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

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.

Figures (15)

• Figure 1: Fixed vs. flexible goal assignment under precedence constraints $(g_1 \!\prec\! g_2,\; g_3 \!\prec\! g_4)$. $J$ denotes sum of path costs; assigned goal sequences are shown below each panel. (a) Fixed Assignment (MAPF-PC): $J_0\!=\!15$. (b) Flexible Assignment (TAPF-PC): $J_1\!=\!9$, showing that fixed-assignment optimality does not imply TAPF-PC optimality.
• Figure 2: Main method comparison across seeded benchmark subsets. Each panel reports relative sum of costs reduction over the fixed-assignment seed (higher is better). Top row: By benchmark tier. Bottom row: By map family.
• Figure 3: Improvement frequency and absolute sum of costs reduction. Left: Fraction of improved instances, Right: Boxplots of absolute SoC reduction across all instances. Larger values are better.
• Figure 4: Search behavior on PBS-seeded runs. Curves show median best-so-far relative SoC reduction over wall-clock time, and shaded bands show the interquartile range. The x-axis shows wall-clock time including seed generation and post-refinement.
• Figure 5: Scalability on PBS-seeded runs. Curves show median relative SoC reduction, and shaded bands show interquartile range. Left column: Varying agents with fixed tasks and precedence constraints. Right column: Varying precedence constraints with fixed agents and tasks. Top row: Random map. Bottom row: Warehouse map.