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Pathfinding for 10k agents

Pathfinding for 10k agents

Used in a seminar talk in Cambridge
https://talks.cam.ac.uk/talk/index/204508

Keisuke Okumura | 奥村圭祐

November 01, 2023
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  1. /73
    Pathfinding
    for 10k agents
    Keisuke Okumura1,2
    1st Nov. 2023, Wednesday Seminar, Dept. of Computer Science and Technology, Univ. of Cambridge
    1University of Cambridge
    2National Institute of Advanced Industrial Science and Technology (AIST), Japan
    kei18
    https://kei18.github.io
    [email protected]

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    2
    "Swarm" automation is ubiquitous
    Insider Tech / YouTube
    Ocado’s warehouse

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    3
    Le Goc+ UIST-16
    Flatland Challenge / AIcrowd
    Li+ AAAI-23
    StarCraft / YouTube Zhang+ Automation in Construction. 2018

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    4
    underlying common problem:
    Okumura & Defago. IJCAI-23
    collision-free pathfinding for multiple agents
    • quick, real-time
    • scalable
    • fewer redundant motions (optimality)

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    5
    generated by DALL-E 3
    Two roads
    Decentralization
    Centralization

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    6
    Two roads
    Decentralization
    quick, scalable
    Centralization
    theoretical guarantees
    e.g., completeness, optimality

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    7
    Intel Newsroom / YouTube
    Intel’s Automated Material-Handling System
    (semi-)decentralization is the only way?
    Demands for 1k-10k scale

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    8
    Drone Addicts / YouTube
    Port of Amsterdam
    @tuidelescribano / X
    Shibuya Scramble Crossing, Tokyo
    Decentralization is powerful

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    9
    @yr_6001_as / X
    Skylark Channel / YouTube
    Delivery Robots in Restaurants deadlock
    but with possibility of miscoordination

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    10
    Radio BandNews FM / Facebook
    São Paulo, gridlocked intersection
    Miscoordination
    triggers tragedy

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    11
    Financial Times, https://www.ft.com
    Miscoordination triggers tragedy
    Centralization can
    reduce miscoordination

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    12
    Varambally, S., Li, J., & Koenig, S. Which MAPF Model Works Best for Automated Warehousing? SoCS. 2022.
    simulation for warehouse automation (not my work)
    multi-agent path finding algorithm
    Centralization also improves system performance
    semi-decentralized

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    13
    Can we build scalable centralized pathfinding algorithms,
    while still having nice theoretical guarantees?

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    14
    given agents
    graph
    goals
    solution
    paths without collisions
    cost total travel time, distance,
    makespan, etc
    MAPF: Multi-Agent Path Finding

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  15. /73
    15
    1. Okumura, K., Yonetani, R., Nishimura, M., & Kanezaki, A. CTRMs: Learning to Construct Cooperative Timed Roadmaps for Multi-agent Path Planning in Continuous Spaces. AAMAS. 2022.
    2. Okumura, K., Machida, M., Défago, X., & Tamura, Y. Priority Inheritance with Backtracking for Iterative Multi-agent Path Finding. AIJ. 2022.
    3. Okumura, K., &Defago, X. Quick Multi-Robot Motion Planning by Combining Sampling and Search. IJCAI. 2023.
    4. Okumura, K., Bonnet, F., Tamura, Y., & Défago, X. Offline Time-Independent Multi-Agent Path Planning. T-RO. 2023. Extended from IJCAI-22.
    5. Okumura, K. & Defago, X. Solving Simultaneous Target Assignment and Path Planning Efficiently with Time-Independent Execution. AIJ. 2023. ICAPS-22 Best Student Paper
    6. Okumura, K., & Tixeuil, S. Fault-Tolerant Offline Multi-Agent Path Planning. AAAI. 2023.
    crash tolerance6
    asynchronous execution4 with target assignment5
    continuous spaces1 lifelong planning2 arbitrary shapes3
    Solving MAPF is the foundation of:

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    16
    Centralized MAPF methods are NOT scalable?

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    17
    Hart, P. E., Nilsson, N. J., & Raphael, B. A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. on Systems Science and Cybernetics. 1968.
    start
    goal
    A* search
    start
    goal
    f = g + h
    search tree

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    18

    … …
    … …
    search node
    (configuration)
    goal configuration
    Vanilla A* for MAPF

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    19
    Completealgorithms return solutions for solvable instances in finite time;
    otherwise, they report the non-existence.
    Optimalalgorithms always return solutions having minimum costs.
    Algorithm properties
    A* is complete. It is optimal with admissible heuristics.

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    20
    runtime (sec)
    solved instances (%)













    - 13,900 instances
    - 33 grid maps
    - every 50 agents, up to max. (1000)
    - tested on standard desktop PC
    Stern, R. et al. Multi-Agent Pathfinding: Definitions, Variants, and Benchmarks. SoCS. 2019.
    33 grid maps e.g., random-32-32-20, 200 agents
    Evaluation on MAPF benchmark
    maze-32-32-2, 100 agents
    00.0% A* [Hart+ 68] complete optimal
    algorithm properties
    computation time

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    21
    Reason for poor performance of A*
    start
    goal
    search tree
    branching factor (number of successor nodes)
    O(5^N) N: #agents
    MAPF has a huge branching factor:
    3,125
    9,765,625
    95,367,431,640,625
    931,322,574,615,478,515,625
    9,094,947,017,729,282,379,150,390,625
    88,817,841,970,012,523,233,890,533,447,265,625
    5^5
    5^10
    5^20
    5^30
    5^40
    5^50
    For 10k agents? Ridiculous!

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    22













    runtime (sec)
    solved instances (%)
    0.0% A* [Hart+ 68]
    0.4% ODrM* [Wagner+ AIJ-15]
    complete optimal
    algorithm properties
    A* variant
    Complete and optimal algorithms
    are hopeless in scalability.
    Finding optimal solutions is NP-hard.
    Yu, J., & LaValle, S. Structure and intractability of optimal multi-robot path planning on graphs. AAAI. 2013.
    Banfi, J., Basilico, N., & Amigoni, F. Intractability of time-optimal multirobot path planning on 2D grid graphs with holes. RA-L. 2017.

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    23
    theoretical guarantees
    e.g., completeness, optimality
    planning effort
    c.f., speed, scalability
    Tradeoff in MAPF algorithms

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    Relaxing completness
    Optimalalgorithms always return solutions having minimum costs.
    Completealgorithms return solutions for solvable instances in finite time;
    otherwise, they report the non-existence.
    unable to identify unsolvable instances

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    25
    CBS: Conflict-based Search
    Sharon, G., Stern, R., Felner, A., & Sturtevant, N. R. Conflict-based search for optimal multi-agent pathfinding. AIJ. 2015.
    high-level search
    Image by GraphicMama-team from Pixabay
    identify conflicts in solution candidates
    low-level search
    find a path satisfying constraints
    (e.g., A*)
    query a single-agent path
    that avoids detected conflicts
    return a path
    satisfying constraints

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    26
    opt.
    cost: 5
    t=1
    cost: 5
    replan
    t=1
    cost: 6
    replan
    t=1 t=2
    cost: 6
    replan
    t=1 t=2
    cost: 6
    replan
    stay
    Many powerful extensions are available of CBS, e.g.,
    • Boyarski, E. et al. ICBS: improved conflict-based search algorithm for multi- agent
    pathfinding. IJCAI. 2015.
    • Felner, A. et al. Adding heuristics to conflict-based search for multi-agent path
    finding. ICAPS. 2018
    • Li, J. et al. Pairwise symmetry reasoning for multi-agent path finding search. AIJ. 2021.
    • …
    search when and where each agent cannot use it
    Sharon, G., Stern, R., Felner, A., & Sturtevant, N. R. Conflict-based search
    for optimal multi-agent pathfinding. AIJ. 2015.
    How CBS works
    high-level low-level

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    27
    0.0% A* [Hart+ 68]
    0.4% ODrM* [Wagner+ AIJ-15]
    complete optimal
    runtime (sec)
    solved instances (%)
    8.3% CBS [Sharon+ AIJ-15; Li+ AIJ-21]
    10.7% BCP [Lam+ COR-22] solution complete optimal
    (unable to identify unsolvable instances)
    two-level, but with mathematical optimization at high-level

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    28
    Relaxing Optimality
    Optimalalgorithms always return solutions having minimum costs.
    Completealgorithms return solutions for solvable instances in finite time;
    otherwise, they report the non-existence.
    allowing bounded suboptimal solutions:
    obtained solution cost ≤ w*(optimal solution cost) where w ≥ 1

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    not explored => reducing search effort
    29
    Intuition of finding bounded suboptimal solutions
    goal
    search tree
    to be optimal:
    expand a node with minimum f-value, fmin
    to be bounded suboptimal:
    allowing to expand nodes
    with f ≤ w*fmin
    (w ≥ 1)
    applicable where search schemes exist, e.g., A*-based and CBS

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    30
    0.0% A* [Hart+ 68]
    0.4% ODrM* [Wagner+ AIJ-15]
    8.3% CBS [Sharon+ AIJ-15; Li+ AIJ-21]
    10.7% BCP [Lam+ COR-22]
    complete
    solution complete optimal
    optimal
    (unable to identify unsolvable instances)
    runtime (sec)
    solved instances (%)
    30.9% I-ODrM*-5 [Wagner+ AIJ-15] complete bounded suboptimal
    A* variant

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    31
    Relaxing Completeness and Optimality
    Optimalalgorithms always return solutions having minimum costs.
    Completealgorithms return solutions for solvable instances in finite time;
    otherwise, they report the non-existence.
    allowing bounded suboptimal solutions

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    32
    0.0% A* [Hart+ 68]
    0.4% ODrM* [Wagner+ AIJ-15]
    8.3% CBS [Sharon+ AIJ-15; Li+ AIJ-21]
    10.7% BCP [Lam+ COR-22]
    30.9% I-ODrM*-5 [Wagner+ AIJ-15]
    complete
    solution complete
    complete bounded suboptimal
    optimal
    optimal
    (unable to identify unsolvable instances)
    runtime (sec)
    solved instances (%)













    50.5% EECBS-5 [Li+ AAAI-21] solution complete bounded suboptimal
    CBS variant

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    33
    Give up everything
    Optimalalgorithms always return solutions having minimum costs.
    Completealgorithms return solutions for solvable instances in finite time;
    otherwise, they report the non-existence.

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    34
    PP: Prioritized Planning
    Erdmann, M., & Lozano-Perez, T. On multiple moving objects. Algorithmica. 1987; Silver, D. Cooperative pathfinding. AIIDE. 2005.
    simple, quick, scalable, reasonable solution quality
    1 stay
    2
    2. Perform single-agent pathfinding
    for each agent according to priorities,
    while avoiding collisions
    with already competed paths.
    1 2
    1. Assign priorities to each agent.

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    35
    0.0% A* [Hart+ 68]
    0.4% ODrM* [Wagner+ AIJ-15]
    8.3% CBS [Sharon+ AIJ-15; Li+ AIJ-21]
    10.7% BCP [Lam+ COR-22]
    30.9% I-ODrM*-5 [Wagner+ AIJ-15]
    complete
    solution complete
    complete bounded suboptimal
    optimal
    optimal
    (unable to identify unsolvable instances)
    runtime (sec)
    solved instances (%)













    50.5% EECBS-5 [Li+ AAAI-21] solution complete bounded suboptimal
    61.4% PP [Silver AIIDE-05] incomplete suboptimal

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    36
    MAPF-LNS2: Large Neighborhood Search
    Li, J., Chen, Z., Harabor, D., Stuckey, P. J., & Koenig, S. MAPF-LNS2: fast repairing for multi-agent path finding via large neighborhood search. AAAI. 2022.
    high-level search
    low-level search
    query paths for the subset of agents
    return paths
    identify subset of agents
    (e.g., random selection)
    find paths for the subset
    • without collisions with agents not in the subset
    • with a smaller number of collisions within the subset
    (e.g., PP)

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    37
    runtime (sec)
    solved instances (%)













    0.0% A* [Hart+ 68]
    0.4% ODrM* [Wagner+ AIJ-15]
    8.3% CBS [Sharon+ AIJ-15; Li+ AIJ-21]
    10.7% BCP [Lam+ COR-22]
    30.9% I-ODrM*-5 [Wagner+ AIJ-15]
    complete
    solution complete
    complete bounded suboptimal
    optimal
    optimal
    (unable to identify unsolvable instances)
    50.5% EECBS-5 [Li+ AAAI-21] solution complete bounded suboptimal
    61.4% PP [Silver AIIDE-05]
    incomplete suboptimal
    80.9% LNS2 [Li+ AAAI-22]
    capable of addressing hundreds of agents

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    38
    You're kidding?
    It should be easy!
    Example that PP/LNS2 fails to find a solution

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    39
    Summary so far
    complete
    optimal
    incomplete
    suboptimal
    My research part begins, finally!
    holy grail
    state-of-the-art studies
    theoretical
    guarantees
    planning effort small
    large
    speed & scalability

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    40
    Unblock Me / Google Play
    DavidPlays / YouTube
    goal
    planning stage
    acting stage
    Two styles to solve puzzle
    long-horizon
    (deliberative, offline)
    short-horizon
    (reactive, online)

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    41
    theoretical
    guarantees
    planning effort small
    large
    speed & scalability
    complete
    optimal
    incomplete
    suboptimal
    long-horizon
    (deliberative, offline)
    short-horizon
    (reactive, online)
    Planning Horizon
    planning stage
    acting stage

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    42
    theoretical
    guarantees
    planning effort small
    large
    speed & scalability
    Strategy to overcome the tradeoff
    short-horizon planning pulls
    long-horizon planning
    integration

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    43
    This is just a metaphor.. Image by OpenClipart-Vectors from Pixabay
    PIBT
    Okumura+ AIJ-22
    LaCAM*
    Okumura AAAI-23, IJCAI-23

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    44
    This is just a metaphor.. Image by OpenClipart-Vectors from Pixabay
    PIBT
    Okumura+ AIJ-22
    LaCAM*
    Okumura AAAI-23, IJCAI-23

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    45
    PIBT: Priority Inheritance with Backtracking
    Okumura, K., Machida, M., Défago, X., & Tamura, Y. Priority Inheritance with Backtracking for Iterative Multi-agent Path Finding. AIJ. 2022. (extended from IJCAI-19*)
    collision-free configuration while reflecting preferences
    PIBT
    1
    desired
    2
    3
    4
    5
    4
    2
    1
    desired
    3
    *originally developed for lifelong pathfinding scenarios
    preference & priority
    +
    configuration
    High
    Low

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    46
    PIBT
    PIBT
    initial configuration
    PIBT
    goal configuration
    Vanilla PIBT for MAPF
    incomplete and suboptimal

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    47
    greedy assignment with priorities is incomplete
    stuck
    high
    low
    mid
    How PIBT works – 1/4

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    48
    high
    low
    mid as high
    priority inheritance
    Sha+ IEEE Trans Comput-90
    How PIBT works – 2/4

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    49
    high as high
    as high as high
    as high stuck
    but still not feasible
    How PIBT works – 3/4

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    50
    invalid
    valid
    re-plan
    re-plan
    valid You can move
    invalid You must re-plan, I will stay
    introduce backtracking
    How PIBT works – 4/4
    always generate collision-free configurations

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    51
    Multi-agent Pickup & Delivery
    Sushi
    Sushi plates are guaranteed to be delivered

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    52
    Performance of PIBT
    random-32-32-20
    32x32
    30sec timeout







    #agents
    success
    rate
    EECBS
    PP
    LNS2
    0%
    PIBT
    runtime
    (sec)





    #agents
    EECBS PP
    ost003d
    194x194 four-connected grid
    LNS2
    blazing fast!
    worst: 550ms
    PIBT
    quick but shortsighted

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    53
    runtime (sec)
    solved instances (%)













    0.0% A* [Hart+ 68]
    0.4% ODrM* [Wagner+ AIJ-15]
    8.3% CBS [Sharon+ AIJ-15; Li+ AIJ-21]
    10.7% BCP [Lam+ COR-22]
    30.9% I-ODrM*-5 [Wagner+ AIJ-15]
    complete
    solution complete
    complete bounded suboptimal
    optimal
    optimal
    (unable to identify unsolvable instances)
    50.5% EECBS-5 [Li+ AAAI-21] solution complete bounded suboptimal
    61.4% PP [Silver AIIDE-05]
    incomplete suboptimal
    80.9% LNS2 [Li+ AAAI-22]
    67.4% PIBT [Okumura+ AIJ-22]
    PIBT is convenient, blazing fast, but…

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    54
    This is just a metaphor.. Image by OpenClipart-Vectors from Pixabay
    PIBT
    Okumura+ AIJ-22
    LaCAM*
    Okumura AAAI-23, IJCAI-23

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    55

    … …
    … …
    search node
    (configuration)
    goal configuration
    Recap: A*
    exponential number of
    node generation
    greedy search: 44 nodes

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    56
    PIBT
    initial configuration
    Recap: PIBT
    use PIBT to
    guide exhaustive search
    only 4 configurations
    PIBT
    goal configuration
    PIBT

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    57
    … …
    PIBT
    initial configuration
    … …
    PIBT
    goal configuration
    Okumura, K. LaCAM: Search-Based Algorithm for Quick Multi-Agent Pathfinding. AAAI. 2023
    LaCAM: Lazy Constraints
    Addition Search for MAPF

    PIBT
    not generated
    immediately
    1. Configurations are generated
    in a lazy manner
    exhaustive search with two tricks
    2. Use other MAPF algorihtms to
    generate a promising configuration
    greedy: 44 nodes
    LaCAM: 4 nodes
    => quick & complete MAPF

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    must go left in the next config.
    58
    constraint tree
    (maintained implicitly)
    invoked multiple times
    during the search
    Lazy constraints addition – 1/4

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    1st invoke
    configuration generation with
    no constraint
    Lazy constraints addition – 2/4

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    2nd invoke
    configuration generation with
    Lazy constraints addition – 3/4

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    e.g., breadth-first search
    24th invoke
    configuration generation with
    Lazy constraints addition – 4/4
    completeness proof:
    Each configuration eventually generates all neighbor configurations.

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    62














    EECBS
    PP
    LNS2
    PIBT
    worst: 11sec
    LaCAM
    #agents
    success
    rate
    random-32-32-20, 32x32, 30sec timeout, 400 agents
    Performance of LaCAM

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    63













    runtime (sec)
    solved instances (%)
    0.0% A* [Hart+ 68]
    0.4% ODrM* [Wagner+ AIJ-15]
    8.3% CBS [Sharon+ AIJ-15; Li+ AIJ-21]
    10.7% BCP [Lam+ COR-22]
    30.9% I-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]
    complete
    solution complete
    complete
    solution complete bounded suboptimal
    bounded suboptimal
    optimal
    optimal
    (unable to identify unsolvable instances)
    incomplete suboptimal
    85.6% LaCAM [Okumura AAAI-23] complete suboptimal
    Start breaking the tradeoff!

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    0.0% A* [Hart+ 68]
    0.4% ODrM* [Wagner+ AIJ-15]
    8.3% CBS [Sharon+ AIJ-15; Li+ AIJ-21]
    10.7% BCP [Lam+ COR-22]
    30.9% I-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]
    85.6% LaCAM [Okumura AAAI-23]
    complete
    solution complete
    complete
    solution complete
    complete
    bounded suboptimal
    bounded suboptimal
    optimal
    optimal
    suboptimal
    (unable to identify unsolvable instances)
    incomplete suboptimal
    Before LaCAM: scalability ≠ solvability

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    65













    runtime (sec)
    solved instances (%)
    85.6% LaCAM [Okumura+ AAAI-23] complete suboptimal
    99.0% LaCAM* (initial solution) complete eventually optimal
    Okumura, K. Improving LaCAM for Scalable Eventually Optimal Multi-Agent Pathfinding. IJCAI. 2023.
    LaCAM* with fine-tuned PIBT

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    66













    runtime (sec)
    solved instances (%)
    99.0% LaCAM* (initial solution) complete eventually optimal
    LaCAM* establishes a landmark result!
    Okay, it’s too crazy...
    remaining 1%: only maze-128-128-1

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    67













    runtime (sec)
    solved instances (%)
    0.0% A* [Hart+ 68]
    0.4% ODrM* [Wagner+ AIJ-15]
    8.3% CBS [Sharon+ AIJ-15; Li+ AIJ-21]
    10.7% BCP [Lam+ COR-22]
    30.9% I-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]
    complete
    solution complete
    complete
    solution complete bounded suboptimal
    bounded suboptimal
    optimal
    optimal
    (unable to identify unsolvable instances)
    incomplete suboptimal
    85.6% LaCAM [Okumura AAAI-23]
    99.0% LaCAM* [Okumura IJCAI-23]
    complete
    complete eventually optimal
    suboptimal
    lose
    nice
    props.

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    68
    LaCAM* suboptimally solves MAPF for 10kagents
    in a warehouse-style map with many narrow corridors,
    in 5 secondson my laptop

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    69
    Can we build scalable centralized pathfinding algorithms,
    while still having nice theoretical guarantees?

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    70
    Short-horizon planning pulls long-horizon planning
    LaCAM*
    with PIBT

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    71
    Jan. 2021. When I was a 1st-year PhD student:
    Centralized pathfinding for 10k agents?
    You’re a dreamer!
    To be honest, I agreed at the time.

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    Jan. 2021. When I was a 1st-year PhD student:
    Centralized pathfinding for 10k agents?
    You’re a dreamer!
    To be honest, I agreed at the time.
    LaCAM*
    2023
    Image by naobimfrom Pixabay

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    73
    What do you want to do with 10k agents?
    LaCAM*
    2023

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    Thank you for listening!
    Acknowledgements to mentors / collaborators:
    X. Defago, Y. Tamura, F. Bonnet, M. Machida, R. Yonetani, M. Nishimura, A. Kanezaki, S. Tixeuil
    Funding:
    JSPS DC & Overseas Research Fellowship, JST ACT-X, Yoshida Scholarship Foundation
    And, A. Prorok + members of PROROK Lab for hosting me at Cambridge!
    kei18
    https://kei18.github.io
    [email protected]
    Questions / research collaboration proposals are more than welcome:

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