Engineering LaCAM∗: Towards Real-Time, Large-Scale, and Near-Optimal Multi-Agent Pathfinding Keisuke Okumura1,2 AAMAS, Auckland, 6th – 10th May 2024 1University of Cambridge 2National Institute of Advanced Industrial Science and Technology (AIST) https://kei18.github.io/lacam3 LaCAM*, IJCAI-22 this work

/30 2 MAPF: Multi-Agent Path Finding given agents (starts) graph goals solution paths without collisions cost total travel time, distance, makespan, etc

/30 3 … … … … … search node (configuration) goal configuration Vanilla A* for MAPF [Hart+ 68] exponential number of node generation

/30 4 runtime (sec) solved instances (%) Evaluation on Benchmark - 13,900 instances - 33 grid maps - every 50 agents, up to max. (1000) - tested on standard desktop PC [Stern+ SOCS-19], data from [Okumura IJCAI-23] 33 grid maps e.g., random-32-32-20, 200 agents 00.0% A* [Hart+ 68] complete optimal

/30 5 PIBT PIBT initial configuration PIBT goal configuration scalable but imcomplete Vanilla PIBT for MAPF Priority Inheritance with Backtracking [Okumura+ AIJ-22]

/30 6 runtime (sec) solved instances (%) 00.0% A* [Hart+ 68] 67.4% PIBT [Okumura+ AIJ-22] complete incomplete suboptimal optimal

/30 7 … … … … … PIBT PIBT PIBT not generated immediately 1. Configurations are generated in a lazy manner 2. Use other MAPF algorihtms to generate a promising configuration exhaustive search with two tricks LaCAM(*) Lazy Constraints Addition Search [Okumura AAAI/IJCAI-23]

/30 8 PIBT LaCAM* This is just a metaphor. Image by OpenClipart-Vectors from Pixabay

/30 9 runtime (sec) solved instances (%) 00.0% A* [Hart+ 68] 67.4% PIBT [Okumura+ AIJ-22] complete incomplete suboptimal optimal 99.0% LaCAM* [Okumura IJCAI-23] complete eventually optimal

/30 10 runtime (sec) solved instances (%) 00.0% A* [Hart+ 68] 00.4% ODrM* [Wagner+ AIJ-15] 08.3% CBS [Sharon+ AIJ-15; Li+ AIJ-21] 10.7% BCP [Lam+ COR-22] 30.9% ODrM*-5 [Wagner+ AIJ-15] 50.5% EECBS-5 [Li+ AAAI-21] 61.4% PP [Silver AIIDE-05] 80.9% LNS2 [Li+ AAAI-22] 67.4% PIBT [Okumura+ AIJ-22] 90.5% PIBT+ [Okumura+ AIJ-22] 85.6% LaCAM [Okumura+ AAAI-23] 99.0% LaCAM* [Okumura IJCAI-23] complete solution complete complete solution complete incomplete complete complete eventually optimal bounded suboptimal suboptimal bounded suboptimal optimal optimal suboptimal (unable to identify unsolvable instances)

/30 11 LaCAM* suboptimally solve MAPF for 10,000 agents in several seconds on my laptop

/30 12 Is LaCAM* the universally dominant MAPF solver? No.

/30 13 Is LaCAM* the universally dominant MAPF solver? No. solution quality ≥1000 agents in seconds ≤100 agents in minutes optimal suboptimal optimal methods: A*, CBS, M*, BCP, SAT-based bounded suboptimal methods: (E)ECBS, I-ODrM* unbounded suboptimal methods: PP, PBS, LNS2 speed & scalability extremely scalable methods: PIBT, LaCAM* eventually optimal; hopeless with large instances tradeoff holy grail

/30 14 flowtime1 / LB instance x25 LNS2 random-32-32-20 409 agents, 30s timeout No. vanilla LaCAM* – initial solution 1LaCAM* aims to optimize sum-of-loss (≠ flowtime); check the paper for details. Is LaCAM* the universally dominant MAPF solver?

/30 15 instance x25 LNS2 random-32-32-20 409 agents, 30s timeout No. vanilla LaCAM* – initial solution vanilla LaCAM* – after 30s 1LaCAM* aims to optimize sum-of-loss (≠ flowtime); check the paper for details. Is LaCAM* the universally dominant MAPF solver? flowtime1 / LB

/30 16 solution quality optimal suboptimal ≥1000 agents in seconds ≤100 agents in minutes speed & scalability holy grail Towards Real-Time, Large-Scale, and Near-Optimal MAPF Vanilla LaCAM* is a good starting point

/30 17 initial solution planning deadline 1. improve initial solution quality 2. improve convergence speed Improving Anytime Planning vanilla LaCAM* computation time solution cost solution

/30 18 Vanilla LaCAM* LaCAM* fine-tuned PIBT

/30 19 Contributions of this study: Engineered LaCAM* LaCAM* fine-tuned PIBT Monte-Carlo sampling dynamic incoporation of alternative solutions recursive LaCAM* non-deterministic node extraction1 with space utilization optimization improve initial solution quality improve convergence speed 1Not explained in this talk.

/30 20 Tech-1: Space Utilization Optimization (SUO) configuration, priority, and preference collision-free configuration PIBT 1 (desired) 2 3 4 5 b a High Low cost:3+2 cost:3+3 b a Vanilla PIBT either chooses ‘a’ or ‘b’ blindly => significant effect with more agents original idea from: Han, S.,& Yu, J. Optimizing space utilization for more effective multi-robot path planning. ICRA. 2022. Also check: Chen, Z., Harabor, D., Li, J., & Stuckey, P. J. Traffic Flow Optimisation for Lifelong Multi-Agent Path Finding. AAAI. 2024.

/30 21 Tech-1: Space Utilization Optimization (SUO) Step 1: Compute spatially dispersed paths Collisions are allowed Pickup an agent and recompute its path while minimizing collisions runtime (sec) cost / LB vanilla LaCAM* LaCAM* with SUO 12% random-32-32-20, 409 agents Step 2: Run PIBT, while encouraging agents to follow the precomputed paths original idea from: Han, S.,& Yu, J. Optimizing space utilization for more effective multi-robot path planning. ICRA. 2022. Also check: Chen, Z., Harabor, D., Li, J., & Stuckey, P. J. Traffic Flow Optimisation for Lifelong Multi-Agent Path Finding. AAAI. 2024.

/30 22 Tech-2: Monte-Carlo Configuration Generation expected cost: determined non-deterministically by PIBT 3+2 3+3 initial config. goal config. search tree

/30 23 Tech-2: Monte-Carlo Configuration Generation 3+2 3+3 … … 1. Generate multiple configurations by PIBT 2. Pickup the best w.r.t. f-value => successor node runtime (sec) cost / LB vanilla LaCAM* with 10 Monte-Carlo Sampling 6.1% random-32-32-20, 409 agents

/30 24 computation time solution cost planning deadline vanilla LaCAM* Tech-3: Dynamic Incorporation of Alternative Solutions Surynek, P. Redundancy elimination in highly parallel solutions of motion coordination problems. IJAIT. 2013. De Wilde, B., Ter Mors, A. W., & Witteveen, C. Push and rotate: a complete multi-agent pathfinding algorithm. JAIR. 2014. Okumura, K., Tamura, Y., & Défago, X. Iterative refinement for real-time multi-robot path planning. IROS. 2021. Li, J., Chen, Z., Harabor, D., Stuckey, P. J., & Koenig, S. Anytime multi-agent path finding via large neighborhood search. IJCAI. 2021. … Effective local repair methods exist to improve solution quality: local repair (parallel run) incorporate solutions and continue the search

/30 25 when alternative solutions found, configuration & cost (e.g., makespan) parent – children other neighbors Tech-3: Dynamic Incorporation of Alternative Solutions 1 2 3 3 2 3 0 4 1 initial config. search tree goal config.

/30 26 2 Tech-3: Dynamic Incorporation of Alternative Solutions 1 2 3 3 2 3 0 3 1 when alternative solutions found, incorporate them with tree rewriting runtime (sec) cost / LB vanilla LaCAM* with the dynamic incorporation (LNS-based refinement) 13% random-32-32-20, 409 agents This scheme is more powerful than it looks: It is theoretically possible to eventually find optimal solutions from arbitrary suboptimal solutions

/30 27 Tech-4: Recursive LaCAM* computation time solution cost planning deadline vanilla LaCAM* local repair (parallel run) 1. Create a sub-MAPF instance from the current solution 2. Solve this with engineered LaCAM*

/30 28 instance x25 vanilla LaCAM* – initial solution LNS2 random-32-32-20 409 agents, 30s timeout vanilla LaCAM* – after 30s engineered LaCAM* – after 30s engineered LaCAM* – initial solution ~30% improvement! Can we do more? I believe so… 1LaCAM* aims to optimize sum-of-loss (≠ flowtime); check the paper for details. flowtime1 / LB Performance of Engineered LaCAM*

/30 29 vanilla LaCAM* – initial solution vanilla LaCAM* – after 30s engineered LaCAM* – after 30s engineered LaCAM* – initial solution Performance of Engineered LaCAM* instance x25

/30 30 Concluding Remarks – Engineering LaCAM* for MAPF I think LaCAM* is not so far from industrial use in large-scale logistics systems! Solving large-scale MAPF is no longer difficult recently, at least for the gridworld. Instead, the frontiers are gradually approaching real-time, large-scale, and near-optimal MAPF. This is achieved by combinations of several MAPF methods – LaCAM* is indeed a meta-algorithm.