Pith. sign in

REVIEW 5 major objections 5 minor 2 cited by

Adaptive-Horizon Conflict-Based Search for Closed-Loop Multi-Agent Path Finding

T0 review · 5 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A closed-loop MAPF planner proves anytime optimality by reusing one search tree as the horizon grows.

desk verdict The active-prefix constraint-tree reuse is a genuine idea, but the optimality theorem's bridge to SOC-optimality doesn't hold as written—worth a revise, not a desk reject. read the letter →

arxiv 2602.12024 v3 pith:F66FFFXU submitted 2026-02-12 cs.RO

Jiarui Li , Federico Pecora , Runyu Zhang , Gioele Zardini This is my paper · ORCID
classification cs.RO
keywords multi-agentpathfindingclosed-loopplanningconflict-basedsearchanytimealgorithmhorizonadaptationconstrainttreereusesumofcosts
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

ACCBS (Anytime Closed-Loop Conflict-Based Search) is a multi-agent path-finding algorithm that plans only a short horizon, executes the first step, then replans from the new state in a feedback loop. The paper's central claim is that if the maximum planning horizon is chosen at least as long as the makespan of some optimal solution, and if the planner is given unlimited time, ACCBS terminates with a globally optimal sum-of-costs trajectory — making it the first closed-loop MAPF method with a formal performance guarantee. The algorithm gets its anytime behavior from widening the horizon whenever the budget allows, while reusing the same conflict-resolution tree, so longer thinking strictly improves or maintains solution quality. This matters because existing MAPF methods either plan all movements in advance (slow to start, fragile to disturbances) or react online with no quality guarantee.

What carries the argument

The active prefix and the cost-invariance/tree-reuse pair. The active prefix is the portion of the joint Hmax-step trajectory on which conflict-freedom is currently enforced, defined by the running horizon hr. Lemma III.1 shows that node costs do not change when hr increases, provided the low-level planner finishes each trajectory with a shortest path to the goal after the last constrained time. Proposition III.1 then shows this makes the constraint tree for horizon hr a rooted subtree of the tree for horizon hr+1, so ACCBS can continue searching on the same tree when the horizon grows, giving the anytime property without recomputation.

What would settle it

Take a one-shot instance where the optimal makespan is M, run ACCBS with an Hmax smaller than M (so the theorem's premise is violated), and show the returned trajectory's SOC exceeds the optimal SOC. More directly, construct a low-level planner that, after the last constrained time, does not follow a shortest path to the goal; then Lemma III.1's cost invariance fails, and the same node can have different costs under different running horizons, breaking the tree-reuse argument.

Watch

Extended reading notes

Core claim

The paper establishes Theorem III.1: for a one-shot MAPF instance, if the nominal horizon Hmax is at least the makespan of some sum-of-costs-optimal solution and no time limit is imposed, ACCBS terminates in finite time and returns a conflict-free joint trajectory of length Hmax that is globally optimal with respect to the finite-horizon cost J_Hmax, which coincides with the sum of costs. This is achieved by a best-first search over a single constraint tree in which the running horizon hr grows from 1 to Hmax; conflicts are only resolved inside the 'active prefix' of length hr, and conflicts later in time are temporarily ignored. Two properties make this work: the cost of any node is invaria

Load-bearing premise

The optimality and completeness proof assumes the planner is handed an Hmax that is at least as large as the makespan of some sum-of-costs-optimal solution; no procedure is given for finding such an Hmax, and if it is chosen too small the algorithm is only optimal with respect to the truncated horizon cost, not the true sum of costs.

Editorial extensions

If this is right

  • As the computational budget grows, ACCBS's returned cost is monotonically non-increasing and converges; the first-step movement is always available, so execution can start immediately.
  • With a large enough Hmax and unlimited time, ACCBS is complete and SOC-optimal, matching the guarantees of classical CBS despite being closed-loop.
  • Finite-horizon planning scales to larger instances than infinite-horizon CBS, as shown in the paper's Table I.
  • ACCBS naturally handles uncertainties like changing goals, execution delays, and new agent arrivals, which open-loop planners cannot.
  • The cost invariance property makes the MPC-style finite-horizon cost consistent as the horizon expands, so the anytime improvement is well-defined.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The main practical risk is horizon selection: Hmax is required to be at least the optimal makespan for the optimality theorem, and that quantity is NP-hard to know a priori, so in practice ACCBS may be optimal only for a truncated proxy cost; a principled way to set Hmax (e.g., online from an upper bound) would be needed to transfer the guarantee.
  • The anytime guarantee is about the best solution in the internal tree, but the paper notes that returns are not strictly monotonic in the executed trajectory; a testable extension would be to measure whether the actual executed SOC improves monotonically with budget on benchmark instances.
  • The tree-reuse idea is not specific to CBS: the same active-prefix mechanism could wrap other bounded-suboptimal CBS variants (as the paper itself notes), or even other search-based planners, to give them closed-loop anytime behavior with formal guarantees.
  • The one-shot optimality theorem relies on a perfect-actuation, static-environment setting; extending the proof to lifelong goals or stochastic delays would require more than the current argument, since the feedback loop changes the effective cost.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper proposes ACCBS, a closed-loop, receding-horizon variant of Conflict-Based Search (CBS) for multi-agent path finding. The planner maintains a running horizon and an 'active prefix' over which conflicts are resolved, reusing a single constraint tree as the horizon grows. The authors prove a cost-invariance lemma (Lemma III.1) and a constraint-tree-reuse proposition (Proposition III.1), and claim that, under an idealized one-shot regime with Hmax at least the makespan of an SOC-optimal solution and unlimited time, ACCBS is complete and SOC-optimal (Theorem III.1). Experiments compare ACCBS with PIBT on benchmark maps for one-shot, lifelong, and uncertainty settings.

Significance. If the theoretical claims were correct, ACCBS would be a significant contribution: an anytime, closed-loop MAPF algorithm that preserves CBS optimality while allowing early execution. The cost-invariance and tree-reuse ideas are interesting and potentially reusable, and the experimental study covers relevant scenarios. However, as analyzed below, the central optimality theorem is not established as written, and the claimed bridge from finite-horizon prefix optimization to full SOC-optimality is missing. The paper would need a substantial reworking of the theory or a careful restatement of the guarantees before the headline contribution is credible.

major comments (5)
  1. [Section III-E, Theorem III.1(2)] The reduction to 'standard CBS with horizon Hmax' in the proof is not valid. Standard CBS optimizes complete start-to-goal trajectories. ACCBS optimizes Hmax-step prefixes with terminal cost gamma(v_Hmax) (Definition III.4). A node can be conflict-free on [0,Hmax] while some agents are not yet at their goals at Hmax; the appended shortest-path suffixes from Lemma III.1 may conflict after Hmax. In that case J_Hmax(n) is strictly less than the SOC of any valid completion, so optimality w.r.t. J_Hmax does not imply SOC-optimality. The proof shows only optimality of the prefix, not that the optimal prefix has all agents at their goals by Hmax or that the suffixes are conflict-free. This is a load-bearing gap in the main theorem.
  2. [Algorithm 2, line 31; Section III-E] Algorithm 2 returns EXTRACTFIRSTSTEPMOVEMENT(tau_best), not a full trajectory. Yet Theorem III.1(2) states that ACCBS 'returns a conflict-free joint trajectory of length Hmax.' No argument is given that one call of ACCBS produces an executable optimal plan; the closed-loop controller replans at every step, and there is no MPC-style invariant transferring single-call optimality to the executed closed-loop trajectory. The theorem therefore does not support the paper's claim of being the first closed-loop MAPF algorithm with performance guarantees.
  3. [Section III-C, Lemma III.1 and Proposition III.1] Both results assume that after the largest constrained time index, the low-level planner INDPLAN extends each agent's trajectory along a shortest path to its goal and then waits. This property is asserted in the text but not derived from Algorithm 1 or 2, nor is INDPLAN specified. If the low-level planner does not satisfy this property, the cost-invariance identity J_h(n)=J_{h+1}(n) fails, and the constraint-tree-reuse claim collapses. As it stands, this is an unproven axiom on which the entire horizon-adaptation mechanism rests.
  4. [Section III-E, Theorem III.1(1)] The proof of the anytime property is logically inverted. It says the feasible set shrinks as h_r grows, 'so the optimal value for the larger horizon is no better than for smaller horizons.' But shrinking the feasible set makes the optimal value non-decreasing, not non-increasing. Moreover, when h_r increases, the current incumbent may no longer be conflict-free and must be discarded, so the best-cost sequence can increase. The theorem's claim of 'monotonically non-increasing' best cost is contradicted by Remark III.4, which concedes that strict monotonic improvement is not guaranteed. This needs correction or a different definition of the anytime metric.
  5. [Section III-E, choice of Hmax] The optimality theorem is conditional on choosing Hmax at least as large as the makespan of some SOC-optimal solution. That quantity is not known a priori (computing it is NP-hard), and the paper provides no procedure to set Hmax. If Hmax is too small, ACCBS solves a truncated proxy and the SOC-optimality claim is void. Unless the authors give a verifiable sufficient condition or a bound on Hmax, the theorem is an idealized statement with limited algorithmic content.
minor comments (5)
  1. [Algorithm 2, lines 16–23] When a node is conflict-free at h_r = Hmax, the algorithm does not return immediately; it exits the inner while and continues the outer loop. The description in Section III-D says the loop stops when such a node is found, but the pseudocode does not implement that. Either add a return statement or align the text.
  2. [Algorithm 2, lines 5 and 27] The INDPLAN call at line 5 passes Hmax, while the calls in lines 27–28 omit the horizon argument. The signature is inconsistent. Also define INDPLAN's inputs in the text.
  3. [Definition III.4] The running cost index uses t (the current time) and then ℓ for steps; the notation is confusing. Also the terminal cost gamma(v, a_i) is used even when v is not reachable within the remaining steps; clarify that gamma is the graph distance, not a time-constrained distance.
  4. [Section IV, Fig. 3 and Fig. 4] The y-axis in Fig. 3 is labeled SOC but appears to be normalized or per-agent; please clarify units. Also the comparison baselines are mostly PIBT; CBS is only shown in Table I as a runtime reference, not as a quality baseline for large instances. A richer comparison with other anytime or windowed methods would strengthen the empirical claims.
  5. [Abstract and Section I] The phrase 'asymptotically optimal as the budget increases' is used without a formal definition. Theorem III.1 gives a one-shot guarantee for infinite time, not an asymptotic statement. Align the terminology with the actual results.

Circularity Check

0 steps flagged · score 0.0 of 10

No load-bearing circularity; the optimality proof leans on external CBS results and explicit definitions, with correctness gaps that are not circular reductions.

full rationale

The paper's central optimality claim (Theorem III.1) is not circular. The proof explicitly inherits completeness and optimality from standard CBS, an external result [15], and the step from J_Hmax optimality to SOC-optimality is a stated definitional bridge under the assumption that Hmax upper-bounds the makespan of an SOC-optimal solution. The cost-invariance Lemma III.1 is an internal argument resting on an explicit low-level-planner suffix assumption; it is not a fitted parameter renamed as a prediction, nor does it presuppose the theorem it supports. The self-citations to FICO [23] and Anytime PIBT [31] frame the closed-loop formulation and related work, but they do not supply the claimed optimality result or forbid alternatives; they are not load-bearing. There are genuine correctness risks noted in the manuscript: the low-level planner INDPLAN is unspecified and the suffix-shortest-path property is asserted rather than derived from Algorithm 1, and the proof's transition from an Hmax-step prefix with terminal cost to a full conflict-free executed trajectory is not fully bridged. However, these are omissions or proof gaps, not circular definitions, fitted-input-as-prediction schemes, or self-citation chains. No specific reduction of the derived result to its own inputs by construction is present, so the circularity score is 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central theoretical claims rest on standard CBS optimality, an ideal static regime, an uncomputable bound on Hmax, and an unverified property of the low-level planner. There are no new physical entities and no fitted constants; the algorithm's performance inputs are Hmax and the time budget.

free parameters (2)
  • Hmax (nominal maximal horizon) = not specified; must be at least the makespan of some SOC-optimal solution
    Introduced in Definition III.7 and Theorem III.1. The optimality guarantee is conditional on choosing Hmax large enough, but no procedure to obtain such Hmax is given; in general it requires knowing an optimal solution.
  • per-step time budget t_max = 0.5 to 30 seconds in experiments
    Used in Algorithm 2 and varied across experiments. Performance and anytime behavior depend on it, and the paper explicitly leaves principled budget allocation to future work.
assumptions (4)
  • ad hoc to paper Low-level planner INDPLAN produces trajectories whose suffix after the largest constrained time index follows a shortest path to the goal.
    Invoked in Lemma III.1 and Proposition III.1, but not proven from Algorithm 1's definition; INDPLAN itself is not specified.
  • domain assumption Conflict selection in the constraint tree is consistent when the running horizon increases, so the parent-child relations in T_h are identical in T_{h+1}.
    Proposition III.1(b) requires that the same conflicts at times at most h are chosen in both trees, but no conflict-priority tie-breaking rule is specified.
  • domain assumption Standard CBS is complete and optimal with respect to the finite-horizon cost J_Hmax.
    Used in the proof of Theorem III.1 as an inherited external result.
  • domain assumption The theoretical analysis is restricted to a static one-shot instance, perfect actuation, and Hmax at least the makespan of some SOC-optimal solution.
    Section III-E explicitly restricts completeness and optimality to this idealized regime, which does not cover the closed-loop disturbance scenarios in the experiments.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Adaptive-Horizon Conflict-Based Search for Closed-Loop Multi-Agent Path Finding." pith.science (2026). https://pith.science/paper/F66FFFXU

@misc{pith2026260212024,
  author       = {Pith},
  title        = {Pith review of: Adaptive-Horizon Conflict-Based Search for Closed-Loop Multi-Agent Path Finding},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/F66FFFXU}},
  note         = {Machine review of arXiv:2602.12024}
}
read the original abstract

Multi-Agent Path Finding (MAPF) is a core coordination problem for large robot fleets in automated warehouses and logistics. Existing approaches are typically either open-loop planners, which must compute complete trajectories before execution and therefore may incur substantial planning latency before actions can be taken, or closed-loop heuristics without reliable performance guarantees, limiting their use in safety-critical deployments. This paper presents Anytime Closed-Loop Conflict-Based Search (ACCBS), a closed-loop algorithm built on a finite-horizon variant of Conflict-Based Search (CBS) with a horizon-changing mechanism inspired by iterative horizon-deepening in Model Predictive Control (MPC). ACCBS dynamically adjusts the planning horizon based on the available computational budget, and reuses a single constraint tree to enable seamless transitions between horizons. As a result, it produces high-quality feasible solutions quickly while being asymptotically optimal as the budget increases, exhibiting anytime behavior. Extensive case studies demonstrate that ACCBS achieves a favorable balance between computational efficiency, solution quality, and execution flexibility, while naturally accommodating online disturbances through its closed-loop formulation.

Figures

Figures reproduced from arXiv: 2602.12024 by the authors.

Figure 1
Figure 1. Constraint tree in ACCBS. Colors indicate succes￾sive stages of the search. The same constraint tree is reused as the planning horizon grows, enabling seamless transitions between different horizon lengths (Proposition III.1). Among these algorithms, Conflict-Based Search (CBS) [15] serves as the fundamental computational backbone and core optimizer. CBS organizes the search in a binary constraint tree whose nodes s… view at source ↗
Figure 2
Figure 2. Example of active prefix. Only conflicts inside the active prefix (shaded region) are resolved; conflicts in the tail are ignored until the running horizon grows to cover them. horizon remains valid for a larger one. Thus, as the running horizon grows from 1 to Hmax, search effort is preserved: larger-horizon searches are warm-started from trees built for smaller horizons, and the overall complexity is comparable to… view at source ↗
Figure 4
Figure 4. ACCBS can naturally deal with lifelong MAPF with [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: Tradeoff between planning time and performance. Performance gains from longer “thinking” time may not justify the cost, making budget selection non-trivial. 50 75 100 125 150 175 200 Number of Agents 0.5 1.0 1.5 SOC ACCBS (with PC) ACCBS (without PC) (a) Large Empty Ma…
Figure 6
Figure 6. Figure 6: Effect of the prioritized conflict mechanism. The overhead of conflict classification may outweigh gains in tree exploration efficiency, leading to lower-quality solutions. horizon schedule for different applications. In addition, other CBS variants, such as ECBS [22] …

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. PRIMAL3: Pathfinding via Reinforcement and Imitation Multi-Agent Learning - Leveraging LaCAM3

    cs.RO 2026-08 conditional novelty 6.0 of 10

    A dual-graph, reinforcement-and-imitation learning framework for MAPF that scales to 100,000 agents, with results close to search-based solvers on random maps.

  2. Dual-Informed Vertical Expansion for Multi-Objective Node Selection in Anytime Conflict-Based Search

    cs.RO 2026-06 unverdicted novelty 6.0 of 10

    DIVE is a best-bound-between-dives and depth-oriented-within-dive node selection policy for exact CBS that reduces dive breaks and queue memory while supplying early certified incumbents.

Reference graph

Works this paper leans on

33 extracted references · 6 linked inside Pith · cited by 2 Pith papers

  1. [1]

    Multi-agent pathfinding: Definitions, variants, and benchmarks,

    R. Stern, N. R. Sturtevant, A. Felner, S. Koenig, H. Ma, T. T. Walker, J. Li, D. Atzmon, L. Cohen, T. K. S. Kumar, E. Boyarski, and R. Bartak, “Multi-agent pathfinding: Definitions, variants, and benchmarks,”Symposium on Combinatorial Search (SoCS), pp. 151– 158, 2019

    2019

  2. [2]

    Guest editorial: A revolution in the warehouse: A retrospective on kiva systems and the grand challenges ahead,

    R. D’Andrea, “Guest editorial: A revolution in the warehouse: A retrospective on kiva systems and the grand challenges ahead,”IEEE Transactions on Automation Science and Engineering, vol. 9, no. 4, pp. 638–639, 2012

    2012

  3. [3]

    Accelerating search- based planning for multi-robot manipulation by leveraging online- generated experiences,

    Y . Shaoul, I. Mishani, M. Likhachev, and J. Li, “Accelerating search- based planning for multi-robot manipulation by leveraging online- generated experiences,” inProceedings of the International Conference on Automated Planning and Scheduling, vol. 34, 2024, pp. 523–531

    2024

  4. [4]

    Lns2+ rl: Combining multi-agent reinforcement learning with large neighborhood search in multi-agent path finding,

    Y . Wang, T. Duhan, J. Li, and G. Sartoretti, “Lns2+ rl: Combining multi-agent reinforcement learning with large neighborhood search in multi-agent path finding,” inNat. Conf. on Artificial Intelligence (AAAI), vol. 39, no. 22, 2025, pp. 23 343–23 350

    2025

  5. [5]

    Multi agent path finding using evolu- tionary game theory,

    S. Paul and J. V . Deshmukh, “Multi agent path finding using evolu- tionary game theory,”arXiv preprint arXiv:2212.02010, 2022

    arXiv 2022

  6. [6]

    Coordinating hundreds of cooperative, autonomous vehicles in warehouses,

    P. R. Wurman, R. D’Andrea, and M. Mountz, “Coordinating hundreds of cooperative, autonomous vehicles in warehouses,”AI magazine, vol. 29, no. 1, pp. 9–9, 2008

    2008

  7. [7]

    Finding optimal solutions to cooperative pathfinding problems,

    T. Standley, “Finding optimal solutions to cooperative pathfinding problems,” inNat. Conf. on Artificial Intelligence (AAAI), vol. 24, no. 1, 2010, pp. 173–178

    2010

  8. [8]

    Planning optimal paths for multiple robots on graphs,

    J. Yu and S. M. LaValle, “Planning optimal paths for multiple robots on graphs,” in2013 IEEE International Conference on Robotics and Automation. IEEE, 2013, pp. 3612–3617

    2013

Show all 33 references
  1. [9]

    Mapf- lns2: Fast repairing for multi-agent path finding via large neighborhood search,

    J. Li, Z. Chen, D. Harabor, P. J. Stuckey, and S. Koenig, “Mapf- lns2: Fast repairing for multi-agent path finding via large neighborhood search,” inNat. Conf. on Artificial Intelligence (AAAI), vol. 36, no. 9, 2022, pp. 10 256–10 265

    2022

  2. [10]

    Lacam: Search-based algorithm for quick multi-agent pathfinding,

    K. Okumura, “Lacam: Search-based algorithm for quick multi-agent pathfinding,” inNat. Conf. on Artificial Intelligence (AAAI), vol. 37, no. 10, 2023, pp. 11 655–11 662

    2023

  3. [11]

    Anytime multi-agent path finding via large neighborhood search,

    J. Li, Z. Chen, D. Harabor, P. J. Stuckey, and S. Koenig, “Anytime multi-agent path finding via large neighborhood search,” inIntl. Joint Conf. on AI (IJCAI), 2021, pp. 4127–4135

    2021

  4. [12]

    Improving lacam for scalable eventually optimal multi- agent pathfinding,

    K. Okumura, “Improving lacam for scalable eventually optimal multi- agent pathfinding,”arXiv preprint arXiv:2305.03632, 2023

    2023 arXiv

  5. [13]

    Engineering lacam*: Towards real-time, large-scale, and near- optimal multi-agent pathfinding,

    ——, “Engineering lacam*: Towards real-time, large-scale, and near- optimal multi-agent pathfinding,”arXiv preprint arXiv:2308.04292, 2023

    2023 arXiv

  6. [14]

    Tracking progress in multi-agent path finding,

    B. Shen, Z. Chen, M. A. Cheema, D. D. Harabor, and P. J. Stuckey, “Tracking progress in multi-agent path finding,”arXiv preprint arXiv:2305.08446, 2023

    2023 arXiv

  7. [15]

    Conflict-based search for optimal multi-agent pathfinding,

    G. Sharon, R. Stern, A. Felner, and N. R. Sturtevant, “Conflict-based search for optimal multi-agent pathfinding,”Artificial Intelligence, vol. 219, pp. 40–66, 2015

    2015

  8. [16]

    Branch-and- cut-and-price for multi-agent path finding,

    E. Lam, P. Le Bodic, D. Harabor, and P. J. Stuckey, “Branch-and- cut-and-price for multi-agent path finding,”Computers & Operations Research, vol. 144, p. 105809, 2022

    2022

  9. [17]

    The increasing cost tree search for optimal multi-agent pathfinding,

    G. Sharon, R. Stern, M. Goldenberg, and A. Felner, “The increasing cost tree search for optimal multi-agent pathfinding,”Artificial Intel- ligence, vol. 195, pp. 470–495, 2013

    2013

  10. [18]

    Icbs: The improved conflict-based search algorithm for multi-agent pathfinding,

    E. Boyarski, A. Felner, R. Stern, G. Sharon, O. Betzalel, D. Tolpin, and E. Shimony, “Icbs: The improved conflict-based search algorithm for multi-agent pathfinding,” inProceedings of the International Symposium on Combinatorial Search, vol. 6, no. 1, 2015, pp. 223–225

    2015

  11. [19]

    Eecbs: A bounded-suboptimal search for multi-agent path finding,

    J. Li, W. Ruml, and S. Koenig, “Eecbs: A bounded-suboptimal search for multi-agent path finding,” inNat. Conf. on Artificial Intelligence (AAAI), vol. 35, no. 14, 2021, pp. 12 353–12 362

    2021

  12. [20]

    Subdimensional expansion for multirobot path planning,

    G. Wagner and H. Choset, “Subdimensional expansion for multirobot path planning,”Artificial Intelligence, vol. 219, pp. 1–24, 2015

    2015

  13. [21]

    Search-based optimal solvers for the multi-agent pathfinding problem: Summary and challenges,

    A. Felner, R. Stern, S. Shimony, E. Boyarski, M. Goldenberg, G. Sharon, N. Sturtevant, G. Wagner, and P. Surynek, “Search-based optimal solvers for the multi-agent pathfinding problem: Summary and challenges,” inProceedings of the International Symposium on Combinatorial Searc...

    2017

  14. [22]

    Suboptimal variants of the conflict-based search algorithm for the multi-agent pathfinding problem,

    M. Barer, G. Sharon, R. Stern, and A. Felner, “Suboptimal variants of the conflict-based search algorithm for the multi-agent pathfinding problem,” inProceedings of the International Symposium on Combi- natorial Search, vol. 5, no. 1, 2014, pp. 19–27

    2014

  15. [23]

    Fico: Finite- horizon closed-loop factorization for unified multi-agent path finding,

    J. Li, A. Zanardi, F. Pecora, R. Zhang, and G. Zardini, “Fico: Finite- horizon closed-loop factorization for unified multi-agent path finding,” arXiv preprint arXiv:2511.13961, 2025

    2025

  16. [24]

    Constrained model predictive control: Stability and optimality,

    D. Q. Mayne, J. B. Rawlings, C. V . Rao, and P. O. Scokaert, “Constrained model predictive control: Stability and optimality,”Au- tomatica, vol. 36, no. 6, pp. 789–814, 2000

    2000

  17. [25]

    Continuity and monotonicity of the mpc value function with respect to sampling time and prediction horizon,

    V . Bachtiar, E. C. Kerrigan, W. H. Moase, and C. Manzie, “Continuity and monotonicity of the mpc value function with respect to sampling time and prediction horizon,”Automatica, vol. 63, pp. 330–337, 2016

    2016

  18. [26]

    Lifelong multi-agent path finding for online pickup and delivery tasks,

    H. Ma, J. Li, T. Kumar, and S. Koenig, “Lifelong multi-agent path finding for online pickup and delivery tasks,”arXiv preprint arXiv:1705.10868, 2017

    2017 arXiv

  19. [27]

    Multi-agent path finding with delay probabilities,

    H. Ma, T. S. Kumar, and S. Koenig, “Multi-agent path finding with delay probabilities,” inNat. Conf. on Artificial Intelligence (AAAI), vol. 31, no. 1, 2017

    2017

  20. [28]

    Lifelong multi-agent path finding in large-scale warehouses,

    J. Li, A. Tinka, S. Kiesel, J. W. Durham, T. S. Kumar, and S. Koenig, “Lifelong multi-agent path finding in large-scale warehouses,” inNat. Conf. on Artificial Intelligence (AAAI), vol. 35, no. 13, 2021, pp. 11 272–11 281

    2021

  21. [29]

    S. M. LaValle,Planning algorithms. Cambridge university press, 2006

    2006

  22. [30]

    Priority inheritance with backtracking for iterative multi-agent path finding,

    K. Okumura, M. Machida, X. Défago, and Y . Tamura, “Priority inheritance with backtracking for iterative multi-agent path finding,” Artificial Intelligence, vol. 310, p. 103752, 2022

    2022

  23. [31]

    Anytime single-step mapf planning with anytime pibt,

    N. Gandotra, R. Veerapaneni, M. S. Saleem, D. Harabor, J. Li, and M. Likhachev, “Anytime single-step mapf planning with anytime pibt,” arXiv preprint arXiv:2504.07841, 2025

    2025 arXiv

  24. [32]

    An empirical comparison of the hardness of multi-agent path finding under the makespan and the sum of costs objectives,

    P. Surynek, A. Felner, R. Stern, and E. Boyarski, “An empirical comparison of the hardness of multi-agent path finding under the makespan and the sum of costs objectives,” inProceedings of the International Symposium on Combinatorial Search, vol. 7, no. 1, 2016, pp. 145–146

    2016

  25. [33]

    Grne and J

    L. Grne and J. Pannek,Nonlinear model predictive control: theory and algorithms. Springer Publishing Company, Incorporated, 2013

    2013

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.