Improving LaCAM for Scalable Eventually Optimal Multi-Agent Pathfinding

IJCAI-23
https://kei18.github.io/lacam2/

Transcript

1. Improving LaCAM
   for Scalable Eventually Optimal
   Multi-Agent Pathfinding
   Keisuke Okumura
   Macao, 19th – 25th Aug. 2023
   IJCAI-23
   https://kei18.github.io/lacam2
   National Institute of Advanced Industrial Science and Technology (AIST)
   University of Cambridge
   

   View Slide

2. /31
   2
   MAPF: Multi-Agent Path Finding
   given agents (starts)
   graph
   goals
   solution paths without collisions
   cost total travel time, distance,
   makespan, etc
   

   View Slide

3. /31
   3
   solvability
   & quality
   high
   low
   effort small
   large
   speed & scalability
   complete
   optimal
   incomplete
   suboptimal
   Tradeoff in MAPF Algorithms
   

   View Slide

4. /31
   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]
   33 grid maps
   e.g., random-32-32-20, 200 agents
   00.0% A* [Hart+ 68]
   complete optimal
   

   View Slide

5. /31
   5
   
   
   
   
   
   
   
   
   
   
   
   
   
   runtime (sec)
   solved instances (%)
   00.0% A* [Hart+ 68]
   00.4% ODrM* [Wagner+ AIJ-15]
   complete optimal
   

   View Slide

6. /31
   6
   
   
   
   
   
   
   
   
   
   
   
   
   
   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]
   complete
   solution complete optimal
   optimal
   (unable to identify unsolvable instances)
   

   View Slide

7. /31
   7
   
   
   
   
   
   
   
   
   
   
   
   
   
   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]
   complete
   solution complete
   complete bounded suboptimal
   optimal
   optimal
   (unable to identify unsolvable instances)
   

   View Slide

8. /31
   8
   
   
   
   
   
   
   
   
   
   
   
   
   
   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]
   complete
   solution complete
   complete
   solution complete bounded suboptimal
   bounded suboptimal
   optimal
   optimal
   (unable to identify unsolvable instances)
   

   View Slide

9. /31
   9
   
   
   
   
   
   
   
   
   
   
   
   
   
   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]
   complete
   solution complete
   complete
   solution complete
   incomplete
   bounded suboptimal
   suboptimal
   bounded suboptimal
   optimal
   optimal
   (unable to identify unsolvable instances)
   

   View Slide

10. /31
    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]
    complete
    solution complete
    complete
    solution complete
    incomplete
    bounded suboptimal
    suboptimal
    bounded suboptimal
    optimal
    optimal
    (unable to identify unsolvable instances)
    85.6% LaCAM [Okumura+ AAAI-23] complete suboptimal
    

    View Slide

11. /31
    11
    
    
    
    
    
    
    
    
    
    
    
    
    
    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* (initial solution)
    complete
    solution complete
    complete
    solution complete
    incomplete
    complete
    complete eventually optimal
    bounded suboptimal
    suboptimal
    bounded suboptimal
    optimal
    optimal
    suboptimal
    (unable to identify unsolvable instances)
    this study
    

    View Slide

12. /31
    12
    [Okumura AAAI-23]
    contributions of this study:
    two enhancements over LaCAM
    1. LaCAM*: eventually optimal version for accumulative transition costs
    2. successor generation tuning for obtaining initial solutions quickly
    

    View Slide

13. /31
    13
    [Okumura AAAI-23]
    contributions of this study:
    two enhancements over LaCAM
    1. LaCAM*: eventually optimal version for accumulative transition costs
    2. successor generation tuning for obtaining initial solutions quickly
    

    View Slide

14. /31
    14
    …
    … …
    … …
    search node
    (configuration)
    goal configuration
    Vanilla A* for MAPF
    complete but very slow
    greedy search: 44 nodes
    in general: (5^N)xT nodes
    N: agents, T: depth
    intractable even with
    perfect heuristics
    

    View Slide

15. /31
    15
    PIBT
    PIBT
    PIBT
    repeat one-timestep planning until termination
    use PIBT to guide exhaustive search
    initial configuration
    PIBT
    goal configuration
    [Okumura+ AIJ-22]
    quick but incomplete
    greedy search: 44 nodes
    only 4 configurations
    

    View Slide

16. /31
    16
    …
    … …
    … …
    LaCAM
    [Okumura AAAI-23]
    lazy constraints addition search for MAPF; complete
    greedy: 44 nodes
    LaCAM: 4 nodes
    => quick & complete MAPF
    lazy successor generation
    using other MAPF algorithms
    PIBT
    PIBT
    PIBT
    not generated
    no quality guarantee
    

    View Slide

17. /31
    17
    configuration &
    cost (makespan)
    1
    2
    3
    4
    6
    5
    0 initial config.
    5
    goal config.
    LaCAM stops the search
    when finding the goal config.
    search tree
    parent – children
    other neighbors
    LaCAM*
    

    View Slide

18. /31
    18
    1
    2
    3
    4
    5
    6
    0
    5
    LaCAM* continues the search
    after finding the goal config.
    LaCAM*
    parent – children
    other neighbors
    initial config.
    goal config.
    search tree
    configuration &
    cost (makespan)
    1
    

    View Slide

19. /31
    19
    1
    2
    3
    4
    5
    6
    0
    5
    1
    LaCAM*
    new edge when finding new connections,
    

    View Slide

20. /31
    20
    1
    2
    3
    3
    2
    3
    0
    4
    1
    LaCAM*
    This is an anytime algorithm,
    and eventually optimal
    if the solution cost is
    accumulative transition costs
    when finding new connections,
    rewrite the tree by Dijkstra
    

    View Slide

21. /31
    21
    [Okumura AAAI-23]
    contributions of this study:
    two enhancements over LaCAM
    1. LaCAM*: eventually optimal version for accumulative transition costs
    2. successor generation tuning for obtaining initial solutions quickly
    

    View Slide

22. /31
    22
    
    
    
    
    
    
    
    
    
    
    
    
    
    runtime (sec)
    solved instances (%)
    99.0% LaCAM*
    improvement on successor generation
    85.6% LaCAM [Okumura+ AAAI-23]
    poor performance in graphs with narrow corridors
    search iterations (until finding initial solutions)
    128 23,907 287,440
    Too much! optimal solution length = 5
    

    View Slide

23. /31
    23
    …
    … …
    … …
    LaCAM with PIBT
    lazy successor generation
    using other MAPF algorithms
    PIBT
    PIBT
    PIBT
    performance heavily relies on
    the underlying algorithm
    

    View Slide

24. /31
    24
    Pitfall in PIBT
    PIBT tries to assign each agent
    to the vertex closest to the goal
    

    View Slide

25. /31
    25
    Incorporating Swap
    PIBT tries to assign each agent
    to the vertex closest to the goal
    reverse this in specific situations
    - check the paper for details
    - inspired by Push and Swap/Rotate [Luna+ IJCAI-11; de Wilde+ JAIR-14]
    

    View Slide

26. /31
    26
    128 23,907 287,440
    6 8 8
    search iterations
    until finding initial solutions
    original
    with reversing
    

    View Slide

27. /31
    27
    What can the current LaCAM* do?
    

    View Slide

28. /31
    28
    optimally solve small congested MAPF instances within a second
    

    View Slide

29. /31
    29
    suboptimally solve MAPF for 10,000 agents in a warehouse-style map
    with narrow corridors, in a few seconds on my laptop
    

    View Slide

30. /31
    30
    
    
    
    
    
    
    
    
    
    
    
    
    
    runtime (sec)
    solved instances (%; 13900)
    suboptimally solve 99% of MAPF benchmark instances
    within 10 seconds
    remaining 1%:
    only maze-128-128-1
    
    
    
    
    
    
    
    
    agents
    success rate
    in 30sec
    LaCAM*
    other
    algorithms
    LaCAM*
    33 grid maps
    

    View Slide

31. /31
    31
    Concluding Remarks
    https://kei18.github.io/lacam2
    improving covergence speed (current: very slow)
    improving initial solution quality (current: not excellent)
    LaCAM* is just a graph pathfinding algorithm; other applications?
    LaCAM*
    realization of quick, scalable, complete, and eventually optimal MAPF algorithm
    future directions
    

    View Slide