The rapid advancement of GPU technology has unlocked powerful parallel processing capabilities, creating new opportunities to enhance classic search algorithms. This hardware has been exploited in best-first search algorithms with neural network-based heuristics by creating batched versions of A* and Weighted A* that delay heuristic evaluation until sufficiently many states can be evaluated in parallel on the GPU. But, research has not addressed how depth-first algorithms like IDA* or Budgeted Tree Search (BTS) can have their heuristic computations batched. This is more complicated in a tree search, because progress in the search tree is blocked until heuristic evaluations are complete. In this paper we show that GPU parallelization of heuristics can be effectively performed when the tree search is parallelized on the CPU while heuristic evaluations are parallelized on the GPU. We develop a parallelized cost-bounded depth-first search (CB-DFS) framework that can be applied to both IDA* and BTS, significantly improving their performance. We demonstrate the strength of the approach on the 3x3 Rubik's Cube and the 4x4 sliding tile puzzle (STP) with both classifier-based and regression-based heuristics.

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 paper introduces Dynamic Suboptimality Weighted A* (DSWA*), a search framework that allows suboptimality to be dynamically distributed at runtime, based on the properties of the search. Experiments show that dynamic policies can consistently outperform existing algorithms across a diverse set of domains, particularly those with dynamic costs.

In recent years the understanding of optimal bidirectional heuristic search (BiHS) has progressed significantly. Yet, Bi-HS is relatively unexplored in unbounded suboptimal search. Front-to-end (F2E) and front-to-front (F2F) bidirectional search have been used in optimal algorithms, but adapting them for unbounded suboptimal search remains an open challenge. We introduce a framework for suboptimal BiHS, called anchor search, and use it to derive a parameterized family of algorithms. Because our new algorithms need F2F heuristic evaluations, we propose using pattern databases (PDBs) as differential heuristics (DHs) to construct F2F heuristics. Our experiments evaluate three anchor search instances across diverse domains, outperforming existing methods, particularly as the search scales.

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.

Among the most popular games played worldwide, Bridge stands out for having had little AI progress for over 25 years. Ginsberg's Partition Search algorithm (1996) was a breakthrough for double-dummy Bridge play, allowing a program to reason about sets of states rather than individual states. Partition Search supports the current state of the art for both bidding and cardplay. In the time since, virtually no progress has been made in Bridge bidding. Inspired by Ginsberg's idea, this paper presents Setrograde Analysis, a new set-based algorithm for perfectly solving Bridge hands. Using this approach, we have solved all 7-trick (28-card) hands — 10^30 states, which can be reduced to 10^17 unique states using preexisting techniques. This was done by considering five orders of magnitude fewer sets than the traditional state-based Retrograde Analysis algorithm. This work suggests that the entire 13-trick (52-card) state space can be solved with modern technology using this new approach. The 7-trick computation represents the largest endgame database to date in any game.

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.

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.

Parallelization and External Memory (PEM) techniques have significantly enhanced the capabilities of search algorithms when solving large-scale problems. Previous research on PEM has primarily centered on unidirectional algorithms, with only one publication on bidirectional PEM that focuses on the meet-in-the-middle (MM) algorithm. Building upon this foundation, this paper presents a framework that integrates both uni- and bi-directional best-first search algorithms into this framework. We then develop a PEM variant of the state-of-the-art bidirectional heuristic search (BiHS) algorithm BAE* (PEM-BAE*). As previous work on BiHS did not focus on scaling problem sizes, this work enables us to evaluate bidirectional algorithms on hard problems. Empirical evaluation shows that PEM-BAE* outperforms the PEM variants of A* and the MM algorithm, as well as a parallel variant of IDA*. These findings mark a significant milestone, revealing that bidirectional search algorithms clearly outperform unidirectional search algorithms across several domains, even when equipped with state-of-the-art heuristics.

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.

This paper investigates methods for training parameterized functions for guiding state-space search algorithms. Existing work commonly generates data for training such guiding functions by solving problem instances while leveraging the current version of the guiding function. As a result, as training progresses, the guided search algorithm can solve more difficult instances that are, in turn, used to further train the guiding function. These methods assume that a set of problem instances of varied difficulty is provided. Since previous work was not designed to distinguish the instances that the search algorithm can solve from those that cannot be solved with the current guiding function, the algorithm commonly wastes time attempting and failing to solve many of these instances. In this paper, we improve upon these training methods by generating a curriculum for learning the guiding function that directly addresses this issue. Namely, we propose and evaluate a Teacher-Student Curriculum (TSC) approach where the teacher is an evolutionary strategy that attempts to generate problem instances of ``correct difficulty'' and the student is a guided search algorithm utilizing the current guiding function. The student attempts to solve the problem instances generated by the teacher. We conclude with experiments demonstrating that TSC outperforms the current state-of-the-art Bootstrap Learning method in three representative benchmark domains and three guided search algorithms, with respect to the time required to solve all instances of the test set.

While most work in heuristic search concentrates on goal-specific heuristics, which estimate the shortest path cost from any state to the goal, we explore all-pair heuristics that estimate distances between all pairs of states. We examine the relationship between these heuristic functions and the shortest distance function they estimate, revealing that all-pair consistent heuristics may violate the triangle inequality. Thus, we introduce a new property for heuristics called Δ-consistency, requiring adherence to the triangle inequality. Additionally, we present a method for transforming standard consistent heuristics to be Δ-consistent, showcasing its benefits through a synthetic example. We then show that common heuristic families inherently exhibit Δ-consistency. This positive finding encourages the use of all-pair consistent heuristics, and prompts further investigation into the optimality of A*, when given an all-pair heuristic instead of a goal-specific heuristic.

Parallelization and External Memory (PEM) techniques significantly enhance the capabilities of search algorithms for solving large-scale problems. While previous research on PEM has primarily centered on unidirectional algorithms, this work presents a versatile PEM framework that integrates both uni- and bi-directional best-first search algorithms.

While the study of unit-cost Multi-Agent Pathfinding (MAPF) problems has been popular, many real-world problems require continuous time and costs. In this context, this paper studies symmetry-breaking enhancements for Continuous-Time Conflict-Based Search (CCBS), a solver for continuous-time MAPF. Resolving conflict symmetries in MAPF can require an exponential amount of work. We adapt known symmetry-breaking enhancements from unit-cost domains for CCBS: bypassing and biclique constraints. We then improve upon these to produce a new state-of-the-art algorithm: CCBS with disjoint k-partite cliques (CCBS+DK). Finally, we show empirically that CCBS+DK solves for up to 20% more agents in the same amount of time when compared to previous state-of-the-art.

The FastMap algorithm has been proposed as an inexpensive metric embedding which provides admissible distance estimates between all vertices in an embedding. As an embedding, it also supports additional operations such as taking the median location of two vertices, which is important in some problems. This paper studies several aspects of FastMap embeddings, showing the relationship of FastMap to general additive heuristics. As an admissible heuristic, FastMap is not as strong as previous suggested. However, by combining FastMap with the ideas of differential heuristics, we can significantly improve the performance of FastMap heuristics. We show the impact of these ideas in both single-agent pathfinding and the Multi-Agent Meeting problem, where the performance of algorithms using our improved FastMap embedding is improved by up to a factor of two.

Recent research on bidirectional heuristic search (BiHS) is based on the must-expand pairs theory (MEP theory), which describes which pairs of nodes must be expanded during the search to guarantee the optimality of solutions. A separate line of research in BiHS has proposed algorithms that use lower bounds that are derived from consistent heuristics during search. This paper links these two directions, providing a comprehensive unifying view and showing that both existing and novel algorithms can be derived from the MEP theory. An extended set of bounds is formulated, encompassing both previously discovered bounds and new ones. Finally, the bounds are empirically evaluated by their contribution to the efficiency of the search

Historically applied exclusively to perfect information games, depth-limited search with value functions has been key to recent advances in AI for imperfect information games. Most prominent approaches with strong theoretical guarantees require *subgame decomposition* - a process in which a subgame is computed from public information and player beliefs. However, subgame decomposition can itself require non-trivial computations, and its tractability depends on the existence of efficient algorithms for either full enumeration or generation of the histories that form the root of the subgame. Despite this, no formal analysis of the tractability of such computations has been established in prior work, and application domains have often consisted of games, such as poker, for which enumeration is trivial on modern hardware. Applying these ideas to more complex domains requires understanding their cost. In this work, we introduce and analyze the computational aspects and tractability of filtering histories for subgame decomposition. We show that constructing a single history from the root of the subgame is generally intractable, and then provide a necessary and sufficient condition for efficient enumeration. We also introduce a novel Markov Chain Monte Carlo-based generation algorithm for trick-taking card games - a domain where enumeration is often prohibitively expensive. Our experiments demonstrate its improved scalability in the trick-taking card game *Oh Hell*. These contributions clarify when and how depth-limited search via subgame decomposition can be an effective tool for sequential decision-making in imperfect information settings.

Most recent theoretical and algorithmic work in bidirectional heuristic search (BiHS) used front-to-end (F2E) heuristics that estimate the distance to the start and goal states. In this paper, we start exploring front-to-front (F2F) heuristics, which estimate the distance between any pair of states. Devising efficient algorithms that use F2F heuristics is a challenging task. Thus, it is important to first understand the benefits of using F2F heuristics compared to F2E heuristics. To this end, we theoretically and experimentally demonstrate that there is a great potential in using F2F heuristics implying that F2F BiHS is a promising area of future research.

Iterative Budgeted Exponential Search (IBEX) is a general search algorithm that can limit the number of re-expansions performed in common problems like iterative-deepening tree search and search with inconsistent heuristics. IBEX has been adapted into a specific tree algorithm, Budgeted Tree Search (BTS), which behaves like IDA* when the problem instance is well-behaved but keeps the worst-case guarantees when problems are not well-behaved. The analogous algorithms on graphs, Budgeted Graph Search (BGS), do not have these same properties. This paper reformulates BGS into Efficient Budgeted Graph Search (BGSe), showing how to implement the algorithm so that it behaves identically to A* when problems are well-behaved, and retains the best-case performance otherwise. Experimental results validate the performance of BGSe on a range of theoretical and practical problem instances.

The combination of tree search and neural networks has achieved super-human performance in challenging domains. We are interested in transferring to humans the knowledge these learning systems generate. We hypothesize the process in which neural-guided tree search algorithms learn how to solve a set of problems can be used to generate curricula for helping human learners. In this paper we show how the Bootstrap learning system can be modified to learn curricula for humans in a puzzle domain. We evaluate our system in two curriculum learning settings. First, given a small set of problem instances, our system orders the instances to ease the learning process of human learners. Second, given a large set of problem instances, our system returns a small ordered subset of the initial set that can be presented to human learners. We evaluate our curricula with a user study where participants learn how to solve a class of puzzles from the game `The Witness.' The user-study results suggest one of the curricula our system generates compares favorably with simple baselines and is competitive with the curriculum from the original `The Witness' game in terms of user retention and effort.

Work in machine learning has grown tremendously in the past years, but has had little to no impact on optimal search approaches. This paper looks at challenges in using deep learning as a part of optimal search, including what is feasible using current public frameworks, and what barriers exist for further adoption. The primary contribution of the paper is to show how to learn admissible heuristics through supervised learning from an existing heuristic. Several approaches are described, with the most successful approach being based on learning a heuristic as a classifier and then adjusting the quantile used with the classifier to ensure heuristic admissibility, which is required for optimal solutions. A secondary contribution is a description of the Batch A* algorithm, which can batch evaluations for more efficient use by the GPU. While ANNs can effectively learn heuristics that produce smaller search trees than alternate compression approaches, there still exists a time overhead when compared to efficient C++ implementations. This point of evaluation points out a challenge for future work.

Recent work introduced XDP and XUP priority functions for best-first bounded-suboptimal search that do not need to perform state re-expansions as long as the search heuristic is consistent. However, that work had several limitations that are rectified here. This paper analyzes the sufficiency and necessity of the conditions used to formulate XDP and XUP. The analysis presents a simpler proof and generalizes the result in three aspects: (1) the priority function no longer has to be differentiable everywhere, (2) the quality of the solution does not have to be bounded by a constant factor, and (3) directed graphs are handled correctly. These results allow the introduction of more priority functions, such as piecewise linear functions, and more variants of bounded-suboptimal search, such as constant suboptimality. Several new priority functions are presented in this paper that, according to empirical results, can significantly outperform existing approaches including XDP.

Quests are a popular topic of study in many academic fields. However, literature has not settled on the elements in a quest, much less a specific definition or even debate between two or three definitions. The purpose of this paper is to take a preliminary quest definition from our previous work, and revise it to be more broadly applicable. To inform the revision, we analyze quests from a few published games. Then, we propose a few modifications to the definition which allows it to more fully explain some design patterns in games. Finally, we evaluate our definition against other definitions proposed in past research.

This paper gives a summary of published conditions needed for a priority function to return bounded-optimal solutions when not performing re-expansions of previously expanded states in best-first search.

This extended abstract presents a bidirectional heuristic search algorithm called IDBiHS that operates under restricted memory. Several variants of this algorithm are introduced for different types of memory restrictions, and are compared against existing algorithms with similar restrictions.

This abstract looks at one version of the pathfinding problem in games and discusses how it motived our recent work at the AIIDE 2019 conference.

The main idea of conflict-based search (CBS), a popular, state-of-the-art algorithm for multi-agent pathfinding is to resolve conflicts between agents by systematically adding constraints to agents. Recently, CBS has been adapted for new domains and variants, including non-unit costs and continuous time settings. These adaptations require new types of constraints. This paper introduces a new automatic constraint generation technique called bipartite reduction (BR). BR converts the constraint generation step of CBS to a surrogate bipartite graph problem. The properties of BR guarantee completeness and optimality for CBS. Also, BR's properties may be relaxed to obtain suboptimal solutions. Empirical results show that BR yields significant speedups in 2k connected grids over the previous state-of-the-art for both optimal and suboptimal search.

In the Multi-Agent Meeting problem (MAM), the task is to find a meeting location for multiple agents, as well as a path for each agent to that location. In this paper, we introduce MM*, a Multi-Directional Heuristic Search algorithm that finds the optimal meeting location under different cost functions. MM* generalizes the Meet in the Middle (MM) bidirectional search algorithm to the case of finding an optimal meeting location for multiple agents. Several admissible heuristics are proposed, and experiments demonstrate the benefits of MM*.

Recent work on bidirectional search defined a lower bound on costs of paths between pairs of nodes, and introduced a new algorithm, NBS, which is based on this bound. Building on these results, we introduce DVCBS, a new algorithm that aims to to further reduce the number of expansions. Generalizing beyond specific algorithms, we then propose a method for enhancing heuristics by propagating such lower bounds (lb-propagation) between frontiers. This lb-propagation can be used in existing algorithms, often improving their performance, as well as making them "well behaved".

In the Multi-Agent Meeting (MAM) problem, the task is to find a meeting location for multiple agents, as well as a path for each agent to that location. In this paper, we introduce MM*, a Multi-Directional Search algorithm that finds the optimal meeting location under different cost functions. MM* generalizes the Meet in the Middle (MM) bidirectional search algorithm to the case of finding optimal meeting locations for multiple agents. A number of admissible heuristics are proposed and experiments demonstrate the benefits of MM*.

Budgeted Tree Search (BTS), a variant of Iterative Budgeted Exponential Search, is a new algorithm that has the same performance as IDA* on problems where the state space grows exponentially, but has far better performance than IDA* in other cases where IDA* fails. The goal of this paper is to provide a detailed guide to BTS with worked examples to make the algorithm more accessible to practitioners in heuristic search.

NBS is a non-parametric bidirectional search algorithm proven to expand at most twice the number of node expansions required to verify the optimality of a solution. We introduce new variants of NBS that are aimed at finding all optimal solutions. We then introduce an algorithmic framework that includes NBS as a special case. Finally, we introduce DVCBS, a new algorithm in this framework that aims to further reduce the number of expansions. Unlike NBS, DVCBS does not have any worst-case bound guarantees, but in practice it outperforms NBS in verifying the optimality of solutions.

Trick-taking card games feature a large amount of private information that slowly gets revealed through a long sequence of actions. This makes the number of histories exponentially large in the action sequence length, as well as creating extremely large information sets. As a result, these games become too large to solve. To deal with these issues many algorithms employ inference, the estimation of the probability of states within an information set. In this paper, we demonstrate a Policy Based Inference (PI) algorithm that uses player modelling to infer the probability we are in a given state. We perform experiments in the German trick-taking card game Skat, in which we show that this method vastly improves the inference as compared to previous work, and increases the performance of the state-of-the-art Skat AI system Kermit when it is employed into its determinized search algorithm.

With the advent of the fighting game AI competition, there has been recent interest in two-player fighting games. Monte-Carlo Tree-Search approaches currently dominate the competition, but it is unclear if this is the best approach for all fighting games. In this paper we study the design of two-player fighting games and the consequences of the game design on the types of AI that should be used for playing the game, as well as formally define the state space that fighting games are based on. Additionally, we also characterize how AI can solve the game given a simultaneous action game model, to understand the characteristics of the solved AI and the impact it has on game design.

Many practical problems are too difficult to solve optimally, motivating the need to found suboptimal solutions, particularly those with bounds on the final solution quality. Algorithms like Weighted A*, A*-epsilon, Optimistic Search, EES, and DPS have been developed to find suboptimal solutions with solution quality that is within a constant bound of the optimal solution. However, with the exception of weighted A*, all of these algorithms require performing node re-expansions during search. This paper explores the properties of priority functions that can find bounded suboptimal solution without requiring node re-expansions. After general bounds are developed, two new convex priority functions are developed that can outperform weighted A*.

We tackle two long-standing problems related to re-expansions in heuristic search algorithms. For graph search, A* can require Ω(2ⁿ) expansions, where n is the number of states within the final f bound. Existing algorithms that address this problem like B and B’ improve this bound to Ω(n²). For tree search, IDA* can also require Ω(n²) expansions. We describe a new algorithmic framework that iteratively controls an expansion budget and solution cost limit, giving rise to new graph and tree search algorithms for which the number of expansions is O(n log C*), where C* is the optimal solution cost. Our experiments show that the new algorithms are robust in scenarios where existing algorithms fail. In the case of tree search, our new algorithms have no overhead over IDA* in scenarios to which IDA* is well suited and can therefore be recommended as a general replacement for IDA*.

While computing resources have continued to grow, methods for building and using large heuristics have not seen significant advances in recent years. We have observed that direction-optimizing breadth-first search, developed for and used broadly in the Graph 500 competition, can also be applied for building heuristics. But, the algorithm cannot run efficiently using external memory -- when the heuristics being built are larger than RAM. This paper shows how to modify direction-optimizing breadth-first search to build external-memory heuristics. We show that the new approach is not effective in state spaces with low asymptotic branching factors, but in other domains we are able to achieve up to a 3x reducing in runtime when building an external-memory heuristic. The approach is then used to build a 2.6TiB Rubik's Cube heuristic with 5.8 trillion entries, the largest pattern database heuristic ever built.

A* is optimally efficient with regard to node expansions among unidirectional admissible algorithms — those that only assume that the heuristic used is admissible. This paper studies algorithms that are optimally efficient for bidirectional search algorithms. We present the Fractional MM algorithm and its sibling, the MT algorithm, which is simpler to analyze. We then develop variants of these algorithms that are optimally efficient, each under different assumptions on the information available to the algorithm.

Suboptimal search algorithms can often solve much larger problems than optimal search algorithms, and thus have broad practical use. This paper returns to early algorithms like WA*, A*_e and Optimistic search. It studies the commonalities between these approaches in order to build a new bounded-suboptimal algorithm. Combined with recent research on avoiding node re-expansions in bounded-optimal search, a new solution quality bound is developed, which often provides proof of the solution bound much earlier during the search. Put together, these ideas provide a new state-of-the-art in bounded-optimal search.

Recent work in bidirectional heuristic search characterize pairs of nodes from which at least one node must be expanded in order to ensure optimality of solutions. We use these findings to propose a method for improving existing heuristics by propagating lower bounds between the forward and backward frontiers. We then define a number of desirable properties for bidirectional heuristic search algorithms, and show that applying the bound propagations adds these properties to many existing algorithms (e.g. to the MM family of algorithms). Finally, experimental results show that applying these propagations significantly reduce the running time of various algorithms.

NBS is a non-parametric bidirectional search algorithm, proved to expand at most twice the number of node expansions required to verify the optimality of a solution. We introduce new variants of NBS that are aimed at finding all optimal solutions. We then introduce an algorithmic framework that includes NBS as a special case. Finally, we introduce DVCBS, a new algorithm in this framework that aims to further reduce the number of expansions. Unlike NBS, DVCBS does not have any worst-case bound guarantees, but in practice it outperforms NBS in verifying the optimality of solutions.

The multi-agent pathfinding problem (MAPF) is the fundamental problem of planning paths for multiple agents, where the key constraint is that the agents will be able to follow these paths concurrently without colliding with each other. Applications of MAPF include automated warehouses, autonomous vehicles, and robotics. Research on MAPF has been flourishing in the past couple of years. Different MAPF research papers assume different sets of assumptions, e.g., whether agents can traverse the same road at the same time, and have different objective functions, e.g., minimize makespan or sum of agents' actions costs. These assumptions and objectives are sometimes implicitly assumed or described informally. This makes it difficult for establishing appropriate baselines for comparison in research papers, as well as making it difficult for practitioners to find the papers relevant to their concrete application. This paper aims to fill this gap and facilitate future research and practitioners by providing a unifying terminology for describing the common MAPF assumptions and objectives. In addition, we also provide pointers to two MAPF benchmarks. In particular, we introduce a new grid-based benchmark for MAPF, and demonstrate experimentally that it poses a challenge to contemporary MAPF algorithms.

Conflict-Based Search (CBS) is a state of the art algorithm for multi-agent pathfinding (MAPF). CBS has been studied in many domains, however, most research has focused on classic domains with point agents that move with unit time steps and unit costs. In this work, we are interested in MAPF solutions for classic domains and complex domains, that is, domains which include shaped agents, actions with non-unit costs, non-uniform action durations and/or non-holonomic or kinodynamic movement constraints. Prior work on sub-optimal formulations of CBS has focused on heuristics. Instead, our work introduces new types of constraints. We show that certain constraint formulations have properties that can cause CBS to run orders of magnitude faster, but may cause the algorithm to be incomplete and yield sub-optimal results. We introduce new conditional constraints which allow CBS to exploit constraint properties which cause it to run faster and still retain algorithmic completeness. We additionally formulate a new constraint accumulation technique called constraint overloading which utilizes conditional constraints in order to achieve further performance gains.

The state of the art in bidirectional search has changed significantly a very short time period; we now can answer questions about unidirectional and bidirectional search that until very recently we were unable to answer. This paper is designed to provide an accessible overview of the recent research in bidirectional search in the context of the broader efforts over the last 50 years. We give particular attention to new theoretical results and the algorithms they inspire for optimal and near-optimal node expansions when finding a shortest path.

Multi-agent pathfinding (MAPF) has applications in navigation, robotics, games and planning. Most work on search-based optimal algorithms for MAPF has focused on simple domains with unit cost actions and unit time steps. Although these constraints keep many aspects of the algorithms simple, they also severely limit the domains that can be used. In this paper we introduce a new definition of the MAPF problem for non-unit cost and non-unit time step domains along with new multiagent state successor generation schemes for these domains. Finally, we define an extended version of the increasing cost tree search algorithm (ICTS) for non-unit costs, with two new sub-optimal variants of ICTS: epsilon-ICTS and w-ICTS. Our experiments show that higher quality sub-optimal solutions are achievable in domains with finely discretized movement models in no more time than lower-quality, optimal solutions in domains with coarsely discretized movement models.

Multi-Agent Path Finding (MAPF) is an NP-hard problem that has been well studied in artificial intelligence and robotics. Recently, randomized MAPF solvers have been shown to exhibit heavy-tailed distributions of runtimes, which can be exploited to boost their success rate for a given runtime limit. In this paper, we discuss different ways of randomizing MAPF solvers and evaluate simple rapid randomized restart strategies for state-of-the-art MAPF solvers such as iECBS, M* with highways and CBS-CL.

The problem of finding optimal paths in 3D space is computationally more complex than in a 2D plane. While a range of different approaches have been developed across different fields, there has been relatively little work studying the complexities and tradeoffs of implementations for path planning in 3D space. This paper describes the 3D path planning problem faced in the game Warframe. The solution used by industry was tuned for their own constraints, but little is known about the applicability of other approaches to solving this problem. Thus, the makers of this game have made their underlying planning data available for researchers to use. This paper describes this new data set which is publicly available for study and dissemination.

A* is optimally effective with regard to node expansions among unidirectional admissible algorithms—those that only assume that the heuristic used is admissible. Among bidirectional algorithms the Fractional MM algorithm is optimally effective (given the correct parameters) among admissible algorithms.This paper generalizes the bidirectional result to more complex settings where more information on the problem domain can be exploited: (1) When the cost of the minimal edge is known. (2) When the algorithm knows that the heuristics are consistent. This characterization uses a novel algorithm called MT. MT is similar to Fractional MM and is also optimally effective, but simpler to analyze.

One common pattern database compression technique is to merge adjacent database entries and store the minimum of merged entries to maintain heuristic admissibility. In this paper we propose a compression technique that preserves every entry, but reduces the number of bits used to store each entry, therefore limiting the values that can be represented. Even when this technique throws away low values in the heuristic, it can still have better performance than the traditional approach. We develop a theoretical basis for selecting which values to keep and show improved performance in both unidirectional and bidirectional search.

It is well-known that any admissible unidirectional heuristic search algorithm must expand all states whose f-value is smaller than the optimal solution cost when using a consistent heuristic. Such states are called “surely expanded” (s.e.). A recent study characterized s.e. pairs of states for bidirectional search with consistent heuristics: if a pair of states is s.e. then at least one of the two states must be expanded. This paper derives a lower bound, VC, on the minimum number of expansions required to cover all s.e. pairs, and present a new admissible front-to-end bidirectional heuristic search algorithm, Near-Optimal Bidirectional Search (NBS), that is guaranteed to do no more than 2VC expansions. We further prove that no admissible front-to-end algorithm has a worst case better than 2VC. Experimental results show that NBS competes with or outperforms existing bidirectional search algorithms, and often outperforms A* as well.

Multi-agent pathfinding (MAPF) is an area of expanding research interest. At the core of this research area, numerous diverse search-based techniques were developed in the past 6 years for optimally solving MAPF under the sum-of-costs objective function. In this paper we survey these techniques, while placing them into the wider context of the MAPF field of research. Finally, we provide analytical and experimental comparisons that show that no algorithm dominates all others in all circumstances. We conclude by listing important future research directions.

Pattern databases are among the strongest known heuristics for many classical search benchmarks such as sliding-tile puzzles, the 4-peg Towers of Hanoi puzzles, Rubik's Cube, and TopSpin. Min-compression is a generally applicable technique for augmenting pattern database heuristics that has led to marked experimental improvements in some settings, while being ineffective in others. We provide a theoretical explanation for these experimental phenomena by studying the interaction between the ranking function used to order abstract states in a pattern database, the compression scheme used to abstract states, and the dependencies between state variables in the problem representation.

A* is optimal among admissible unidirectional algorithms when searching with a consistent heuristic. Recently, similar optimality bounds have been established for bidirectional search, but no practical algorithm is guaranteed to always achieve this bound. In this paper we study the nature of the number of nodes that must be expanded in any front-to-end bidirectional search. We present an efficient algorithm for computing that number and show that a theoretical parameterized generalization of MM, with the correct parameter, is the optimal front-to-end bidirectional search. We then experimentally compare various algorithms and show how far they are from optimal.

We present MM, the first bidirectional heuristic search algorithm whose forward and backward searches are guaranteed to ''meet in the middle'', i.e. never expand a node beyond the solution midpoint. We also present a novel framework for comparing MM, A*, and brute-force search, and identify conditions favoring each algorithm. Finally, we present experimental results that support our theoretical analysis.

Pathfinding is a common task across many domains and platforms, whether in games, robotics, or road maps. Given the breadth of domains, there are also a wide variety of representations used for pathfinding, and there are many techniques which have been shown to improve performance. In the last few years, the state-of-the-art in grid-based pathfinding has been significantly improved with domain-specific techniques such as Jump Point Search (JPS), Subgoal Graphs, and Compressed Path Databases. In this paper we look at a specific implementation of the general idea of Geometric Containers, showing that, while it is effective on grid maps, when combined with JPS+ it provides state-of-the-art performance.

Bidirectional search algorithms interleave a search forward from the start state (start ) and a search backward (i.e. using reverse operators) from the goal state (goal). We say that the two searches “meet in the middle” if neither search expands a node whose g-value (in the given direction) exceeds C*/2 , where C* is the cost of an optimal solution. The only bidirectional heuristic search algorithm that is guaranteed to meet in the middle under all circumstances is the recently introduced MM algorithm (Holte et al. 2016). The feature of MM that provides this guarantee is its unique priority functions for nodes on its open lists. In this short note we present MMe, which enhances MM’s priority function and is expected to expand fewer nodes than MM under most circumstances. We sketch a proof of MMe’s correctness, describe conditions under which MMe will expand fewer nodes than MM and vice versa, and experimentally compare MMe and MM on the 10-Pancake problem.

The Jump Point Search (JPS) algorithm is designed explicitly for search on grids; it uses grid-specific properties to reduce symmetry and provide faster optimal search without pre-computation. Recent work has broken the algorithm down into three components: a best-first search, a canonical ordering of states, and a jumping policy. This paper shows how a canonical ordering can be built on general graphs and used in a similar manner to the canonical ordering of JPS. This approach is able to significantly reduce the number of states generated by an A* search, but more work is needed to optimize and fully characterize the correctness of the approach.

Real-time agent-centered heuristic search is a well-studied problem where an agent that can only reason locally about the world must travel to a goal location using bounded computation and memory at each step. Many algorithms have been proposed for this problem and theoretical results have also been derived for the worst-case performance with simple examples demonstrating worst-case performance in practice. Lower bounds, however, have not been widely studied. In this paper we study best-case performance more generally and derive theoretical lower bounds for reaching the goal using LRTA*, a canonical example of a real-time agent-centered heuristic search algorithm. The results show that, given some reasonable restrictions on the state space and the heuristic function, the number of steps an LRTA*-like algorithm requires to reach the goal will grow asymptotically faster than the state space, resulting in ``scrubbing'' where the agent repeatedly visits the same state. We then show that while the asymptotic analysis does not hold for more complex real-time search algorithms, experimental results suggest that it is still descriptive of practical performance.

The nine papers in this special section focus on the development of physics-based simulation video games (PBSG). The focus is on artificial intelligence for specific PBSGs competitions such as Angry Birds and computational pool, as well as on further developments of physics simulators in order to launch the next generation of PBSGs.

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.

In the Real-Time Agent-Centered Search (RTACS) problem,an agent has to arrive at a goal location while acting and reasoningin the physical world. Traditionally, RTACS problemsare solved by propagating and updating heuristic values ofstates visited by the agent. In existing RTACS algorithms theagent may revisit each state many times causing the entireprocedure to be quadratic in the state space. We study theIterative Deepening (ID) approach for solving RTACS andintroduce Exponential Deepening A* (EDA*), an RTACS algorithmwhere the threshold between successive Depth-Firstcalls is increased exponentially. EDA* is proven to hold aworst case bound that is linear in the state space. Experimentalresults supporting this bound are presented and demonstrateup to 10x reduction over existing RTACS solvers wrtdistance traveled, states expanded and CPU runtime.

The use of inconsistent heuristics with A* can result in increased runtime due to the need to re-expand nodes. Poor performance can also be seen with Weighted A* if nodes are re-expanded. While the negative impact of re-expansions can often be minimized by setting these algorithms to never expand nodes more than once, the result can be a lower solution quality. In this paper, we formally show that the loss in solution quality can be bounded based on the amount of inconsistency along optimal solution paths. This bound holds regardless of whether the heuristic is admissible or inadmissible, though if the heuristic is admissible the bound can be used to show that not re-expanding nodes can have at most a quadratic impact on the quality of solutions found when using A*. We then show that the bound is tight by describing a process for the construction of graphs for which a best-first search that does not re-expand nodes will find solutions whose quality is arbitrarily close to that given by the bound. Finally, we will use the bound to extend a known result regarding the solution quality of WA* when weighting a consistent heuristic, so that it also applies to other types of heuristic weighting.

In this paper we introduce Stratified Sampling with Duplicate Detection (SSDD), an algorithm for estimating the number of state expansions performed by heuristic search algorithms seeking solutions in state spaces represented by undirected graphs. SSDD is general and can be applied to estimate other state-space properties. We test SSDD on two tasks: (i) prediction of the number of A* expansions in a given f-layer when using a consistent heuristic function, and (ii) prediction of the state-space radius. SSDD has the asymptotic guarantee of producing perfect estimates in both tasks. Our empirical results show that in task (i) SSDD produces good estimates in all four domains tested, being in most cases orders of magnitude more accurate than a competing scheme, and in task (ii) SSDD quickly produces accurate estimates of the radii of the 4x4 Sliding-Tile Puzzle and the 3x3x3 Rubik's Cube.

This paper introduces Exponential Deepening A* (EDA*), an Iterative Deepening (ID) algorithm where the threshold between successive Depth-First calls is increased exponentially. EDA* can be viewed as a Real-Time Agent-Centered (RTACS) algorithm. Unlike most existing RTACS algorithms, EDA* is proven to hold a worst case bound that is linear in the state space. Experimental results demonstrate up to 5x reduction over existing RTACS solvers wrt distance traveled, states expanded and CPU runtime. A full version of this paper appears in AAAI-14.

Real-time agent-centered heuristic search is a well-studied problem where an agent that can only reason locally about the world must travel to a goal location using bounded computation and memory at each step. Many algorithms have been proposed for this problem, and theoretical results have also been derived for the worst-case performance. Assuming sufficiently poor tie-breaking, among other conditions, we derive theoretical best-case bounds for reaching the goal using LRTA*, a canonical example of a real-time agent-centered heuristic search algorithm. We show that the number of steps required to reach the goal can grow asymptotically faster than the state space, resulting in a "scrubbing" when the agent repeatedly visits the same state. This theoretical result, supported by experimental data, encourages recent work in the field that uses novel tie-breaking schemas and/or perform different types of learning.

Pattern Databases (PDBs) are a common form of abstraction-based heuristic whichare often compressed so that a large PDB can fit inmemory. Partial Pattern Databases (PPDBs) achieve this by storing only layersof the PDB which are close to the goal. This paper studies the problem of howto best compress and use the 457 GB 12-edge Rubik's cube PDB, suggesting anumber of ways that Bloom filters can be used to effectively compress PPDBs. Wethen develop a theoretical model of the common min compression approach and ourBloom filters, showing that the original method of compressed PPDBs can neverbe better than min compression. We conclude with experimental results showingthat Bloom filter compression of PPDBs provides superior performance to mincompression in Rubik's cube.

When solving instances of problem domains that feature a large branching factor, A* may generate a large number of nodes whose cost is greater than the cost of the optimal solution. We designate such nodes as surplus. Generating surplus nodes and adding them to the OPEN list may dominate both time and memory of the search. A recently introduced variant of A* called Partial Expansion A* (PEA*) deals with the memory aspect of this problem. When expanding a node n, PEA* generates all of its children and puts into OPEN only the children with f = f (n). n is re-inserted in the OPEN list with the f -cost of the best discarded child. This guarantees that surplus nodes are not inserted into OPEN. In this paper, we present a novel variant of A* called Enhanced Partial Expansion A* (EPEA*) that advances the idea of PEA* to address the time aspect. Given a priori domain- and heuristic- specific knowledge, EPEA* generates only the nodes with f = f(n). Although EPEA* is not always applicable or practical, we study several variants of EPEA*, which make it applicable to a large number of domains and heuristics. In particular, the ideas of EPEA* are applicable to IDA* and to the domains where pattern databases are traditionally used. Experimental studies show significant improvements in run-time and memory performance for several standard benchmark applications. We provide several theoretical studies to facilitate an understanding of the new algorithm.

The Increasing Cost Tree Search (ICTS) algorithm is used to produce optimal solutions to the multi-agent path finding problem (MAPF). In this problem, multiple agents are trying to reach their goals without conflicting with each other, while minimizing the total cost of the paths. ICTS has been shown to be very effective in finding optimal solutions. In this paper we consider the problem of finding solutions with bounded suboptimality by changing the order in which ICTS searches its increasing cost tree. With a variety of strategies, we are unable to consistently and significantly reduce the cost of ICTS. Further experimentation suggests why significantly more work is needed to modify ICTS to find suboptimal solutions.

It is known that A* is optimal with respect to the expanded nodes (Dechter and Pearl 1985) (D&P). The exact meaning of this optimality varies depending on the class of algorithms and instances over which A* is claimed to be optimal. A* does not provide any optimality guarantees with respect to the generated nodes. However, such guarantees may be critical for optimally solving instances of domains with a large branching factor. In this paper, we introduce two new variants of the recently introduced Enhanced Partial Expansion A* algorithm (EPEA*) (Felner et al. 2012). We leverage the results of D&P to show that these variants possess optimality with respect to the generated nodes in much the same sense as A* possesses optimality with respect to the expanded nodes. The results in this paper are theoretical. A study of the practical performance of the new variants is beyond the scope of this paper.

In this paper we introduce techniques for state pruning atruntime in a priori unknown domains. We describe how toidentify states that can be deleted from the state-space whenlooking for both optimal and suboptimal solutions. We discussgeneral graphs and special cases like 8-connected grids.Experimental results show a speed up of up to an order ofmagnitude when applying our techniques on real-time agentcenteredsearch problems.

A* is often described as being `optimal', in that it expands the minimum number of unique nodes. But, A* may generate many extra nodes which are never expanded. This is a performance loss, especially when the branching factor is large. Partial Expansion A* addresses this problem when expanding a node, n, by generating all the children of n but only storing children with the same f-cost as n. n is re-inserted into the OPEN list, but with the f-cost of the next best child. This paper introduces an enhanced version of PEA* (EPEA*). Given a priori domain knowledge, EPEA* generates only the children with the same f-cost as the parent. EPEA* is generalized to its iterative-deepening variant, EPE-IDA*. For some domains, these algorithms yield substantial performance improvements. State-of-the-art results were obtained for the pancake puzzle and for some multi-agent pathfinding instances. Drawbacks of EPEA* are also discussed.

In the multi agent path finding problem (MAPF) paths should be found for several agents, each with a different start and goal position such that agents do not collide. Previous optimal solvers applied global A*-based searches. We present a new search algorithm called Conflict Based Search (CBS). CBS is a two-level algorithm. At the high level, a search is performed on a tree based on conflicts between agents. At the low level, a search is performed only for a single agent at a time. In many cases this reformulation enables CBS to examine fewer states than A* while still maintaining optimality. We analyze CBS and show its benefits and drawbacks. Experimental results on various problems shows a speedup of up to a full order of magnitude over previous approaches.

In looking back on the last five to ten years of work in heuristic search a few trends emerge. First, there has been a broadening of research topics studied. Second, there has been a deepened understanding of the theoretical foundations of search. Third, and finally, there have been increased connections with work in other fields. This paper, corresponding to a AAAI 2012 invited talk on recent work in heuristic search, highlights these trends in a number of areas of heuristic search. It is our opinion that the sum of these trends reflects the growth in the field and the fact that heuristic search has come of age.

A* is often described as being 'optimal,' in that it expands the minimum number of unique nodes. But, A* may generate many extra nodes which are never expanded. This is a performance loss, especially when the branching factor is large. Partial Expansion A* (PEA*) addresses this problem when expanding a node, n, by generating all the children of n but only storing children with the same f-cost as n. We introduce an enhanced version of PEA* (EPEA*). Given a priori domain knowledge, EPEA* only generates the children with the same f-cost as the parent. State-of-the-art results were obtained for a number of domains. Drawbacks of EPEA* are also discussed. A full version of this paper appears in the proceedings of AAAI-2012

The task in the multi-agent path finding problem (MAPF) isto find paths for multiple agents, each with a different startand goal position, such that agents do not collide. It is possibleto solve this problem optimally with algorithms that arebased on the A* algorithm. Recently, we proposed an alternativealgorithm called Conflict-Based Search (CBS) (Sharonet al. 2012), which was shown to outperform the A*-basedalgorithms in some cases. CBS is a two-level algorithm. Atthe high level, a search is performed on a tree based on conflictsbetween agents. At the low level, a search is performedonly for a single agent at a time. While in some cases CBSis very efficient, in other cases it is worse than A*-based algorithms.This paper focuses on the latter case by generalizingCBS to Meta-Agent CBS (MA-CBS). The main idea isto couple groups of agents into meta-agents if the number ofinternal conflicts between them exceeds a given bound. MACBSacts as a framework that can run on top of any completeMAPF solver. We analyze our new approach and provideexperimental results demonstrating that it outperforms basicCBS and other A*-based optimal solvers in many cases.

We present a new two-level search algorithm for optimal multi-agent path finding called Conflict Based Search (CBS). At the high level, a search is performed on a tree based on conflicts between agents. At the low level, a search is performed only for a single agent at a time. Experimental results on various problems shows a speedup of up to a full order of magnitude over previous approaches.

The study of algorithms on grids has been widespread in a number of research areas. Grids are easy to implement and offer fast memory access. Because of their simplicity, they are used even in commercial video games. But, the evaluation of work on grids has been inconsistent between different papers. Many research papers use different problem sets, making it difficult to compare results between papers. Furthermore, the performance characteristics of each test set are not necessarily obvious. This has motivated the creation of a standard test set of maps and problems on the maps that are open for all researchers to use. In addition to creating these sets, we use a variety of metrics to analyze the properties of the test sets. The goal is that these test sets will be useful to many researchers, making experimental results more comparable across papers, and improving the quality of research on grid-based domains.

The differential heuristic (DH) is an effective memory-based heuristic for explicit state spaces. In this paper we aim to improve its performance and memory usage. We introduce a compression method for DHs which stores only a portion of the original uncompressed DH, while preserving enough information to enable efficient search. Compressed DHs (CDH) are flexible and can be tuned to fit any size of memory, even smaller than the size of the state space. Furthermore, CDHs can be built without the need to create and store the entire uncompressed DH. Experimental results across different domains show that, for a given amount of memory, a CDH significantly outperforms an uncompressed DH.

We pose the problem of constructing good search heuristics as an optimization problem: minimizing the loss between the true distances and the heuristic estimates subject to admissibility and consistency constraints. For a well-motivated choice of loss function, we show performing this optimization is tractable. In fact, it corresponds to a recently proposed method for dimensionality reduction. We prove this optimization is guaranteed to produce admissible and consistent heuristics, generalizes and gives insight into differential heuristics, and show experimentally that it produces strong heuristics on problems from three distinct search domains.

Real-time agent-centric algorithms have been used for learning and solving problems since the in-troduction of the LRTA * algorithm in 1990. In this time period, numerous variants have been pro-duced, however, they have generally followed the same approach in varying parameters to learn a heuristic which estimates the remaining cost to arrive at a goal state. Recently, a different ap-proach, RIBS, was suggested which, instead of learning costs to the goal, learns costs from the start state. RIBS can solve some problems faster, but in other problems has poor performance. We present a new algorithm, f-cost Learning Real-Time A * (f-LRTA*), which combines both ap-proaches, simultaneously learning distances from the start and heuristics to the goal. An empiri-cal evaluation demonstrates that f-LRTA * outper-forms both RIBS and LRTA*-style approaches in a range of scenarios. 1

The differential heuristic (DH) is an effective memory-based heuristic for explicit state spaces. In this paper, we aim to improve its performance and memory usage. We introduce a compression method for DHs which stores only a portion of the original uncompressed DH, while preserving enough information to enable efficient search. Compressed DHs (CDH) can be tuned to fit any size of memory, even smaller than the size of the state space.Experimental results across different domains show that, for a given amount of memory, a CDH significantly outperforms an uncompress

Multi-agent pathfinding, where multiple agents must travel to their goal locations without getting stuck, has been studied in both theoretical and practical contexts, with a variety of both optimal and sub-optimal algorithms proposed for solving problems. Recent work has shown that there is a linear-time check for whether a multi-agent pathfinding problem can be solved in a tree, however this was not used to actually produce solutions. In this paper we provide a constructive proof of how to solve multi-agent pathfinding problems in a tree that culminates in a novel approach that we call the tree-based agent swapping strategy (TASS). Experimental results showed that TASS can find solutions to the multi-agent pathfinding problem on a highly crowded tree with 1000 nodes and 996 agents in less than 8 seconds. These results are far more efficient and general than existing work, suggesting that TASS is a productive line of study for multi-agent pathfinding.

Real-time agent-centric algorithms have been used for learning and solving problems since the introduction of the LRTA* algorithm in 1990. In this time period, numerous variants have been produced, however, they have generally followed the same approach in varying parameters to learn a heuristic which estimates the remaining cost to arrive at a goal state. This short paper discusses the history and implications of learning g-costs, both alone and in conjunction with learning h-costs as an introduction to the new f-LRTA* algorithm which learns both.

On the surface, bidirectional search (BDS) is an attractive idea with the potential for significant asymptotic reductions in search effort. However, the results in practice often fall far short of expectations. We introduce a new bidirectional search algorithm, Single-Frontier Bidirectional Searc (SFBDS). Unlike traditional BDS which keeps two frontiers, SFBDS uses a single frontier. Each node in the tree can be seen as an independent task of finding the shortest path between the current start and current goal. At a particular node we can decide to search from start to goal or from goal to start, choosing the direction with the highest potential for minimizing the total work done. Theoretical results give insights as to when this approach will work and experimental data validates the algorithm for a broad range of domains.

Perfect Information Monte Carlo (PIMC) search is a practical technique for playing imperfect information games that are too large to be optimally solved. Although PIMC search has been criticized in the past for its theoretical deficiencies, in practice it has often produced strong results in a variety of domains. In this paper, we set out to resolve this discrepancy. The contributions of the paper are twofold. First, we use synthetic game trees to identify game properties that result in strong or weak performance for PIMC search as compared to an optimal player. Second, we show how these properties can be detected in real games, and demonstrate that they do indeed appear to be good predictors of the strength of PIMC search. Thus, using the tools established in this paper, it should be possible to decide a priori whether PIMC search will be an effective approach to new and unexplored games.

Almost no research has been done on designing pinball games although much research has been done on designing video games. We are interested in designing pinball games on pinball machines to teach computer science students about how to interface to mechanical systems in a fun and motivating way. Thus, we have developed a pinball machine interface between a PC and a recent Lord of the Rings pinball machine. We demonstrate that it is easy to innovate pinball games by designing and implementing Pinhorse, a pinball game that avoids some of the design problems of existing pinball games. For example, it features a true multiplayer mode where each player directly influences the game of the other player within a limited amount of play time. This paper describes both our innovative pinball game and the hardware and software of our pinball machine interface that enables game designers to develop such pinball games on real pinball machines.

True distance memory-based heuristics (TDHs) were recently introduced as a way to obtain admissible heuristics for explicit state spaces. In this paper, we introduce a new TDH, the portal-based heuristic. The domain is partitioned into regions and portals between regions are identified. True distances between all pairs of portals are stored and used to obtain admissible heuristics throughout the search. We introduce an A*-based algorithm that takes advantage of the special properties of the new heuristic. We study the advantages and limitations of the new heuristic. Our experimental results show large performance improvements over previously-reported TDHs for commonly used classes of maps.

We introduce a new bidirectional search algorithm, Single-Frontier Bidirectional Search (SFBDS). Unlike traditional BDS which keeps two frontiers, SFBDS uses a single frontier. At a particular node we can decide to search from start to goal or from goal to start, choosing the direction with the highest potential for minimizing the total work done. We provide theoretical analysis that explains when SFBDS will work validated by experimental results.

Many search algorithms have parameters that need to be tuned to get the best performance. Typically, the parameters are tuned offline, resulting in a generic setting that is supposed to be effective on all problem instances. For suboptimal single-agent search, problem-instance-specific parameter settings can result in substantially reduced search effort. We consider the use of dovetailing as a way to take advantage of this fact. Dovetailing is a procedure that performs search with multiple parameter settings simultaneously. Dovetailing is shown to improve the search speed of weighted IDA* by several orders of magnitude and to generally enhance the performance of weighted RBFS. This procedure is trivially parallelizable and is shown to be an effective form of parallelization for WA* and BULB. In particular, using WA* with parallel dovetailing yields good speedups in the sliding-tile puzzle domain, and increases the number of problems solved when used in an automated planning system.

An anytime algorithm is capable of returning a response to the given task at essentially any time; typically the quality of the response improves as the time increases. Here, we consider the challenge of learning when we should terminate such algorithms on each of a sequence of iid tasks, to optimize the expected average reward per unit time. We provide a system for addressing this challenge, which combines the global optimizer Cross-Entropy method with local gradient ascent. This paper theoretically investigates how far the estimated gradient is from the true gradient, then empirically demonstrates that this system is effective by applying it to a toy problem, as well as on a real-world face detection task.

Computer games are a multi-billion dollar industry and have become an important part of our private and social lives. It is only natural, then, that the technology used to create games should become part of a computing science curriculum. However, game development is more than a massive programming endeavor. Today's games are largely about generating content within multidisciplinary teams. CMPUT 250 is a new computing science course at the University of Alberta that emphasizes creating games in multidisciplinary teams. This paper describes our experiences with the course, emphasizing the issues of multidisciplinary interactions: teaching, teamwork, and evaluation.

Real-time heuristic search methods are used by situated agents in applications that require the amount of planning per move to be independent of the problem size. Such agents plan only a few actions at a time in a local search space and avoid getting trapped in local minima by improving their heuristic function over time. We extend a wide class of real-time search algorithms with automatically-built state abstraction and prove completeness and convergence of the resulting family of algorithms. We then analyze the impact of abstraction in an extensive empirical study in real-time pathfinding. Abstraction is found to improve efficiency by providing better trading offs between planning time, learning speed and other negatively correlated performance measures.