The rapid adoption of electric vehicles (EVs) in modern transport systems has made energy-aware routing a critical task in their successful integration, especially within large-scale transport networks. In cases where an EV's remaining energy is limited and charging locations are not easily accessible, some destinations may only be reachable through an energy-optimal path: a route that consumes less energy than all other alternatives. The feasibility of such energy-efficient paths depends heavily on the accuracy of the energy model used for planning, and thus failing to account for vehicle dynamics can lead to inaccurate energy estimates, rendering some planned routes infeasible in reality. This paper explores the impact of vehicle dynamics on energy-optimal path planning for EVs. We first investigate how energy model accuracy influences energy-optimal pathfinding and, consequently, feasibility of planned trips, using a novel data-driven model that incorporates key vehicle dynamics parameters into energy calculations. Additionally, we introduce two novel online reweighting and energy heuristic functions that accelerate path planning with negative energy costs arise due to regenerative braking, making our approach well-suited for real-time applications. Extensive experiments on real-world transport networks demonstrate that our method significantly improves both the computational efficiency of energy-optimal pathfinding for EVs.

We study the problem of optimizing a guidance policy capable of dynamically guiding the agents for lifelong Multi-Agent Path Finding based on real-time traffic patterns. Multi-Agent Path Finding (MAPF) focuses on moving multiple agents from their starts to goals without collisions. Its lifelong variant, LMAPF, continuously assigns new goals to agents. In this work, we focus on improving the solution quality of PIBT, a state-of-the-art rule-based LMAPF algorithm, by optimizing a policy to generate adaptive guidance. We design two pipelines to incorporate guidance in PIBT in two different ways. We demonstrate the superiority of the optimized policy over both static guidance and human-designed policies. Additionally, we explore scenarios where task distribution changes over time, a challenging yet common situation in real-world applications that is rarely explored in the literature.

In multi-agent systems, when we account for the possibility of delays during execution, online planning becomes more complicated, as both execution and planning should be able to handle delays when agents are moving. Lifelong Multi-Agent Path Finding (LMAPF) is the problem of (re)planning the collision-free moves of agents to their goals in a shared space, while agents continuously receive new goals. PIE (Planning and Improving while Executing) is a recent approach to LMAPF which concurrently replans later parts of agents' trajectories while execution occurs. However, the execution is assumed to be perfect. Existing approaches either use policy-based methods to quickly coordinate agents every timestep with instant delay feedback, or deploy an execution policy to adjust a solution for delays on the fly. These approaches may introduce large amounts of unnecessary delays to agents due to their planner guarantees or simple delay-handling policies. In this paper, we extend PIE to define a framework for solving the lifelong MAPF problem with execution delays. We instantiate our framework with different execution and replanning strategies, and experimentally evaluate them. Overall, we find that this framework can substantially improve the throughput by up to a factor 3 for lifelong MAPF, compared to approaches that handle delays with simple execution policies.

The Multi-objective Shortest Path (MOSP) problem is a classic network optimization problem that aims to find all Pareto-optimal paths between two points in a graph with multiple edge costs. Recent studies on multi-objective search with A* (MOA*) have demonstrated superior performance in solving difficult MOSP instances. This paper presents a novel search framework that allows efficient parallelization of MOA* with different objective orders. The framework incorporates a unique upper-bounding strategy that helps the search reduce the problem's dimensionality to one in certain cases. Experimental results demonstrate that the proposed framework can enhance the performance of recent A*-based solutions, with the speed-up proportional to the problem dimension.

This volume contains the papers accepted for presentation at ICAPS 2025, the Thirty-Fifth International Conference on Automated Planning and Scheduling, to be held in Melbourne, Australia, November 9-14, 2025. The annual ICAPS conference series was formed in 2003 through the merger of two pre-existing biennial conferences, the International Conference on Artificial Intelligence Planning and Scheduling (AIPS) and the European Conference on Planning (ECP). ICAPS continues the traditional high standards of AIPS and ECP as an archival forum for new research in the field of automated planning and scheduling. ICAPS 2025 was co-located with two other events: The International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR), and The International Conference on the Principles of Knowledge Representation and Reasoning (KR). Existing research into methods and representations for Automated Planning and Scheduling has drawn heavily from the research conducted by these communities. We believe that the co-location of these conferences with ICAPS can only boost these beneficial relationships.The frontmatter contains a Preface and lists both the ICAPS 2025 Organising Committee and the ICAPS 2025 Program Committee.

Search, especially pathfinding search, is a foundational problem-solving technique in Computer Science for sequential-decision making problems. Such algorithms appear widely in the academic literature and they have found broad applicability including in personal navigation, robotics and computer games. Despite their importance, search algorithms can be challenging for practitioners to implement and difficult for learners to understand. In this work, we present POSTHOC, a visualisation and debugging tool which aims to improve the situation. Our approach relies on search traces, textual records of key operations that occur during the search process; e.g., node expansion, successor generation and other events of interest. We employ search traces to visualise the decision-making process and to construct domain-specific representations for each event. We show how these traces can be used — in a variety of contexts — to inspect, debug, and better understand search algorithms. Finally, we demonstrate POSTHOC in a range of different real-world case studies.

Delays in public transport are common, often impacting users through prolonged travel times and missed transfers. Existing solutions for handling delays remain limited; backup plans based on historical data miss opportunities for earlier arrivals, while snapshot planning accounts for current delays but not future ones. With the growing availability of live delay data, users can adjust their journeys in real-time. However, the literature lacks a framework that fully exploits this advantage for system-scale dynamic replanning. To address this, we formalise the dynamic replanning problem in public transport routing and propose two solutions: a "pull" approach, where users manually request replanning, and a novel "push" approach, where the server proactively monitors and adjusts journeys. Our experiments show that the push approach outperforms the pull approach, achieving significant speedups. The results also reveal substantial arrival time savings enabled by dynamic replanning.

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.

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.

Prioritised Planning (PP) is a popular approach for multi-agent and multi-robot navigation. In PP, collision-free paths are computed for one agent at a time, following a total order over the agents, called a priority ordering. Many MAPF algorithms follow this approach or use it in some way, including several state-of-the-art MAPF algorithms, although it is known that PP is neither complete nor optimal. In this work, we characterise the space of problems a PP algorithm can solve, and define the search problem of identifying whether a given MAPF problem is in that space. We call this search problem Prioritised MAPF (P-MAPF) and investigate its computational complexity, showing that it is generally NP-hard. Then, we develop a novel efficient search algorithm called Path and Priority Search (PaPS), which solves P-MAPF, providing guarantees of completeness and optimality. We next observe that PP algorithms operate with two primary degrees of freedom – the choice of priority ordering, and the choice of individual paths for agents. Accordingly, we further divide P-MAPF into two planning problems corresponding to the two degrees of freedom. We call them Priority-Function Constrained MAPF (PFC-MAPF), where the path choice is fixed while the priority ordering is not, and Priority Constrained MAPF (PC-MAPF), where the priority ordering is fixed while the path choice is not. We analyse these problems as well, and show how PaPS can be easily adapted to create algorithms that solve these problems optimally. We experiment with our algorithms in a range of settings, including comparisons with existing PP baselines. Our results show how the different degrees of freedom of PP-based algorithms affect their behaviour, and provide the first-known results for solution-quality optimality for PP-based algorithms on a popular MAPF benchmark set. The latter can be used as a lower bound for any PP algorithm.

Multi-Agent Path Finding (MAPF) is a fundamental problem in robotics that asks us to compute collision-free paths for a team of agents, all moving across a shared map. Although many works appear on this topic, all current algorithms struggle as the number of agents grows. The principal reason is that existing approaches typically plan free-flow optimal paths, which creates congestion. To tackle this issue, we propose a new approach for MAPF where agents are guided to their destination by following congestion-avoiding paths. We evaluate the idea in two large-scale settings: one-shot MAPF, where each agent has a single destination, and lifelong MAPF, where agents are continuously assigned new destinations. Empirically, we report large improvements in solution quality for one-short MAPF and in overall throughput for lifelong MAPF.

The point-to-point Multi-objective Shortest Path (MOSP) problem is a classic yet challenging task that involves finding all Pareto-optimal paths between two points in a graph with multiple edge costs. Recent studies have shown that employing A* search can lead to state-of-the-art performance in solving MOSP instances with non-negative costs. This paper proposes a novel A*-based multi-objective search framework that not only handles graphs with negative costs and even negative cycles but also incorporates multiple speed-up techniques to enhance the efficiency of exhaustive search with A*. Through extensive experiments, our algorithm demonstrates remarkable success in solving difficult MOSP instances, outperforming leading solutions by several factors.

In applications of Multi-Agent Path Finding (MAPF), it is often the sum of planning and execution times that needs to be minimised (i.e., the Goal Achievement Time). Yet current methods seldom optimise for this objective. Optimal algorithms reduce execution time, but may require exponential planning time. Non-optimal algorithms reduce planning time, but at the expense of increased path length. To address these limitations we introduce PIE (Planning and Improving while Executing), a new framework for concurrent planning and execution in MAPF. We show how different instantiations of PIE affect practical performance, including initial planning time, action commitment time and concurrent vs. sequential planning and execution. We then adapt PIE to Lifelong MAPF, a popular application setting where agents are continuously assigned new goals and where additional decisions are required to ensure feasibility. We examine a variety of different approaches to overcome these challenges and we conduct comparative experiments vs. recently proposed alternatives. Results show that PIE substantially outperforms existing methods for One-shot and Lifelong MAPF.

Multi-Agent Path Finding (MAPF) is a fundamental problem in robotics that asks us to compute collision-free paths for a team of agents, all moving across a shared map. Existing scalable approaches struggle as the number of agents grows, as they typically plan free-flow optimal paths, which creates congestion. To tackle this issue, we propose a new approach for MAPF where agents are guided to their destination by following congestion-avoiding paths. Empirically, we report large improvements in overall throughput for lifelong MAPF while coordinating more than ten thousand agents.

We explore the earliest arrival time problem in public transport journey planning. A journey typically consists of multiple scheduled public transport legs. The actual time required to transfer between these legs can substantially influence route planning. Therefore, we properly model transfers by incorporating their exact costs. We then introduce a novel oracle-based routing algorithm that constructs an efficient transfer database, considering the proposed transfer model. The database is leveraged online to quickly reconstruct the optimal journey in response to an earliest arrival time query. Our experimental results show that neglecting exact transfer costs often lead to either infeasible or suboptimal route plans. Furthermore, the findings highlight the efficiency of our algorithm in handling queries, demonstrated by response times within mere microseconds.

Symmetry breaking and weighted-suboptimal search are two popular speed up techniques used in pathfinding search. It is a commonly held assumption that they are orthogonal and easily combined. In this paper we illustrate that this is not necessarily the case when combining a number of symmetry breaking methods, based on Jump Point Search, with Weighted A*, a bounded suboptimal search approach which does not require node re-expansions. Surprisingly, the combination of these two methods can cause search to fail, finding no path to a target node when clearly such paths exist. We demonstrate this phenomena and show how we can modify the combination to always succeed with low overhead.

Prioritised Planning (PP) is a family of incomplete and sub-optimal algorithms for multi-agent and multi-robot navigation. In PP, agents compute collision-free paths in a fixed order, one at a time. Although fast and usually effective, PP can still fail, leaving users without explanation or recourse. In this work, we give a theoretical and empirical basis for better understanding the underlying problem solved by PP, which we call Priority Constrained MAPF (PC-MAPF). We first investigate the complexity of PC-MAPF and show that the decision problem is NP-hard. We then develop Priority Constrained Search (PCS), a new algorithm that is both complete and optimal with respect to a fixed priority ordering. We experiment with PCS in a range of settings, including comparisons with existing PP baselines, and we give first-known results for optimal PC-MAPF on a popular benchmark set.

In applications of Multi-Agent Path Finding (MAPF), it is often the sum of planning and execution times that needs to be minimised (i.e., the Goal Achievement Time). Yet current methods seldom optimise for this objective. Optimal algorithms reduce execution time, but may require exponential planning time. Non-optimal algorithms reduce planning time, but at the expense of increased path length. To address these limitations we introduce PIE (Planning and Improving while Executing), a new framework for concurrent planning and execution in MAPF. We first show how PIE for one-shot MAPF improves practical performance compared to sequential planning and execution.We then adapt PIE to Lifelong MAPF, a popular application setting where agents are continuously assigned new goals and where additional decisions are required to ensure feasibility. We examine a variety of different approaches to overcome these challenges and we conduct comparative experiments vs. recently proposed alternatives. Results show that PIE substantially outperforms existing methods for One-shot and Lifelong MAPF.

Abstract The classic problem of constrained pathfinding is a well‐studied, yet challenging, network optimization problem with a broad range of applications in various areas such as communication and transportation. The weight constrained shortest path problem (WCSPP), the base form of constrained pathfinding with only one side constraint, aims to plan a cost‐optimum path with limited weight/resource usage. Given the bi‐criteria nature of the problem (i.e., dealing with the cost and weight of paths), methods addressing the WCSPP have some common properties with bi‐objective search. This article leverages the recent state‐of‐the‐art techniques in both constrained pathfinding and bi‐objective search and presents two new solution approaches to the WCSPP on the basis of A* search, both capable of solving hard WCSPP instances on very large graphs. We empirically evaluate the performance of our algorithms on a set of large and realistic problem instances and show their advantages over the state‐of‐the‐art algorithms in both time and space metrics. This article also investigates the importance of priority queues in constrained search with A*. We show with extensive experiments on both realistic and randomized graphs how bucket‐based queues without tie‐breaking can effectively improve the algorithmic performance of exhaustive A*‐based bi‐criteria searches.

In many computer games up to hundreds of agents navigate in real-time across a dynamically changing weighted grid map. Pathfinding in these situations is challenging because the grids are large, traversal costs are not uniform, and because each shortest path has many symmetric permutations, all of which must be considered by an optimal online search. In this work we introduce Weighted Jump Point Search (JPSW), a new type of pathfinding algorithm which breaks weighted grid symmetries by introducing a tiebreaking policy that allows us to apply effective pruning rules in symmetric regions. We show that these pruning rules preserve at least one optimal path to every grid cell and that their application can yield large performance improvements for optimal pathfinding. We give a complete theoretical description of the new algorithm, including pseudo-code. We also conduct a wide-ranging experimental evaluation, including data from real games. Results indicate JPSW is up to orders of magnitude faster than the nearest baseline, online search using A*.

Voxel grids are an increasingly common enabler for pathfinding in 3D spaces. Currently in this area there exists only a limited number of publicly available benchmarks. This makes it difficult to establish state-of-the-art performance and to compare the strengths and weaknesses of competing search techniques. In this work, we introduce three new and diverse sets of voxel benchmarks intended to help fill this gap. We further describe our methodology for generating and selecting a representative set of pathfinding queries. Our dataset comprises 46 distinct voxel maps and 92,000 problem instances. The data is drawn from distinct application domains: computer video games, industrial plant layouts and sandstone porosity scans. Featuring distinctive geometric properties and a variety of challenging query types, these new datasets allow practitioners to evaluate algorithmic performance across a variety of settings encountered when pathfinding in practice.

Current approaches for real-world Multi-Agent Path Finding (MAPF) usually start with a simplified MAPF model and modify the resulting plans so they are kinematically feasible. We investigate one such problem, called MAPF with turn actions MAPF_T, and show that ignoring the kinematic constraints significantly increases solution cost. A first modification of the popular Conflict-Based Search algorithm to MAPF_T yields significantly better plans but comes at the cost of substantial decreases in scalability. We then introduce several techniques that can improve the performance of CBS for MAPF_T, including stronger and generalised versions of existing symmetry-breaking constraints and a novel pruning technique that eliminates redundant branches in the CBS constraint tree. Experimental results on six popular MAPF domains show convincing improvements for CBS success rate and substantial reductions in node expansions and runtime.

JPS (Jump Point Search) is a state-of-the-art optimal algorithm for online grid-based pathfinding. Widely used in games and other navigation scenarios, JPS nevertheless can exhibit pathological behaviours which are not well studied: (i) it may repeatedly scan the same area of the map to find successors; (ii) it may generate and expand suboptimal search nodes. In this work, we examine the source of these pathological behaviours, show how they can occur in practice, and propose a purely online approach, called Constrained JPS (CJPS), to tackle them efficiently. Experimental results show that CJPS has low overheads and is often faster than JPS in dynamically changing grid environments: by up to 7x in large game maps and up to 14x in pathological scenarios.

Multi-Agent Path Finding (MAPF) is the problem of planning collision-free paths for multiple agents in a shared environment. In this paper, we propose a novel algorithm MAPF-LNS2 based on large neighborhood search for solving MAPF efficiently. Starting from a set of paths that contain collisions, MAPF-LNS2 repeatedly selects a subset of colliding agents and replans their paths to reduce the number of collisions until the paths become collision-free. We compare MAPF-LNS2 against a variety of state-of-the-art MAPF algorithms, including Prioritized Planning with random restarts, EECBS, and PPS, and show that MAPF-LNS2 runs significantly faster than them while still providing near-optimal solutions in most cases. MAPF-LNS2 solves 80% of the random-scenario instances with the largest number of agents from the MAPF benchmark suite with a runtime limit of just 5 minutes, which, to our knowledge, has not been achieved by any existing algorithms.

Multi-Agent Path Finding (MAPF) is the problem of finding collision-free paths for multiple agents that minimize the sum of path costs. EECBS is a leading two-level algorithm that solves MAPF bounded-suboptimally, that is, within some factor w of the minimum sum of path costs C*. It uses focal search to find bounded-suboptimal paths on the low level and Explicit Estimation Search (EES) to resolve collisions on the high level. EES keeps track of a lower bound LB on C* to find paths whose sum of path costs is at most w LB in order to solve MAPF bounded-suboptimally. However, the costs of many paths are often much smaller than w times their minimum path costs, meaning that the sum of path costs is much smaller than w C*. In this paper, we therefore propose Flexible EECBS (FEECBS), which uses a flex(ible) distribution of the path costs (that relaxes the requirement to find bounded-suboptimal paths on the low level) in order to reduce the number of collisions that need to be resolved on the high level while still guaranteeing to solve MAPF bounded suboptimally. We address the drawbacks of flex distribution via techniques such as restrictions on the flex distribution, restarts of the high-level search with EECBS, and low-level focal-A* search. Our empirical evaluation shows that FEECBS substantially improves the efficiency of EECBS on MAPF instances with large maps and large numbers of agents.

Weight constrained path finding, known as a challenging variant of the classic shortest path problem, aims to plan cost optimum paths whose weight/resource usage is limited by a side constraint. Given the bi-criteria nature of the problem (i.e., the presence of cost and weight), solutions to the Weight Constrained Shortest Path Problem (WCSPP) have some properties in common with bi-objective search. This paper leverages the state-of-the-art bi-objective search algorithm BOBA* and presents WC-BA*, an exact A*-based WCSPP method that explores the search space in different objective orderings bidirectionally. We also enrich WC-BA* with two novel heuristic tuning approaches that can significantly reduce the number of node expansions in the exhaustive search of A*. The results of our experiments on a large set of realistic problem instances show that our new algorithm solves all instances and outperforms the state-of-the-art WCSPP algorithms in various scenarios.

Multi-Train Path Finding (MTPF) is a coordination problem that asks us to plan collision-free paths for a team of moving agents, where each agent occupies a sequence of locations at any given time. MTPF is useful for planning a range of real-world vehicles, including rail trains and road convoys. MTPF is closely related to another coordination problem known as k-Robust Multi-Agent Path Finding (kR-MAPF). Although similar in principle, the performance of optimal MTPF algorithms in practice lags far behind that of optimal kR-MAPF algorithms. In this work, we revisit the connection between them and reduce the performance gap. First, we show that, in many cases, a valid kR-MAPF plan is also a valid MTPF plan, which leads to a new and faster approach for collision resolution. We also show that many recently introduced improvements for kR-MAPF, such as lower-bounding heuristics and symmetry reasoning, can be extended to MTPF. Finally, we explore a new type of pairwise symmetry specific to MTPF. Our experiments show that these improvements yield large efficiency gains for optimal MTPF.

This paper presents a novel algorithm for solving the traffic assignment problem (TAP). Contrary to traditional algorithms, which use the one-to-all shortest path algorithm to solve the problem for all origin destinations (OD) pairs, this algorithm tracks the changes of the edges and (at certain iterations) solves the problem only for critical edges whose flows have changed substantially using a state-of-the-art edge p2p shortest path algorithm. When additionally, only OD pairs with larger flows are considered, this enhancement halves the time needed to optimize the solution with a very small error in a large-scale network.

Pathfinding is a central topic in AI for games, with many approaches having been suggested. But comparing different algorithms is tricky, because design choices stem from different practical considerations; e.g., some pathfinding systems are grid-based, others rely on a navigation mesh or visibility graph and so on. Current benchmarks mirror this trend, focusing on one set of assumptions while ignoring the rest. In this work we present a new unified benchmark using data from the game Iron Harvest. For 35 different levels in the game we generate several complementary map representations (grid, mesh and obstacle-set) and we provide a common set of challenging instances. We describe and analyse the new benchmark and then compare several leading pathfinding algorithms that begin from different assumption sets. Our goal is to allow researchers and practitioners to better understand the relative strengths and weakness of competing techniques.

The Euclidean Shortest Path Problem (ESPP) asks us to find a minimum length path between two points on a 2D plane while avoiding a set of polygonal obstacles. Existing approaches for ESPP, based on Dijkstra or A* search, are primal methods that gradually build up longer and longer valid paths until they reach the target. In this paper we define an alternative algorithm for ESPP which can avoid this problem. Our approach starts from a path that ignores all obstacles, and generates longer and longer paths, each avoiding more obstacles, until eventually the search finds an optimal valid path.

The ability to quickly compute shortest paths in 3D grids is a technological enabler for several applications such as pipe routing and computer video games. The main challenge is how to deal with the many symmetric permutations of each shortest path. We tackle this problem by adapting Jump Point Search (JPS), a well-known symmetry breaking technique developed for fast pathfinding in 2D grids. We give a rigorous reformulation of the JPS pathfinding system into 3D and we prove that our new algorithm, JPS-3D, is optimality preserving. We also develop a novel method for limiting scan depth during jump operations, which can further reduce search time. Experimental results show significant improvements versus online A* search and previous attempts at generalising JPS. We demonstrate that searching with adaptive scan limits can yield additional speedups of over an order of magnitude.

Resource constrained path finding is a well studied topic in AI, with real-world applications in different areas such as transportation and robotics. This paper introduces several heuristics in the resource constrained path finding context that significantly improve the algorithmic performance of the initialisation phase and the core search. We implement our heuristics on top of a bidirectional A* algorithm and evaluate them on a set of large instances. The experimental results show that, for the first time in the context of constrained path finding, our fast and enhanced algorithm can solve all of the benchmark instances to optimality, and compared to the state of the art algorithms, it can improve existing runtimes by up to four orders of magnitude on large-size network graphs.

Conflict-Based Search (CBS) is a leading two-level algorithm for optimal Multi-Agent Path Finding (MAPF). The main step of CBS is to expand nodes by resolving conflicts (where two agents collide). Choosing the ‘right’ conflict to resolve can greatly speed up the search. CBS first resolves conflicts where the costs (g-values) of the resulting child nodes are larger than the cost of the node to be split. However, the recent addition of high-level heuristics to CBS and expanding nodes according to f=g+h reduces the relevance of this conflict prioritization method. Therefore, we introduce an expanded categorization of conflicts, which first resolves conflicts where the f-values of the child nodes are larger than the f-value of the node to be split, and present a method for identifying such conflicts. We also enhance all known heuristics for CBS by using information about the cost of resolving certain conflicts, and with only a small computational overhead. Finally, we experimentally demonstrate that both the expanded categorization of conflicts and the improved heuristics contribute to making CBS even more efficient.

During Multi-Agent Path Finding (MAPF) problems, agentscan be delayed by unexpected events. To address suchsituations recent work describes k-Robust Conflict-BasedSearch (k-CBS): an algorithm that produces coordinated andcollision-free plan that is robust for up tokdelays. In thiswork we introducing a variety of pairwise symmetry break-ing constraints, specific tok-robust planning, that can effi-ciently find compatible and optimal paths for pairs of con-flicting agents. We give a thorough description of the newconstraints and report large improvements to success rate ina range of domains including: (i) classic MAPF benchmarks;(ii) automated warehouse domains and; (iii) on maps fromthe 2019 Flatland Challenge, a recently introduced railwaydomain wherek-robust planning can be fruitfully applied toschedule trains.

Electric Vehicles (EVs) are set to replace vehicles based on internal combustion engines. Path planning and vehicle routing for EVs need to take their specific characteristics into account, such as reduced range, long charging times, and energy recuperation. This paper investigates the importance of vehicle dynamics parameters in energy models for EV routing, particularly in the Pickup-and-Delivery Problem (PDP). We use Constraint Programming (CP) technology to develop a complete PDP model with different charger technologies. We adapt realistic instances that consider vehicle dynamics parameters such as vehicle mass, road gradient and driving speed to varying degrees. The results of our experiments show that neglecting such fundamental vehicle dynamics parameters can affect the feasibility of planned routes for EVs, and fewer/shorter charging visits will be planned if we use energy-efficient paths instead of conventional shortest paths in the underlying system model.

Bi-objective search is a well-known algorithmic problem, concerned with finding a set of optimal solutions in a two-dimensional domain. This problem has a wide variety of applications such as planning in transport systems or optimal control in energy systems. Recently, bi-objective A*-based search (BOA*) has shown state-of-the-art performance in large networks. This paper develops a bi-directional and parallel variant of BOA*, enriched with several speed-up heuristics. Our experimental results on 1,000 benchmark cases show that our bi-directional A* algorithm for bi-objective search (BOBA*) can optimally solve all of the benchmark cases within the time limit, outperforming the state of the art BOA*, bi-objective Dijkstra and bi-directional bi-objective Dijkstra by an average runtime improvement of a factor of five over all of the benchmark instances.

Multi-Agent Path Finding (MAPF) is the challenging problem of computing collision-free paths for multiple agents. Algorithms for solving MAPF can be categorized on a spectrum. At one end are (bounded-sub)optimal algorithms that can find high-quality solutions for small problems. At the other end are unbounded-suboptimal algorithms that can solve large problems but usually find low-quality solutions. In this paper, we consider a third approach that combines the best of both worlds: anytime algorithms that quickly find an initial solution using efficient MAPF algorithms from the literature, even for large problems, and that subsequently improve the solution quality to near-optimal as time progresses by replanning subgroups of agents using Large Neighborhood Search. We compare our algorithm MAPF-LNS against a range of existing work and report significant gains in scalability, runtime to the initial solution, and speed of improving the solution.

Multi-Agent Path Finding (MAPF) is the combinatorial problem of finding collision-free paths for multiple agents on a graph. This paper describes MAPF-based software for solving train planning and replanning problems on large-scale railway networks under uncertainty. The software recently won the 2020 Flatland Challenge, a NeurIPS competition trying to determine how to efficiently manage dense traffic on rail networks. The software incorporates many state-of-the-art MAPF, or in general, optimization technologies, such as prioritized planning, large neighborhood search, safe interval path planning, minimum communication policies, parallel computing, and simulated annealing. It can plan collision-free paths for thousands of trains within a few minutes and deliver deadlock-free actions in real-time during execution.

Bi-objective search is a problem of finding a set of optimal solutions in a two-dimensional domain. This study proposes several enhancements to the state-of-the-art bi-objective search with A* and develops its bi-directional variant. Our experimental results on benchmark instances show that our enhanced algorithm is on average five times faster than the state of the art bi-objective search algorithms.

Conflict-Based Search (CBS) is a leading two-level algorithm for optimal Multi-Agent Path Finding (MAPF). At its high level, CBS expands nodes by resolving conflicts. In recent years, admissible heuristics were added to the high level of CBS. We enhance all known heuristic functions for CBS by using information about the cost of resolving certain conflicts, with only a small computational overhead. We experimentally demonstrate that the improved heuristics contribute to making CBS even more efficient.

Multi-Agent Path Finding (MAPF) is the problem of finding collision-free paths for multiple agents. CBS is a leading optimal two-level MAPF solver whose low level plans optimal paths for single agents and whose high level runs a best-first search on a Constraint Tree (CT) to resolve the collisions between the paths. ECBS, a bounded-suboptimal variant of CBS, speeds up CBS by reducing the number of collisions that need to be resolved on the high level. It achieves this by generating bounded-suboptimal paths with fewer collisions with the paths of the other agents on the low level and expanding bounded-suboptimal CT nodes that contain fewer collisions on the high level. In this paper, we propose Flexible ECBS (FECBS) that further reduces the number of collisions that need to be resolved on the high level by using looser suboptimal bounds on the low level while still providing bounded-suboptimal solutions. Instead of requiring the cost of each path to be bounded-suboptimal, FECBS requires only the overall cost of the paths to be bounded-suboptimal, which gives us the freedom to distribute the cost leeway among different agents according to their needs. Our empirical results show that FECBS can solve more MAPF instances than state-of-the-art ECBS variants within 5 minutes.

The shortest path problem (SPP) asks us to find a minimum length path between two points, usually on a graph. In a Euclidean environment the points are in a 2D plane and here the path must avoid a set of polygonal obstacles. Solution methods for this Euclidean SPP (ESPP) typically convert the continuous 2D map into a discretised representation, like a graph or navigation mesh. RayScan is a recent and fast ESPP algorithm which avoids the preprocessing step by using a combination of "ray shooting" and polygon scanning. In this paper we improve the performance of RayScan using spatial reasoning and ray caching techniques. We also extend the algorithm, from single-target search to a multi-target setting. Comparative game map experiments show a substantial speedup.

We consider the design and implementation of a centralised oracle that provides commuters with customised and congestion-aware driving directions. Computing directions for a single journey is straightforward, but doing so at city-scale, in real-time, and under changing conditions is extremely challenging. In this work we describe a new type of centralised oracle which combines fast database-driven path planning with a query management system that distributes work across a small commodity cluster of networked machines. Our system allows large-scale changes to the underlying graph metric, from one query to the next, and it supports a variety of query types including optimal, bounded suboptimal, time-budgeted and k-prefix. Simulated experiments show strong results: we can provide real-time routing for all peak-hour commuter trips in the city of Melbourne, Australia.

Jump Point Search (JPS) is a well known symmetry-breaking algorithm that can substantially improve performance for grid-based optimal pathfinding. When the input grid is static further speedups can be obtained by combining JPS with goal bounding techniques such as Geometric Containers (instantiated as Bounding Boxes) and Compressed Path Databases. Two such methods, JPS+BB and Two-Oracle Path PlannING (Topping), are currently among the fastest known approaches for computing shortest paths on grids. The principal drawback for these algorithms is the overhead costs: each one requires an all-pairs precomputation step, the running time and subsequent storage costs of which can be prohibitive. In this work we consider an alternative approach where we precompute and store goal bounding data only for grid cells which are also jump points. Since the number of jump points is usually much smaller than the total number of grid cells, we can save up to orders of magnitude in preprocessing time and space. Considerable precomputation savings do not necessarily mean performance degradation. For a second contribution we show how canonical orderings, partial expansion strategies and enhanced intermediate pruning can be leveraged to improve online query performance despite a reduction in preprocessed data. The combination of faster preprocessing and stronger online reasoning leads to three new and highly performant algorithms: JPS+BB+ and Two-Oracle Pathfinding Search (TOPS) based on search, and Topping+ based on path extraction. We give a theoretical analysis showing that each method is complete and optimal. We also report convincing gains in a comprehensive empirical evaluation that includes almost all current and cutting-edge algorithms for grid-based pathfinding.

Conflict-Based Search (CBS) is a leading algorithm for optimal Multi-Agent Path Finding (MAPF). CBS variants typically compute MAPF solutions using some form of A* search. However, they often do so under strict time limits so as to avoid exhausting the available memory. In this paper, we present IDCBS, an iterative-deepening variant of CBS which can be executed without exhausting the memory and without strict time limits. IDCBS can be substantially faster than CBS due to incremental methods that it uses when processing CBS nodes.

We consider optimal and anytime algorithms for the Euclidean Shortest Path Problem (ESPP) in two dimensions. Our approach leverages ideas from two recent works: Polyanya, a mesh-based ESPP planner which we use to represent and reason about the environment, and Compressed Path Databases, a speedup technique for pathfinding on grids and spatial networks, which we exploit to compute fast candidate paths. In a range of experiments and empirical comparisons we show that: (i) the auxiliary data structures required by the new method are cheap to build and store; (ii) for optimal search, the new algorithm is faster than a range of recent ESPP planners, with speedups ranging from several factors to over one order of magnitude; (iii) for anytime search, where feasible solutions are needed fast, we report even better runtimes.

We consider two new types of pairwise path symmetries which appear in the context of Multi-Agent Path Finding (MAPF). The first of them, corridor symmetry, arises when two agents attempt to pass through the same narrow passage but in opposite directions. The second, target symmetry, arises when the shortest path of one agent requires the target location of a second agent after the second agent has already arrived. These symmetries can produce an exponential blowup in the space of possible collision resolutions, leading to timeout failure even for state-of-the-art algorithms such as Conflict-Based Search. We propose to break symmetries using new reasoning techniques that: (1) detect each type of situation and, (2) resolve them by introducing specialized constraints. We implement our ideas in the context of Conflict-Based Search where, in a range of experiments, we report up to an order-of-magnitude improvement in runtime performance and, in some cases, more than a doubling in success rate.

The 2D Multi-Agent Path Finding (MAPF) problem aims at finding collision-free paths for a number of agents, from a set of start locations to a set of goal positions in a known 2D environment. MAPF has been studied in theoretical computer science, robotics, and artificial intelligence over several decades, due to its importance for robot navigation. It is currently experiencing significant scientific progress due to its relevance in automated warehousing (such as those operated by Amazon) and in other contemporary application areas. In this paper, we demonstrate that some recently developed MAPF algorithms apply more broadly than currently believed in the MAPF research community. In particular, we describe the 3D Pipe Routing (PR) problem, which aims at placing collision-free pipes from given start locations to given goal locations in a known 3D environment. The MAPF and PR problems are similar: a solution to a MAPF instance is a set of blocked cells in x-y-t space, while a solution to the corresponding PR instance is a set of blocked cells in x-y-z space. We show how to use this similarity to apply several recently developed MAPF algorithms to the PR problem, and discuss their performance on real-world PR instances. This opens up a new direction of industrial relevance for the MAPF research community.

Conflict-Based Search (CBS) is a leading algorithm for optimal Multi-Agent Path Finding (MAPF) which features strong performance. In CBS, one conflict in a high-level node is resolved to generate two child nodes, until a node with no conflicts is found. Choosing the right conflict to resolve can greatly speed up the search. It is currently recommended to resolve cardinal conflicts first, resolving them yields two child nodes with a higher cost than the cost of their parent. However, since the recent addition of high-level heuristics to CBS, when resolving cardinal conflicts, the h-value of high-level child nodes often decreases by the same amount as their cost increases. This diminishes the effectiveness of the cardinal conflicts distinction. We propose an expanded categorization of conflicts into f-cardinal, g-cardinal, and non-cardinal. F-cardinal conflicts should be resolved first. Resolving f-cardinal conflicts generates child nodes with an increased f-value relative to their parent. We propose two methods for identifying f-cardinal conflicts. Finally, we demonstrate on standard benchmarks that choosing conflicts according to this expanded categorization increases the effectiveness of modern CBS.

We study prioritized planning for Multi-Agent Path Finding (MAPF). Existing prioritized MAPF algorithms depend on rule-of-thumb heuristics and random assignment to determine a fixed total priority ordering of all agents a priori. We instead explore the space of all possible partial priority orderings as part of a novel systematic and conflict-driven combinatorial search framework. In a variety of empirical comparisons, we demonstrate state-of-the-art solution qualities and success rates, often with similar runtimes to existing algorithms. We also develop new theoretical results that explore the limitations of prioritized planning, in terms of completeness and optimality, for the first time.

We describe a new way of reasoning about symmetric collisions for Multi-Agent Path Finding (MAPF) on 4-neighbor grids. We also introduce a symmetry-breaking constraint to resolve these conflicts. This specialized technique allows us to identify and eliminate, in a single step, all permutations of two currently assigned but incompatible paths. Each such permutation has exactly the same cost as a current path, and each one results in a new collision between the same two agents. We show that the addition of symmetry-breaking techniques can lead to an exponential reduction in the size of the search space of CBS, a popular framework for MAPF, and report significant improvements in both runtime and success rate versus CBSH and EPEA* – two recent and state-of-the-art MAPF algorithms.

Compressed Path Databases (CPDs) are a leading technique for optimal pathfinding in graphs with static edge costs. In this work we investigate CPDs as admissible heuristic functions and we apply them in two distinct settings: problems where the graph is subject to dynamically changing costs, and anytime settings where deliberation time is limited. Conventional heuristics derive cost-to-go estimates by reasoning about a tentative and usually infeasible path, from the current node to the target. CPD-based heuristics derive cost-to-go estimates by computing a concrete and usually feasible path. We exploit such paths to bound the optimal solution, not just from below but also from above. We demonstrate the benefit of this approach in a range of experiments on standard gridmaps and in comparison to Landmarks, a popular alternative also developed for searching in explicit state-spaces.

In this paper, we define Jump Point Graphs (JP), a preprocessing-based path-planning technique similar to Subgoal Graphs (SG). JP allows for the first time the combination of Jump Point Search style pruning in the context of abstraction-based speedup techniques, such as Contraction Hierarchies. We compare JP with SG and its variants and report new state-of-the-art results for grid-based pathfinding.

There are currently two broad strategies for optimal Multi-agent Pathfinding (MAPF): (1) search-based methods, which model and solve MAPF directly, and (2) compilation-based solvers, which reduce MAPF to instances of well-known combinatorial problems, and thus, can benefit from advances in solver techniques. In this work, we present an optimal algorithm, BCP, that hybridizes both approaches using Branch-and-Cut-and-Price, a decomposition framework developed for mathematical optimization. We formalize BCP and compare it empirically against CBSH and CBSH-RM, two leading search-based solvers. Conclusive results on standard benchmarks indicate that its performance exceeds the state-of-the-art: solving more instances on smaller grids and scaling reliably to 100 or more agents on larger game maps.

We study prioritized planning for Multi-Agent Path Finding (MAPF). Existing prioritized MAPF algorithms depend on rule-of-thumb heuristics and random assignment to determine a fixed total priority ordering of all agents a priori. We instead explore the space of all possible partial priority orderings as part of a novel systematic and conflict-driven combinatorial search framework. In a variety of empirical comparisons, we demonstrate state-of-the-art solution qualities and success rates, often with similar runtimes to existing algorithms. We also develop new theoretical results that explore the limitations of prioritized planning, in terms of completeness and optimality, for the first time. This paper was published at AAAI 2019.

We describe a new way of reasoning about symmetric collisions for Multi-Agent Path Finding (MAPF) on 4-neighbor grids. We also introduce a symmetry-breaking constraint to resolve these conflicts. This specialized technique allows us to identify and eliminate, in a single step, all permutations of two currently assigned but incompatible paths. Each such permutation has exactly the same cost as a current path, and each one results in a new collision between the same two agents. We show that the addition of symmetry-breaking techniques can lead to an exponential reduction in the size of the search space of CBS, a popular framework for MAPF, and report significant improvements in both runtime and success rate versus CBSH and EPEA* – two recent and state-of-the-art MAPF algorithms.

Contraction hierarchies are graph-based data structure developed to speed up shortest path search in road networks. Built during an offline pre-processing step, contraction hierarchies are always paired with an online query algorithm which is a variation on bi-directional Dijkstra search. Though effective and highly popular this combination can sometimes be difficult to extend, for example in order to leverage goal-directed heuristics or other forward-driven pruning techniques. In this paper we deconstruct the bi-directional query algorithm of contraction hierarchies and derive a new algorithmic schema which is compatible with standard uni-directional or bi-directional search. We then develop a variety of new uni-directional query algorithms to find optimal paths in contraction hierarchies. These are based on the combination of A* search and Geometric Containers, a well known and successful edge-pruning technique. Empirical results show that our approach can improve search times by an order of magnitude vs bi-directional Dijkstra, albeit at the cost of additional memory and pre-processing time.

We consider the k-Nearest Neighbour problem in a two-dimensional Euclidean plane with obstacles (OkNN). Existing and state of the art algorithms for OkNN are based on incremental visibility graphs and as such suffer from a well known disadvantage: costly and online visibility checking with quadratic worst-case running times. In this work we develop a new OkNN algorithm which avoids these disadvantages by representing the traversable space as a collection of convex polygons; i.e. a Navigation Mesh. We then adapt an recent and optimal navigation mesh algorithm, Polyanya, from the single-source single-target setting to the the multi-target case. We also give two new heuristics for OkNN. In a range of empirical comparisons we show that our approach can be orders of magnitude faster than competing methods that rely on visibility graphs.

We want to compute geometric shortest paths in a collection of convex traversable polygons, also known as a navigation mesh. Simple to compute and easy to update, navigation meshes are widely used for pathfinding in computer games. When the mesh is static, shortest path problems can be solved exactly and very fast but only after a costly preprocessing step. When the mesh is dynamic, practitioners turn to online methods which typically compute only approximately shortest paths. In this work we present a new pathfinding algorithm which is compromise-free; i.e. it is simultaneously fast, online and optimal. Our method, Polyanya, extends and generalises Anya; a recent and related interval-based search technique developed for computing geometric shortest paths in grids. We show how that algorithm can be modified to support search over arbitrary sets of convex polygons and then evaluate its performance on a range of realistic and synthetic benchmark problems.

Any-angle pathfinding is a fundamental problem in robotics and computer games. The goal is to find a shortest path between a pair of points on a grid map such that the path is not artificially constrained to the points of the grid. Prior research has focused on approximate online solutions. A number of exact methods exist but they all require super-linear space and pre-processing time. In this study, we describe Anya: a new and optimal any-angle pathfinding algorithm. Where other works find approximate any-angle paths by searching over individual points from the grid, Anya finds optimal paths by searching over sets of states represented as intervals. Each interval is identified on-the-fly. From each interval Anya selects a single representative point that it uses to compute an admissible cost estimate for the entire set. Anya always returns an optimal path if one exists. Moreover it does so without any offline pre-processing or the introduction of additional memory overheads. In a range of empirical comparisons we show that Anya is competitive with several recent (sub-optimal) online and pre-processing based techniques and is up to an order of magnitude faster than the most common benchmark algorithm, a grid-based implementation of A*.

In this work we give a first tractability analysis of Compressed Path Databases, space efficient oracles used to very quickly identify the first arc on a shortest path. We study the complexity of computing an optimal compressed path database for general directed and undirected graphs. We find that in both cases the problem is NP-complete. We also show that, for graphs which can be decomposed along articulalion points, the problem can be decomposed into independent parts, with a corresponding reduction in its level of difficulty. In particular, this leads to simple and tractable algorithms which yield optimal compression results for trees.

The Grid-Based Path Planning Competition has just completed its third iteration. The entriesused in the competition have improved significantly during this time, changing the view ofthe state of the art of grid-based pathfinding. Furthermore, the entries from the competition have beenmade publicly available, improving the ability of researchers to compare their work. Thispaper summarizes the entries to the 2014 competition, presents the 2014 competition results,and talks about what has been learned and where there is room for improvement.

We introduce a novel approach to Compressed Path Databases, space efficient oracles used to very quickly identify the first edge on a shortest path. Our algorithm achieves query running times on the 100 nanosecond scale, being significantly faster than state-of-the-art first-move oracles from the literature. Space consumption is competitive, due to a compression approach that rearranges rows and columns in a first-move matrix and then performs run length encoding (RLE) on the contents of the matrix. One variant of our implemented system was, by a convincing margin, the fastest entry in the 2014 Grid-Based Path Planning Competition. We give a first tractability analysis for the compression scheme used by our algorithm. We study the complexity of computing a database of minimum size for general directed and undirected graphs. We find that in both cases the problem is NP-complete. We also show that, for graphs which can be decomposed along articulation points, the problem can be decomposed into independent parts, with a corresponding reduction in its level of difficulty. In particular, this leads to simple and tractable algorithms with linear running time which yield optimal compression results for trees.

In moving target search, the objective is to guide a hunter agent to catch a moving prey. Even though in game applications maps are always available at developing time, current approaches to moving target search do not exploit preprocessing to improve search performance. In this paper, we propose MtsCopa, an algorithm that exploits precomputed information in the form of compressed path databases (CPDs), and that is able to guide a hunter agent in both known and partially known terrain. CPDs have previously been used in standard, fixed-target pathfinding but had not been used in the context of moving target search. We evaluated MtsCopa over standard game maps. Our speed results are orders of magnitude better than current state of the art. The time per individual move is improved, which is important in real-time search scenarios, where the time available to make a move is limited. Compared to state of the art, the number of hunter moves is often better and otherwise comparable, since CPDs provide optimal moves along shortest paths. Compared to previous successful methods, such as I-ARA*, our method is simple to understand and implement. In addition, we prove MtsCopa always guides the agent to catch the prey when possible.

We introduce a novel preprocessing-based algorithm to solve the problem of determining the first arc of a shortest path in sparse graphs. Our algorithm achieves query running times on the 100 nanosecond scale, being significantly faster than state-of-the-art first-move oracles from the literature. Space consumption is competitive, due to a compression approach that rearranges rows and columns in a first-move matrix and then performs run length encoding (RLE) on the contents of the matrix.

We describe a pathfinding system based on Jump Point Search (JPS): a recent and very successful search strategy that performs symmetry breaking to speed up optimal pathfinding on grid maps. We first modify JPS for grid maps where corner-cutting moves are not allowed. We then describe JPS+: a new derivative search strategy that reformulates an input graph into an equivalent symmetry-reduced form that can be searched more efficiently. JPS and JPS+ were both submitted to the 2012 Grid-based Path Planning Competition.

Pathfinding in uniform-cost grid environments is a problem commonly found in application areas such as robotics and video games. The state-of-the-art is dominated by hierarchical pathfinding algorithms which are fast and have small memory overheads but usually return suboptimal paths. In this paper we present a novel search strategy, specific to grids, which is fast, optimal and requires no memory overhead. Our algorithm can be described as a macro operator which identifies and selectively expands only certain nodes in a grid map which we call jump points. Intermediate nodes on a path connecting two jump points are never expanded. We prove that this approach always computes optimal solutions and then undertake a thorough empirical analysis, comparing our method with related works from the literature. We find that searching with jump points can speed up A* by an order of magnitude and more and report significant improvement over the current state of the art.

Pathfinding systems that operate on uniform-cost grid maps are common in the AI literature and application areas such as robotics and real-time video games. Typical speed-up enhancements in such contexts include reducing the size of the search space using abstraction [Botea et al., 2004] and developing new heuristics to more accurately guide search toward the goal [Sturtevant et al., 2009]. Though effective each of these strategies has shortcomings. For example, abstraction methods usually trade optimality for speed. Meanwhile, improved heuristics usually require significant extra memory. My research proposes to speed up grid-based pathfinding by identifying and eliminating symmetric path segments from the search space. Two paths are said to be symmetric if they are identical save for the order in which the individual moves (or steps) occur. To deal with path symmetries I decompose an arbitrary grid map into a set of empty rectangles and remove from each rectangle all interior nodes and possibly some from along the perimeter. A series of macro edges are then added between selected pairs of remaining nodes in order to facilitate provably optimal traversal through each rectangle. The new algorithm, Rectangular Symmetry Reduction (RSR), can speed up A* search by up to 38 times on a range of uniform cost maps taken from the literature. In addition to being fast and optimal, RSR requires no significant extra memory and is largely orthogonal all existing speedup techniques. When compared to the state of the art, RSR often shows significant improvement across a range of benchmarks.