting coupled TAPF-PC search space, we develop a large neighborhood search approach that starts from a feasible MAPF-PC seed and iteratively improves it through reassignment-based neighborhood repair, restoring feasibility within each selected neighborhood. Experiments across multiple benchmark families and scaling regimes show that the best-performing configuration improves 89.1% of instances over fixed-assignment seed solutions, demonstrating that large neighborhood search effectively captures the gains from flexible reassignment under precedence constraints.