LaCAM: Search-Based Algorithm for Quick Multi-Agent Pathfinding Keisuke Okumura Tokyo Institute of Technology, Japan ౦ژ޻ۀେֶ 5PLZP*OTUJUVUFPG5FDIOPMPHZ Feb. 7st – 14th, 2023 Washington, DC, USA AAAI-23 10k agents, 10sec 400 agents, 30ms 4 agents, 72ms https://kei18.github.io/lacam

/26 2 MAPF: Multi-Agent Path Finding given agents (starts) graph goals solution paths without collisions optimization is intractable in various criteria [Yu+ AAAI-13, Ma+ AAAI-16, Banfi+ RA-L-17, Geft+ AAMAS-22]

/26 3 quick scalable complete optimal Trade-off in MAPF Algorithms

/26 4 solved instances (%; 13,900) runtime (sec) Results on MAPF Benchmark [Stern+ SOCS-19] 13900 instances - 33 grid maps - random scenario - every 50 agents, up to max. (1000) tested on desktop PC 33 grid maps 0.0% A* [Hart+ 68]

/26 5 solved instances (%) runtime (sec) 0.0% A* [Hart+ 68] 0.4% ODrM* [W agner+ AIJ-15] complete & optimal Results on MAPF Benchmark [Stern+ SOCS-19] 13900 instances - 33 grid maps - random scenario - every 50 agents, up to max. (1000) tested on desktop PC

/26 6 solved instances (%) runtime (sec) 0.0% A* [Hart+ 68] 0.4% ODrM* [W agner+ AIJ-15] 8.3% CBS [Sharon+ AIJ-15; Li+ AIJ-21] 10.7% BCP [Lam+ COR-22] Results on MAPF Benchmark 13900 instances - 33 grid maps - random scenario - every 50 agents, up to max. (1000) tested on desktop PC solution complete* & optimal *SC: solution complete: unable to distinguish unsolvable instances comp & optimal

/26 7 solved instances (%) runtime (sec) 0.0% A* [Hart+ 68] 0.4% ODrM* [W agner+ AIJ-15] 8.3% CBS [Sharon+ AIJ-15; Li+ AIJ-21] 10.7% BCP [Lam+ COR-22] 30.9% I-ODrM* [W agner+ AIJ-15] Results on MAPF Benchmark [Stern+ SOCS-19] 13900 instances - 33 grid maps - random scenario - every 50 agents, up to max. (1000) tested on desktop PC comp & bounded sub-opt SC* & optimal *SC: solution complete: unable to distinguish unsolvable instances comp & optimal

/26 8 solved instances (%) runtime (sec) 0.0% A* [Hart+ 68] 0.4% ODrM* [W agner+ AIJ-15] 8.3% CBS [Sharon+ AIJ-15; Li+ AIJ-21] 10.7% BCP [Lam+ COR-22] 30.9% I-ODrM* [W agner+ AIJ-15] 50.5% EECBS [Li+ AAAI-21] Results on MAPF Benchmark [Stern+ SOCS-19] 13900 instances - 33 grid maps - random scenario - every 50 agents, up to max. (1000) tested on desktop PC comp & bounded sub-opt SC & bounded sub-opt SC* & optimal *SC: solution complete: unable to distinguish unsolvable instances comp & optimal

/26 9 solved instances (%) runtime (sec) 0.0% A* [Hart+ 68] 0.4% ODrM* [W agner+ AIJ-15] 8.3% CBS [Sharon+ AIJ-15; Li+ AIJ-21] 10.7% BCP [Lam+ COR-22] 30.9% I-ODrM* [W agner+ AIJ-15] 50.5% EECBS [Li+ AAAI-21] 61.4% PP [Silver AIIDE-05] 80.9% LNS2 [Li+ AAAI-22] comp & bounded sub-opt SC & bounded sub-opt incomp & sub-opt SC* & optimal comp & optimal Results on MAPF Benchmark [Stern+ SOCS-19] 13900 instances - 33 grid maps - random scenario - every 50 agents, up to max. (1000) tested on desktop PC [Stern+ SOCS-19] *SC: solution complete: unable to distinguish unsolvable instances 67.4% PIBT [Okumura+ AIJ-22] 90.5% PIBT+ [Okumura+ AIJ-22]

/26 10 85.6% LaCAM complete & sub-optimal Proposed Algorithm: LaCAM (lazy constraints addition search for MAPF) start breaking the trade-off

/26 11 Algorithm Description

/26 12 Planning Horizon agents 1 2 N … 0 1 T … timestep long planning horizon location A* [Hart+ 68] CBS [Sharon+ AIJ-15] complete, optimal agents 1 2 N … 0 1 T 2 … timestep short planning horizon PIBT [Okumura+ AIJ-22] WHCA* [Silver AIIDE-05] quick, scalable

/26 13 … … … … … search node (configuration) Vanilla A* for MAPF greedy search: 44 nodes in general: (5^N)xT nodes N: agents, T: depth intractable even with perfect heuristics goal configuration complete but slow

/26 14 PIBT for MAPF PIBT PIBT PIBT greedy search: 44 nodes only 4 configurations repeat one-timestep planning until termination use PIBT to guide exhaustive search initial configuration goal configuration [Okumura+ AIJ-22] quick but incomplete

/26 15 … … … … … Concept of LaCAM PIBT PIBT PIBT use other MAPF algorihtms to generate a promising configuration configurations are generated in a lazy manner by two-level search scheme exhaustive search but node generation are dramatically reduced => quick & complete MAPF

/26 16 Lazy Constraints Addition constraint tree (maintained implicitly) invoked multiple times during the search

/26 17 1st invoke configuration generation with Lazy Constraints Addition no constraint

/26 18 Lazy Constraints Addition 2nd invoke configuration generation with

/26 19 Lazy Constraints Addition e.g., breadth-first search 24th invoke Each configuration eventually generates all connected configurations. Theorem: LaCAM is complete discard node from Open configuration generation with

/26 20 Evaluation

/26 21 prioritized planning w/distance-based heuristics [Silver AIIDE-05] A* with operator decomposition greedy version [Standley AAAI-10] EECBS CBS-based, bounded sub-optimal [Li+ AAAI-21] LNS2 large neighborhood search for MAPF [Li+ AAAI-22] PIBT [Okumura+ AIJ-22] Performance on one-shot MAPF 25 instances, on desktop PC 30sec timeout 194x194 four-connected grid LaCAM (w/PIBT) sum-of-costs (normalized; min:1) runtime (sec) success rate agents not so bad blazing fast! worst: 699ms perfect! (diff from PIBT: tie-breaking)

/26 22 agents room-64-64-8 64x64, |V|=3,232 success rate in 30sec LaCAM orz900d 1491x656, |V|=96,603 agents worst: 8sec worst: 394ms random-32-32-20 32x32, |V|=819 agents worst: 11sec 100% MAPF Benchmark LaCAM quickly & sub-optimally solves various problems

/26 23 LaCAM (w/PIBT) PIBT [Okumura+ AIJ-22] PP [Silver AIIDE-05] greedy+OD [Standley AAAI-10] EECBS [Li+ AAAI-21] LNS2 [Li+ AAAI-22] 6/6 0/6 1/6 6/6 3/6 3/6 solved with 10sec timeout tree tunnel loop-chain corners string connector Small Congested Instances from [Luna+ IJCAI-11] animations display refined solutions LaCAM quickly & sub-optimally solves various problems

/26 24 success rate in 1,000sec runtime (sec) agents (x1000) 25 instances, timeout of1000 sec, on desctop PC warehouse-20-40-10-2-2, 340x164; |V|=38,756 Performance with x1000 agents perfect! blazing fast! worst: 26sec for 10,000 agents LaCAM PIBT demo of 10,000 agents LaCAM quickly & sub-optimally solves various problems

/26 25 LaCAM is great but… agents maze-32-32-2 32x32 |V|=666 lt_gallowstemplar_n 251x180 |V|=10,021 agents warehouse-20-40-10-2-1 321x123 |V|=22,599 agents 0% success rate in 30sec narrow corridors can be bottleneck LaCAM necessity for improvements (e.g. configuration generator)

/26 26 Concluding Remarks novel MAPF algorithm: LaCAM quickly solve various MAPF benchmarks small congested instances instances with 10k agents sub-optimal & complete theoretical side empirical side what’s next? LaCAM* w/improved configuration generator eventually converge to optima solve 99% of the MAPF benchmark in 10 sec https://kei18.github.io/lacam