Engineering LaCAM$^\ast$: Towards Real-Time, Large-Scale, and Near-Optimal Multi-Agent Pathfinding

TL;DR

This work tackles real-time, large-scale multi-agent pathfinding by extending the LaCAM$^\ast$ framework with a set of engineering techniques. It introduces non-deterministic node extraction, space utilization optimization with scattered paths, Monte-Carlo configuration generation, dynamic incorporation of alternative solutions, and a recursive refinement approach, all aimed at achieving near-optimality within practical time limits. Across extensive experiments, the combined methods deliver substantial improvements in sum-of-loss and flowtime, solving larger instances than prior methods and even enabling scenarios with up to 10,000 agents under extended time budgets. The results indicate a meaningful step toward practical real-time MAPF at massive scales, with SUO and adaptive refinements contributing the most significant gains.

Abstract

This paper addresses the challenges of real-time, large-scale, and near-optimal multi-agent pathfinding (MAPF) through enhancements to the recently proposed LaCAM* algorithm. LaCAM* is a scalable search-based algorithm that guarantees the eventual finding of optimal solutions for cumulative transition costs. While it has demonstrated remarkable planning success rates, surpassing various state-of-the-art MAPF methods, its initial solution quality is far from optimal, and its convergence speed to the optimum is slow. To overcome these limitations, this paper introduces several improvement techniques, partly drawing inspiration from other MAPF methods. We provide empirical evidence that the fusion of these techniques significantly improves the solution quality of LaCAM*, thus further pushing the boundaries of MAPF algorithms.

Figures (10)

• Figure 1: Solution quality improvements. Each chart illustrates the solution quality across 25 instances using a four-connected grid map, retrieved from the MAPF benchmark stern2019def. Solution quality is assessed through the sum-of-loss, quantifying the total number of actions that agents do not remain at their goals. The scores are normalized by division with their corresponding trivial lower bound, i.e., the sum of the shortest path lengths between the agents' start and goal vertices. Smaller scores are preferable ($\downarrow$), with the minimum is one. For each grid, instances underwent evaluation with the maximum number of agents as specified in the benchmark, mostly a thousand agents. The instances are ordered based on the initial solution quality of the original $\text{LaCAM}^\ast$. Since $\text{LaCAM}^\ast$ is an anytime algorithm, both the initial solution quality and the quality at the 30s time limit are presented. Improved performance over the original $\text{LaCAM}^\ast$ is represented by the difference between orange and pink edges. For reference, the scores of LNS2 li2022mapf, an incomplete suboptimal approach, are included when instances were solved within the time limit (510/800 instances; 64%). The original $\text{LaCAM}^\ast$ solved all instances, while the improved version encountered failure in one instance of maze-32-32-4. The flowtime results corresponding to this figure are available in \ref{['fig:result-soc']}.
• Figure 2: Solution quality improvements of flowtime (aka. sum-of-costs). See also the caption in \ref{['fig:result-top']}. Flowtime is a widely-used metric to evaluate MAPF solutions, computed as the sum of the earliest timesteps that each agent permanently stays at its destination. Although $\text{LaCAM}^\ast$ primarily focuses on minimizing the sum-of-loss metric, the resultant solutions also excel in terms of flowtime.
• Figure 3: Effect of non-deterministic node extraction after finding initial solutions. "original" refers to the original $\text{LaCAM}^\ast$okumura2023lacam2. All methods solved every trial within 10s. For each second, the average sum-of-loss within the solved instances up to that point is depicted. The scores are normalized by dividing by their trivial lower bound, $\sum_i\mathsf{dist}\xspace\xspace(s_i, g_i)$. The charts include the average scores of the initial solutions. Furthermore, they encompass the minimum and maximum scores achieved within the solved instances up to that specific time, visualized with transparent regions. For each method, we tested several probabilities for non-deterministic node extraction, and show those with consistently provided outcomes with smaller costs ("restart": $0.01$, "random": $0.01$).
• Figure 4: Motivation to compute spatially dispersed paths.
• Figure 5: Effect of space utilization optimization. See also the caption of \ref{['fig:result-insert']}. The runtime includes computing $\Pi_{\text{SUO}}$. "SUO-$x$" means to set $m$ in \ref{['algo:scatter']} to $x$. All methods solved all trials.