Proceedings of the International Symposium on Combinatorial Search
Heuristic search and combinatorial optimization are currently very active areas of research. For example, researchers investigate how to search in real-time, how to search with limited (possibly external) memory, how to solve sequences of similar search problems faster than with isolated searches, how to improve the runtime of the searches over time, how to trade-off between the runtime and memory consumption of the search and the resulting solution quality, and how to focus the searches with sophisticated heuristics such as pattern databases. Their results are published in different conferences such as IJCAI, AAAI, ICAPS, NIPS, ICRA, and IROS. The International Symposium on Combinatorial Search (SoCS) is meant to bring these researchers together to exchange their ideas and cross-fertilize the field. Thus, in addition to seeking separate answers to questions like how to design more accurate memory-based heuristics, more I/O-efficient disk-based search algorithms, or more efficient clause-learning strategies, the symposium will stimulate thoughts on combining various techniques originated from different areas of search.
This frontmatter introduces the proceedings of the Eighteenth International Symposium on Combinatorial Search (SoCS 2025), held from August 12–15, 2025, in Scotland, United Kingdom. It includes a preface by the conference co-chairs—Maxim Likhachev, Hana Rudová, and Enrico Scala—along with details on the Best Paper Awards, the organizing and program committees, and the sponsors of this edition.
Copyright (c) 2025 Proceedings of the International Symposium on Combinatorial Search
A Conflict-Driven Approach for Reaching Goals Specified with Negation as Failure
In the context of pathfinding, first-order logic allows for the expressive specification of goals. Using negation as failure, one can specify what must not be true in a goal state instead of what must be true, which can result in succinct goal specifications while also being computationally advantageous. However, due to non-monotonicity, integration of negation as failure can be cumbersome. To address this problem, we introduce conflict-driven goal reaching (CDGR), a conflict-driven algorithm for reaching goals specified with non-monotonic logic that refines a search for a goal state based on conflicts encountered during search. Our results show that CDGR results in significantly shorter paths and can significantly speed up search when compared to not taking conflicts into consideration. Furthermore, our results show that finding paths to goals can be much more efficient when goals are specified with negation as failure instead of without negation as failure.
Copyright (c) 2025 Association for the Advancement of Artificial Intelligence
We consider a game that was played in a German television show that is similar to the sorting balls puzzle. In it, we are assumed to move one colored ball after another in a set of colored tubes so that in the end, each ball is in the tube of its color. We are allowed to use one additional (uncolored) tube. We show general properties for solvability and that the problem of minimizing the number of moves is NP-hard, which is done by a reduction from the Feedback Arc Set Problem. Furthermore, we give an implementation of an algorithm to compute such a minimal sequence of moves. The algorithm is based on breadth-first search and accelerated by a lower bound on the number of moves from the current configuration to the final one that is obtained by solving a small instance of the Feedback Arc Set Problem. Our experiments show that instances with 7 colored tubes of height 4 can be solved in a reasonable amount of time and that the number of tubes is much more critical for the running time than the heights of the tubes.
Finding All Optimal Solutions in Multi-Agent Path Finding
The Multi-Agent Path Finding problem (MAPF) aims to find conflict-free paths for a group of agents, leading each agent to its respective goal. MAPF is applicable in navigating autonomous robots and vehicles to their destination. In this paper, we study the requirement of finding all optimal solutions in MAPF. We discuss the representation of all optimal solutions, propose four algorithms for finding them, and perform an extensive empirical evaluation of the proposed algorithms.
A Problem with the Current Methodology for Comparing Search Algorithms and a Proposed Solution
This paper explores how incompletely described tie-break policies can invalidate the experimental results reported in papers on optimal bidirectional heuristic search (BiHS). Experiments usually use a single implementation of an algorithm with its specific tie-break policy. When the tie-breaks are insufficiently described, we show that the results can be irreproducible, vary dramatically under different implementations, and lead to misleading assessments of an algorithm’s performance. To ensure reproducible and representative results, papers should either provide a description of the algorithm’s implementation, i.e., the complete tie-break policy, or alternatively, give results as a summary statistic representative of all possible tie-break implementations. We developed a software tool for this purpose.
Sub-Microsecond Grid Path Planning, at What Cost?
Tree Cache is a lightweight pre-processing approach to grid path finding which works by generating a shortest path tree: from a root cell to all cells in the map. During online search Tree Cache simply follows the tree: from start and target towards the root, stopping at the first common cell. Although Tree Cache is fast, the resulting paths have no solution quality guarantees. In this paper we improve Tree Cache, in terms of speed and solution quality, by combining symmetry breaking ideas from Jump Point Search. Our new algorithm, Jump Spanning Tree Search (JSTS), can usually generate paths with low average sub-optimality in under one microsecond -- up to two orders of magnitude faster than Tree Cache. We then extend JSTS to derive a new and very fast bounded suboptimal search, which guarantees solution quality in single-digit microseconds on average. Our results establish a remarkable new level of performance in the area. In particular, we show JSTS approaches and often improves upon the output complexity of an idealised oracle, which simply reads off and returns a corresponding but optimal solution path.
New Mechanisms in Flex Distribution for Bounded Suboptimal Multi-Agent Path Finding
Multi-Agent Path Finding (MAPF) is the problem of finding a set of collision-free paths, one for each agent in a shared environment. Its objective is to minimize the sum of path costs (SOC), where the path cost of each agent is defined as the travel time from its start location to its target location. Explicit Estimation Conflict-Based Search (EECBS) is the leading algorithm for bounded-suboptimal MAPF, with the SOC of the solution being at most a user-specified factor w away from optimal. EECBS maintains sets of paths and a lower bound LB on the optimal SOC. Then, it iteratively selects a set of paths whose SOC is at most w times LB and introduces constraints to resolve collisions. For each path in a set, EECBS maintains a lower bound on its optimal path that satisfies constraints. By finding a path with cost at most its threshold, defined as w times its lower bound, EECBS guarantees to find a bounded-suboptimal solution. To speed up EECBS, previous work uses flex distribution to relax the requirement that each path needs to be at most its threshold. Though EECBS with flex distribution guarantees to find a bounded-suboptimal solution, increasing the thresholds may increase the SOC beyond w times LB, forcing EECBS to switch among different sets of paths (whose SOC are still at most w times LB), and thus reducing efficiency. To address this issue, we propose Conflict-Based Flex Distribution that distributes flex in proportion to the number of collisions. We also estimate the extra travel time (i.e., delays) needed to satisfy constraints and propose Delay-Based Flex Distribution. On top of that, we propose Mixed-Strategy Flex Distribution, combining both in a hierarchical framework. We prove that EECBS with our new flex distribution mechanisms is complete and bounded-suboptimal. The experiments show that our approaches outperform the original (greedy) flex distribution. Also, we redesign Focal-A* search from the previous work to improve LB for a congested environment.
A Bucket-Based Priority Queue for Bounded-Suboptimal and Anytime A* Search
We introduce a priority queue data structure, called a bucket heap, which generalizes the bucket queue commonly used to accelerate A* search for shortest-path problems with a small range of integer transition costs. Unlike a bucket queue, a bucket heap speeds up priority queue operations for bounded-suboptimal and Anytime A* algorithms guided by non-admissible node evaluation functions. It also provides direct access---without any additional overhead---to the underlying bucket queue of A*, which we show can be used to improve search performance in further ways.
A Preprocessing Framework for Efficient Approximate Bi-Objective Shortest-Path Computation in the Presence of Correlated Objectives
The bi-objective shortest-path (BOSP) problem seeks to find paths between start and target vertices of a graph while optimizing two conflicting objective functions. We consider the BOSP problem in the presence of correlated objectives. Such correlations often occur in real-world settings such as road networks, where optimizing two positively correlated objectives, such as travel time and fuel consumption, is common. BOSP is generally computationally challenging as the size of the search space is exponential in the number of objective functions and the graph size. Bounded sub-optimal BOSP solvers such as A*pex alleviate this complexity by approximating the Pareto-optimal solution set rather than computing it exactly (given a user-provided approximation factor). As the correlation between objective functions increases, smaller approximation factors are sufficient for collapsing the entire Pareto-optimal set into a single solution. We leverage this insight to propose an efficient algorithm that reduces the search effort in the presence of correlated objectives. Our approach for computing approximations of the entire Pareto-optimal set is inspired by graph-clustering algorithms. It uses a preprocessing phase to identify correlated clusters within a graph and to generate a new graph representation. This allows a natural generalization of A*pex to run up to five times faster on DIMACS dataset instances, a standard benchmark in the field. To the best of our knowledge, this is the first algorithm proposed that efficiently and effectively exploits correlations in the context of bi-objective search while providing theoretical guarantees on solution quality.
Efficient Primal Heuristics for Mixed Binary Quadratic Programs Using Suboptimal Rounding Guidance
Mixed Binary Quadratic Programs (MBQPs) are a class of NP-hard problems that arise in a wide range of applications, including finance, machine learning, and chemical and energy systems. Large-scale MBQPs are challenging to solve with exact algorithms due to the combinatorial search space and nonlinearity. Primal heuristics have been developed to quickly identify high-quality solutions to challenging combinatorial optimization problems. In this paper, we propose an extension for two well-established rounding-based primal heuristics, RENS and Undercover. Instead of using the optimal solution to a relaxation for variable rounding and search as in RENS, we use a suboptimal relaxation solution of the MBQP as the basis for rounding and guidance for searching over a restricted subproblem where a certain percentage of binary variables are free. We apply a similar idea to the Undercover heuristic that fixes a variable cover to the rounded relaxation values. Instead, we relax a subset of the cover variables based on the suboptimal relaxation and search over a larger restricted subproblem. We evaluate our proposed methods on synthetic MBQP benchmarks and real-world wind farm layout optimization problem instances. The results show that our proposed heuristics identify high-quality solutions within a small time limit and significantly reduce the primal gap and primal integral compared to RENS, Undercover, and solvers with additional primal heuristics integrated inside Branch-and-Bound.
Minimizing Fuel in Multi-Agent Pathfinding
The multi-agent pathfinding problem (MAPF) of finding conflict-free paths for multiple agents has attracted a large number of researchers in the past. The cost of the solution is commonly measured by the sum-of-costs (SOC) cost function or, less commonly, by Makespan. In this paper, we focus on the Fuel cost function, which is the number of physical steps the agents traverse. While Fuel was mentioned in many previous papers, our paper is the first to deepen into it. We introduce an A*-based algorithm and a CBS-based algorithm for Fuel. We study Fuel theoretically, showing that it can be (perhaps non-intuitively) more complex than SOC. Finally, we experimentally compare both algorithms against each other and against their SOC counter parts, studying their advantages and disadvantages.
Low-Level Search on Time Intervals in Branch-and-Cut-and-Price for Multi-Agent Path Finding
Multi-agent path finding is the problem of navigating a set of agents from their starting locations to their target locations while avoiding collisions. A leading method for optimal multi-agent path finding is branch-and-cut-and-price, a framework based on mathematical optimization. The reference implementation, named BCP-MAPF, shows highly competitive results against AI-based search. This paper presents BCP2-MAPF, a new implementation of branch-and-cut-and-price paired with a novel low-level path finder based on time intervals. Experimental results demonstrate that BCP2-MAPF significantly outperforms the other state-of-the-art optimal algorithms BCP-MAPF, Lazy CBS and CBSH2-RTC.
Hierarchical DeepPruner: A Novel Framework for Search Space Reduction
Combinatorial optimization (CO) problems on graphs arise in various applications across diverse domains. Many of these problems are NP-hard, and heuristics have been developed to provide near-optimal solutions. In the big data era, the high dimensionality of these problems poses significant challenges for existing heuristic methods, which struggle to scale efficiently. In this paper, we propose Hierarchical DeepPruner, an adaptive framework that employs a two-stage approach to efficiently prune the search space of CO problems on graphs. Compared to state-of-the-art pruning heuristics, our algorithm offers two key advantages: 1) it does not require extensive feature engineering or domain-specific knowledge, and 2) it outperforms all previous methods while consistently pruning over 95% of the ground set, resulting in up to several of tenfold speedups—typically with minimal impact on solution quality. Additionally, our algorithm can successfully reduce the search space of instances even if they lie outside the training distribution, resulting in small optimality gaps across multiple budgets
Lightweight and Effective Preference Construction in PIBT for Large-Scale Multi-Agent Pathfinding
PIBT is a computationally lightweight algorithm that can be applied to a variety of multi-agent pathfinding (MAPF) problems, generating the next collision-free locations of agents given another. Because of its simplicity and scalability, it is becoming a popular underlying scheme for recent large-scale MAPF methods involving several hundreds or thousands of agents. Vanilla PIBT makes agents behave greedily towards their assigned goals, while agents typically have multiple best actions, since the graph shortest path is not always unique. Consequently, tiebreaking about how to choose between these actions significantly affects resulting solutions. This paper studies two simple yet effective techniques for tiebreaking in PIBT, without compromising its computational advantage. The first technique allows an agent to intelligently dodge another, taking into account whether each action will hinder the progress of the next timestep. The second technique is to learn, through multiple PIBT runs, how an action causes regret in others and to use this information to minimise regret collectively. Our empirical results demonstrate that these techniques can reduce the solution cost of one-shot MAPF and improve the throughput of lifelong MAPF. For instance, in densely populated one-shot cases, the combined use of these tiebreaks achieves improvements of around 10-20% in sum-of-costs, without significantly compromising the speed of a PIBT-based planner.
Lazy Heuristic Search for Solving POMDPs with Expensive-to-Compute Belief Transitions
Heuristic search solvers like RTDP-Bel and LAO* have proven effective for computing optimal and bounded sub-optimal solutions for Partially Observable Markov Decision Processes (POMDPs), which are typically formulated as belief MDPs. A belief represents a probability distribution over possible system states. Given a parent belief and an action, computing belief state transitions involves Bayesian updates that combine the transition and observation models of the POMDP to determine successor beliefs and their transition probabilities. However, there is a class of problems, specifically in robotics, where computing these transitions can be prohibitively expensive due to costly physics simulations, raycasting, or expensive collision checks required by the underlying transition and observation models, leading to long planning times. To address this challenge, we propose Lazy RTDP-Bel and Lazy LAO*, which defer computing expensive belief state transitions by leveraging Q-value estimation, significantly reducing planning time. These algorithms are specific instantiations of the broader idea of lazy search for POMDPs. We demonstrate the superior performance of the proposed lazy planners in domains such as contact-rich manipulation for pose estimation, outdoor navigation in rough terrain, and indoor navigation with a 1-D Lidar sensor. Additionally, we discuss practical Q-value estimation techniques for commonly encountered problem classes that our lazy planners can leverage. Our results show that lazy heuristic search methods dramatically improve planning speed by postponing expensive belief transition evaluations while maintaining solution quality.
From Scalable SAT to MaxSAT: Massively Parallel Solution Improving Search
Maximum Satisfiability (MaxSAT) is an essential framework for combinatorial optimization at the core of automated reasoning. However, to date, no notable parallelizations with convincing scaling behaviour exist. We suggest to exploit and transfer recent advances in massively parallel SAT solving to perform scalable solution improving search (SIS) for MaxSAT solving. Building upon the distributed job scheduling and SAT solving platform Mallob, we present the first MaxSAT solver that scales to hundreds of cores through a careful combination of parallel and distributed incremental SAT solving, task parallelism and flexible load balancing, and clause sharing within and across SAT solving tasks. Experiments on up to 768 cores (16 nodes) show that our approach clearly outscales state-of-the-art SIS-based MaxSAT solvers, marking a new baseline for parallel MaxSAT solving.
From Agent Centric to Obstacle Centric Planning: A Makespan-Optimal Algorithm for the Multi-Agent Warehouse Rearrangement Problem
The Multi-Agent Warehouse Rearrangement (MAWR) problem calls for computing agents plans such that they collectively rearrange a warehouse environment from a given layout which species the location of every movable obstacle in the environment, to a goal layout. It is a natural variant of the well-studied Multi-Agent Path Finding (MAPF) and Multi-Agent Pickup and Delivery (MAPD) problems, which have numerous applications in warehouse automation. Similar to MAPF and MAPD, the problem is computationally hard and existing methods forgo any optimality guarantees while computing solutions to the problem. In contrast, in this work we present the first fully-coupled search-based makespan-optimal approach for solving the MAWR problem. This is done by shifting the algorithmic viewpoint from being agent centric to obstacle centric: Common MAPF and MAPD algorithms are agent-centric wherein tasks are assigned to agents, and the agents’ paths are planned to fulfill these tasks. In contrast, the approach we present here is obstacle-centric: Our algorithm iterates between two phases: Ph1 planning optimal paths for the movable obstacles using an adaptation of the celebrated CBS MAPF algorithm and Ph2 attempting to realize the movable obstacles paths using a network-flow algorithm. We prove that our approach guarantees minimal-makespan solutions and empirically demonstrate that it achieves better plans than state-of-the-art approaches for MAWR.
Heuristics for Bounded-Suboptimal Search
In heuristic search, it is well-established that different types of heuristics are suited for optimal heuristic search (OHS) and unbounded suboptimal search (USS). In OHS, the heuristic should minimize the error in estimating the true cost of the shortest path, whereas in USS, it is more beneficial for the heuristic to exhibit a clear gradient toward the goal, regardless of the error. However, no study has specifically investigated which heuristic is most effective for bounded suboptimal search (BSS), and the current standard is to use heuristics designed for OHS. This paper introduces a novel method for creating heuristics tailored to BSS by linearly combining heuristics that were designed for OHS and USS. Through experimental evaluation, the proposed method is compared with those suited for OHS and USS. The results demonstrate that, within certain suboptimality bounds, our new heuristic approach outperforms OHS and USS heuristics for various BSS algorithms.
Task and Motion Planning Using Infinite Completion Tree and Agnostic Skills
This work builds upon existing task and motion planning (TAMP) frameworks by integrating pre-trained Sequencing Task-Agnostic Policies (STAP) and Effort Level Search (ELS) to create a hierarchical approach that decouples high-level task decisions from low-level motion execution. The method enhances the planning process by incorporating a novel success rate estimator (P ), which provides more accurate task success predictions than traditional Q-value estimators. We formalize the problem of long-horizon manipulation tasks, where high-level decisions are made in discrete spaces and low-level actions are executed in continuous space. To guide the search process efficiently, we leverage the infinite completion tree structure of ELS, which dynamically adjusts computational resources based on task complexity. Empirical results demonstrate that our approach significantly improves planning efficiency and execution reliability, outperforming traditional methods by reducing the search space and computational overhead. Our work highlights the effectiveness of combining learned skills from STAP with ELS and P in a hierarchical structure, laying the foundation for scalable robotic planning in complex, real-world manipulation tasks.
Real-time Cost-algebraic Heuristic Search
Planning under time pressure arises in many situations. Real-time heuristic search, in which an agent must compute its next action within a prespecified time bound, has proven to be a useful model of real-time planning. However, it is laborious to prove the completeness of new real-time search algorithms. In this paper, we provide a general proof of the completeness of a standard real-time heuristic search algorithm in any problem domain that obeys the axioms of a cost algebra. The proof includes additional detail on how h values change as the algorithm learns. This foundation clarifies the dependence of the proof on domain and algorithm properties and will ease future applications of real-time planning.
Bi-Objective Search for the Traveling Salesman Problem with Time Windows and Vacant Penalties
This paper investigates a Traveling Salesman Problem with Time Windows and Vacant Penalties (TSP-TW-VP), which plans a path to service a set of machines at different locations within their respective time windows while minimizing two objective functions: the finish time and penalty for machine vacancy. There is often no single solution that optimizes both objectives simultaneously, and the problem thus seeks the Pareto-optimal solutions. TSP-TW-VP generalizes TSP-TW and is therefore NP-hard. To solve the problem, this paper develops an algorithm called Search with Look-Ahead Pruning (S-LAP) that is guaranteed to find all Pareto-optimal solutions for TSP-TW-VP. S-LAP gains computational efficiency by introducing a novel look-ahead pruning rule, and a fast dominance checking method based on both the objective functions and path history. Experimental results show that the proposed look-ahead pruning and fast dominance can speed up the search for 2-8 times over 4 different datasets.
Using Action-Policy Testing in RL to Reduce the Number of Bugs
Reinforcement learning is becoming ever more prominent in solving combinatorial search problems, in particular ones where states are images. Prior work has devised action-policy testing methodology, that identifies so-called bug states where policy performance is sub-optimal. Here we show how to leverage this methodology during the RL process, using action-policy testing to find bugs and injecting those as alternate start states for the training runs. Running experiments across six 2D games, we find that our testing-guided training often achieves similar expected reward while reducing the number of bugs.
On Path Selection for Reduction-Based Solving of Multi-Agent Pathfinding Using Graph Pruning
Multi-agent pathfinding is the task of navigating a set of mobile agents in a shared environment such that they avoid collisions. Finding an optimal solution in terms of the length of the plan is known to be a computationally hard problem (NP-Hard). In general, there are two schools of optimal algorithms: search-based and reduction-based. While search-based algorithms excel in solving large maps where few conflicts can be expected, reduction-based algorithms excel in smaller instances even when agents interact often. However, the reduction-based approaches lag behind in large instances, even with few agents. To mitigate this, a subgraph pruning method was introduced to prune unnecessary vertices to decrease the size of the instance. The pruning is based on the shortest paths for each agent. In the original study, the authors randomly selected the shortest routes. In this study, we replicate the overall approach while selecting the initial shortest path with more care. We provide several approaches for selecting one of the possible shortest paths and experimentally compare them. We note that when the makespan optimal plan is needed, not all agents are required to use the shortest path, as only the longest path dictates the makespan. Using this observation, we also introduce an approach that selects longer paths for some agents if it helps to reduce the total number of interactions between agents. We provide an experimental comparison of all proposed approaches and show that the latter performs significantly better, in most cases outperforming any approach that strictly selects only the shortest path.
Guiding the Search for the Euclidean Shortest Path Problem
We consider the problem of reducing the search space of algorithms which solve the Euclidean Shortest Path Problem by traversing a precomputed navigation mesh. Heuristics can be used to guide this traversal. We show how upper and lower bounds to the optimal path length can be combined into an independent heuristic which considerably reduces the search space of such an algorithm. In our experiments we use our heuristic in an existing routing algorithm and find that our approach yields a substantial speedup for complicated paths.
The vast majority of Multi-Agent Path Finding (MAPF) methods with completeness guarantees require planning full-horizon paths. However, planning full-horizon paths can take too long and be impractical in real-world applications. Instead, real-time planning and execution, which only allows the planner a finite amount of time before executing and replanning, is more practical for real-world multi-agent systems. Several methods utilize real-time planning schemes but none are provably complete, which leads to livelock or deadlock. Our main contribution is Real-Time LaCAM, the first Real-Time MAPF method with provable completeness guarantees. We do this by leveraging LaCAM in an incremental fashion. Our results show how we can iteratively plan for congested environments with a cutoff time of milliseconds while still maintaining the same success rate as full-horizon LaCAM. We also show how it can be used with a single-step learned MAPF policy.
Decoupling Generation and Evaluation for Parallel Greedy Best-First Search
In order to understand and control the search behavior of parallel search, recent work has proposed a class of constrained parallel greedy best-first search algorithms which only expands states that satisfy some constraint. However, enforcing such constraints can be costly, as threads must be waiting idly until a state that satisfies the expansion constraint is available. We propose an improvement to constrained parallel search which decouples state generation and state evaluation and significantly improves state evaluation rate, resulting in better search performance.
Augmenting Exploration with Locally Greedy Probes
Enhancing Greedy Best First Search (GBFS) with stochastic exploration will often greatly improve search performance. In this work, we show that one way exploration does so is by helping the search find states that are "easy" for standard GBFS without exploration. In particular, we show that in problems in which standard GBFS struggles and exploration helps, there are often many states that are reachable from the initial state that standard GBFS can quickly find solutions from. Many such states are actually outside the Bench Transition System (BTS) --- which is a structure that contains all states that standard GBFS may encounter --- meaning GBFS cannot reach them without using exploration. To allow exploration mechanisms to better exploit the existence of such states, we introduce a method called locally greedy probes. Upon a successor having an improved heuristic from its parent, locally greedy probes pause exploration and greedily hill-climb along a single path as long as heuristic improvements keep occurring. Our empirical evaluation shows that this approach is effective at enhancing several exploration mechanisms in a variety of classical planning domains.
Reevaluation of Large Neighborhood Search for MAPF: Findings and Opportunities
Multi-Agent Path Finding (MAPF) aims to arrange collision-free goal-reaching paths for a group of agents. Anytime MAPF solvers based on large neighborhood search (LNS) have gained prominence recently due to their flexibility and scalability, leading to a surge of methods, especially those leveraging machine learning, to enhance neighborhood selection. However, several pitfalls exist and hinder a comprehensive evaluation of these new methods, which mainly include: 1) Lower than actual or incorrect baseline performance; 2) Lack of a unified evaluation setting and criterion; 3) Lack of a codebase or executable model for supervised learning methods. To address these challenges, we introduce a unified evaluation framework, implement prior methods, and conduct an extensive comparison of prominent methods. Our evaluation reveals that rule-based heuristics serve as strong baselines, while current learning-based methods show no clear advantage on time efficiency or improvement capacity. Our extensive analysis also opens up new research opportunities for improving MAPF-LNS, such as targeting high-delayed agents, applying contextual algorithms, optimizing replan order and neighborhood size, where machine learning can potentially be integrated.
Multi-armed Bandit Algorithms for the Boolean Satisfiability Problem: A Survey
This paper provides a survey of recent literature on the use of multi-armed bandit algorithms to solve the Boolean satisfiability problem (SAT), a well-known NP-complete problem with broad applications in academia and industry. The application of bandit algorithms in modern SAT solvers has achieved great success in recent years, as evidenced by the excellent performance of SAT solvers using bandit algorithms in SAT competitions. Bandit algorithms are classic randomized optimization algorithms that strike a balance between exploration and exploitation and can aid in designing and improving heuristics in SAT solvers. In this paper, we introduce several aspects of the application of bandit algorithms in modern SAT solvers, ranging from heuristic methods in CDCL and SLS solvers to strategies in parallel SAT solvers. The use of bandit algorithms in SAT solvers still holds great potential. In conclusion of the survey, we summarize the current issues and suggest possible future research directions.
Should Multi-Agent Path Finding Algorithms Coordinate Target Arrival Times?
Multi-Agent Path Finding (MAPF) deals with finding conflict-free paths for a set of agents from an initial configuration to a given target configuration. The Lifelong MAPF (LMAPF) problem is a well-studied online version of MAPF in which an agent receives a new target when it reaches its current target. The common approach for solving LMAPF is to treat it as a sequence of MAPF problems, periodically replanning from the agents’ current configurations to their current targets. A significant drawback of this approach is that in MAPF the agents must reach a configuration in which all agents are at their targets simultaneously. Coordinating the agents’ paths such that they occupy their targets at the same time is needlessly restrictive for LMAPF. Techniques have been proposed to indirectly mitigate this drawback. In this position paper, we describe cases where these mitigation techniques fail. As an alternative, we propose to solve LMAPF problems by solving a sequence of modified MAPF problems, in which the objective is for each agent to eventually visit its target, but not necessarily for all agents to do so simultaneously. We refer to this MAPF variant as MAPF for Lifelong (MAPF4L) and propose how to solve it by modifying several existing MAPF algorithms. A limited experimental evaluation identifies some cases where using a MAPF4L algorithm can improve the system throughput significantly.
Extracting Problem Structure with LLMs for Optimized SAT Local Search
Encoding combinatorial problems in terms of propositional satisfiability (SAT) enables utilization of highly efficient SAT solvers for combinatorial search. Local search preprocessing accelerates the SAT solver's search by providing high-quality starting points, a technique implemented in several modern SAT solvers. However, existing preprocessing methods employ generic strategies that fail to exploit the structural patterns inherent in problem encodings. This position paper proposes a novel paradigm wherein Large Language Models (LLMs) analyze problem encoding implementations to synthesize specialized preprocessing algorithms. The LLMs examine Python-based code to identify structural patterns, enabling the automatic generation of encoding-specific local search procedures. These procedures operate across all instances sharing the same encoding scheme rather than requiring instance-specific customization. Our preliminary empirical evaluation demonstrates effective automated algorithm synthesis for structure-aware SAT preprocessing, serving as a foundation for similar approaches across multiple domains of combinatorial optimization.
Position Paper: On the Impact of Direction-Selection in BAE*
BAE*, and the independently developed DIBBS, are state-of-the-art bidirectional heuristic search algorithms that exploit heuristic consistency to efficiently prove solution optimality. Historically, BAE* has been studied with various direction-selection policies, determining whether to expand the next state from the forward or backward search. However, some of these policies expand nodes with an f-value exceeding the optimal solution cost, C*, which clearly cannot be part of any optimal solution. In this position paper, we review direction-selection strategies in BAE* and bidirectional search more broadly, analyzing their impact on the behavior of the search. Additionally, we present a low-overhead solution that prevents the expansion of nodes with f > C* across all direction-selection strategies.
Surrogate-Assisted Monte-Carlo Tree Search in Facility Location and Beyond (Extended Abstract)
Combinatorial problems abound in industry. A persistent issue encountered using search-based solutions is that evaluating particular nodes may be expensive. As an example, organisations frequently adjust their facilities network by opening new branches in promising areas and closing branches in areas where they expect low profits, which may be formulated as a combinatorial search problem. In this extended abstract, we examine a particular class of facility location problems, where the objective is to minimize the loss of sales resulting from the removal of several retail stores. However, estimating sales accurately is expensive and time-consuming. To overcome this challenge, we leverage Monte-Carlo Tree Search assisted by a surrogate model that computes evaluations faster. Initial results suggest that MCTS supported by a fast surrogate function can generate solutions faster while maintaining a solution consistent with non-assisted MCTS.
BLAST: Bit-Blasting Numbers for Classical Planning (Extended Abstract)
It is well known that numeric planning can be made decidable if the domain of all numeric state variables is finite. This bounded formulation can be polynomially compiled into classical planning with Boolean conditions and conditional effects preserving the plan size exactly. However, it remains unclear whether this compilation has any practical utility. To explore this aspect, this work revisits the theoretical compilation framework from a practical perspective, focusing on the fragment of simple numeric planning. Specifically, we introduce three different compilations. The first, called one-hot, aims to systematise the current practice among planning practitioners of modelling numeric planning through classical planning. The other two, termed binary compilations, extend and specialise the logarithmic encoding introduced in previous literature. Our experimental analysis reveals that the overly complex logarithmic encoding can, surprisingly, be made practical with some representational expedients. Among these, the use of axioms is particularly crucial. Furthermore, we identify a class of mildly numeric planning problems where a classical planner, i.e., LAMA, when run on the compiled problem, is highly competitive with state-of-the-art numeric planners.
Learning Heuristic Functions with Graph Neural Networks for Numeric Planning (Extended Abstract)
In this paper, we investigate the application of heuristics based on Graph Neural Networks (GNNs) to lifted numeric planning problems, an area that has been relatively unexplored. Building upon the GNN approach for learning general policies proposed by Staahlberg et al., we extend the architecture to make it sensitive to the numeric components inherent in the planning problems we address. We achieve this by observing that, although the state space of a numeric planning problem is infinite, the finite subgoal structure of the problem can be incorporated into the architecture, allowing for the construction of only a finite number of nodes. Instead of learning general policies, we train our models to function as a heuristic within a best-first search algorithm. We explore various configurations of this architecture and demonstrate that the resulting heuristics are highly informative and, in certain domains, offer a better trade-off between guidance and computational cost compared to other inductive and deductive heuristics.
Exploring the Trade-off Between Flexible and Deployable Models for PDDL+ Urban Traffic Control (Extended Abstract)
The problem of traffic signal optimisation has been successfully tackled using the PDDL+ planning formalism, which also provides an ideal ground for simulating traffic behaviour and performing what-if analysis to assess and compare alternative scenarios. This line of research leads to approaches that can efficiently generate high-quality signal plans with significant benefits in terms of congestion and emissions reduction, as demonstrated both in simulations and real-world deployments. Existing models for automated planning-based traffic signal control can be roughly divided into two classes. (i) Models maximising the flexibility of the traffic controller, where the planning system can dynamically adjust the duration of traffic stages without constraints on the overall cycles and on the differences between subsequent cycles. (ii) Models that guarantee the deployability of traffic signal control techniques also on legacy infrastructure, by forcing the AI approach to select the cycle configurations of traffic signals for the controlled junctions from a given pre-defined set. Of course, both classes offer valuable properties and benefits: the extreme flexibility helps shed light on the potential gains achievable through investment in brand-new infrastructure, whereas the deployable approaches ensure the immediate usability of tools to maximise short-term impact. To bridge the gap between different model classes and explore the trade-off between flexibility and deployability, we present the Trade model. It enables the enforcement of key constraints required for deployability while preserving a level of flexibility that surpasses the capabilities of traditional traffic control infrastructure.
Critical Section Macros - New Results (Extended Abstract)
This extended abstract presents new empirical results of recently introduced Critical Section Macro-operators (CSMs) whose design is inspired by using lockable resources in critical sections in parallel computing. In particular, we provide results on the IPC-2023 learning track domains and four planners, including the winner of the agile track of the IPC-2023 and a lifted planner.
Multi-Agent Path Finding for Schedule Constrained Automation (Extended Abstract)
In modern automation settings, jobs are processed across machines with interdependencies and are subject to limited equipment availability. When transportation between machines is considered, the problem evolves into a complex multi-agent routing task with operational constraints. Existing Multi-Agent Path Finding (MAPF) algorithms address challenges such as robustness and uncertainty, but practical applications involving scheduling constraints often require considerable manual effort for adaptation and heuristic design. In this paper, we introduce MAPF-SC, an extension of MAPF that incorporates scheduling constraints for continuous task flows. We explore the challenges of applying existing techniques to this problem, emphasizing the engineering effort involved in addressing these constraints. Our evaluation investigates the impact of temporal and topological variations on performance, highlighting key factors that influence real-world automation scenarios.
Suboptimal Search with Dynamic Distribution of Suboptimality (Extended Abstract)
In bounded-suboptimal heuristic search, the aim is to find a solution path within a given bound as quickly as possible, which is crucial when computational resources are limited. Recent research has demonstrated Weighted A* variants such as XDP that find bounded suboptimal solutions without needing to perform state re-expansions; they work by shifting where the suboptimality in the search is allowed. However, the suboptimality distribution is fixed before the search begins. This abstract describes Dynamic Suboptimality Weighted A* (DSWA*), an algorithm introduced at AAAI 2025 that allows suboptimality to be dynamically distributed at runtime based on the properties of the search.
Hierarchical Seating Allocation (Extended Abstract)
The Hierarchical Seating Allocation Problem (HSAP) is the problem to allocate an organizational hierarchy of teams to a set of seats on a floor plan. This problem is driven by the necessity for large organizations with large hierarchies to ensure that teams with close hierarchical relationships are seated in proximity to one another, such as ensuring a research group occupies a contiguous area. Currently, this problem is managed manually leading to infrequent and suboptimal replanning efforts. To alleviate this manual process, we propose an end-to-end framework to solve the HSAP. A scalable approach to calculate the distance between any pair of seats using a probabilistic road map (PRM) and rapidly-exploring random trees (RRT) which is combined with heuristic search and dynamic programming approach to solve the HSAP using integer programming. We demonstrate our approach under different sized instances by evaluating the PRM framework and subsequent allocations both quantitatively and qualitatively.
You May Split but You Might Work It Out Later: First Steps Toward Merging Nodes in MAPF (Extended Abstract)
CBS is a state-of-the-art MAPF algorithm whose performance has been enhanced over the years by the introduction of heuristics that focus the search and reasoning techniques that identify specific types of conflicts that can be resolved faster. To further improve the efficiency of CBS, we present a novel idea based on constraint-reasoning techniques that merges similar high-level nodes close to the root of the constraint tree while preserving CBS' optimality. As a result, some of CBS' duplicate work that occurs when expanding similar high-level nodes is avoided. Our first experimental results using a simple CBS variant (ICBS-h) show a significant reduction in the number of expanded high-level nodes on average.
Bidirectional Bounded-Suboptimal Heuristic Search with Consistent Heuristics (Extended Abstract)
Recent advancements in bidirectional heuristic search have yielded significant theoretical insights and novel algorithms. While most previous work has concentrated on optimal search methods, this paper focuses on bounded-suboptimal bidirectional search, where a bound on the suboptimality of the solution cost is specified. We build upon the state-of-the-art optimal bidirectional search algorithm, BAE*, designed for consistent heuristics, and introduce several variants of BAE* specifically tailored for the bounded-suboptimal context. Through experimental evaluation, we compare the performance of these new variants against other bounded-suboptimal bidirectional algorithms as well as the standard weighted A* algorithm. Our results demonstrate that each algorithm excels under distinct conditions, highlighting the strengths and weaknesses of each approach.
Bidirectional Heuristic Search in Longest Path Problems (Extended Abstract)
Bidirectional heuristic search has the potential to decrease search time in combinatorial search problems amenable to backward search. To date, bidirectional search has been limited to minimization or shortest path problems. This paper extends the notion of bidirectional heuristic search to (constrained) longest path problems, which turns out to be non-trivial due to the path necessarily being part of the state and the inapplicability of standard bidirectional heuristic search techniques such as meet-in-the-middle (MM) and BAE*. We present a basic bidirectional heuristic search for longest simple path (LSP) in undirected graphs, and prove its correctness. We then suggest several refinements and optimizations, as well as a generalization to other types of longest path problems Coil-in-a-box (CIB). Empirical evaluation shows that, as with many forms of bidirectional search, sometimes unidirectional search wins, but for a sizable chunk of problem instance types, bidirectional search performs better by expanding fewer nodes and achieves a shorter runtime despite the increased overhead per expansion.
Uncertainty in Real-World Vehicle Routing (Extended Abstract)
In our paper, we aim to address common sources of uncertainty in real-world industrial vehicle routing problems. By extending traditional deterministic heuristic solvers with easy-to-integrate, reusable, and computationally efficient mechanisms, we introduce reasoning about uncertainty while retaining the capability of scaling to problems with up to 1,000 customers. We formulate four such mechanisms, including standard chance constraints, two data manipulation methods, and a novel penalty-based method. These mechanisms are evaluated on both standard benchmarks and real-world industrial vehicle routing instances, and their key search-related properties are discussed. This extended abstract presents results previously published at the European Conference on Artificial Intelligence 2024.
Object Packing and Scheduling for Sequential 3D Printing: A Linear Arithmetic Model and a CEGAR-Inspired Optimal Solver (Extended Abstract)
We address the problem of object arrangement and scheduling for sequential 3D printing. Unlike the standard 3D printing, where all objects are printed slice by slice, in sequential 3D printing, objects are completed one after another. In the sequential case, it is necessary to ensure that the moving parts of the printer do not collide with previously printed objects. We propose to express the problem of sequential printing as a linear arithmetic formula, which is then solved using a solver for satisfiability modulo theories (SMT) combined with counterexample guided abstraction refinement (CEGAR).
RAILGUN: A Unified Convolutional Policy for Multi-Agent Path Finding Across Different Environments and Tasks (Extended Abstract)
Multi-Agent Path Finding (MAPF), which focuses on finding collision-free paths for multiple robots, is crucial for applications ranging from aerial swarms to warehouse automation. Solving MAPF is NP-hard so learning-based approaches for MAPF have gained attention, particularly those leveraging deep neural networks. Nonetheless, despite the community's continued efforts, all learning-based MAPF planners still rely on decentralized planning due to variability in the number of agents and map sizes. We have developed the first centralized learning-based policy for MAPF problem called RAILGUN. RAILGUN is not an agent-based policy but a map-based policy. By leveraging a CNN-based architecture, RAILGUN can generalize across different maps and handle any number of agents. We collect trajectories from rule-based methods to train our model in a supervised way. In experiments, RAILGUN outperforms most baseline methods and demonstrates great zero-shot generalization capabilities on various tasks, maps and agent numbers that were not seen in the training dataset.
LSRP*: Scalable and Anytime Planning for Multi-Agent Path Finding with Asynchronous Actions (Extended Abstract)
Multi-Agent Path Finding (MAPF) seeks collision-free paths for multiple agents from their respective starting locations to their respective goal locations while minimizing path costs. Although many MAPF algorithms were developed, most of them rely on a common assumption on synchronized actions, where the actions of all agents start at the same time and always take a time unit. This assumption may limit use of MAPF planners in practice. To get rid of this assumption, recently, an algorithm called Loosely Synchronized Rule-Based Planning (LSRP) is proposed, which can find sub-optimal solutions for many agents. However, LSRP often finds poor quality solutions due to its unbounded sub-optimality. This paper develops a new anytime planner called LSRP* that can keep improving solution quality after the initial solution is obtained until the runtime budget depletes. We analyze the properties of LSPR* and test it against several baselines with up to 1000 agents in various maps. LSRP* can handle up to 25% more agents than LSRP and can reduce up to 40% of the solution cost found by LSRP.