Most games being shipped today use some form of high-level abstraction such as a navmesh or waypoint graph for path planning. These structures can generally be represented in a form which is compact enough to meet the tight memory constraints in a game. But, when such a graph grows too large, finding paths can still be a complex task. This challenge was faced in Dragon Age: Origins and solved by adding an additional level of abstraction.In the last few years a variety of novel approaches have been developed for finding optimal paths through graphs with specific design applications for road networks. Currently these techniques cannot be feasibly applied to the lowest detail of movement possible in a game map, but can be applied to the high-level abstractions which are commonly found in games.In this paper we describe the pathfinding challenge faced before shipping the title Dragon Age: Origins and perform a postmortem analysis on the extended abstraction that was used in comparison to building more advanced heuristics or the use of contraction hierarchies. We show that contraction hierarchies and abstractions have similar overhead and performance and are both useful approaches for high-level planning in games.

Pathfinding systems that operate on regular grids are common in the AI literature and often used in real-time video games. Typical speed-up enhancements include reducing the size of the search space using abstraction, and building more informed heuristics. Though effective each of these strategies has shortcomings. For example, pathfinding with abstraction usually involves trading away optimality for speed. Meanwhile, improving on the accuracy of the well known Manhattan heuristic usually requires significant extra memor We present a different kind of speedup technique based on the idea of identifying and eliminating symmetric path segments in 4-connected grid maps (which allow straight but not diagonal movement). Our method identifies rectangular rooms with no obstacles and prunes all interior nodes, leaving only a boundary perimeter. This process eliminates many symmetric path segments and results in grid maps which are often much smaller and consequently much faster to search than the original. We evaluate our technique on a range of different grid maps including a well known set from the popular video game Baldur's Gate II. On our test data, A* can run up to 3.5 times faster on average. We achieve this without using any significant extra memory or sacrificing solution optimality.

In the standard rules of the board game Risk, players take turns selecting or "drafting" the 42 territories on the board until all territories are owned. We present a technique for drafting territories in Risk that combines the Monte Carlo tree search algorithm UCT with an automated evaluation function. Created through supervised machine learning, this function scores outcomes of drafts in order to shorten the length of a UCT simulation. Using this approach, we augment an existing bot for the computer game Lux Delux, a clone of Risk. Our drafting technique is shown to greatly improve performance against the strongest opponents supplied with Lux Delux. The evidence provided indicates that territory drafting is important to overall success in Risk.

The paper proposes artificial intelligence technique called hill climbing to find numerical solutions of Diophantine Equations. Such equations are important as they have many applications in fields like public key cryptography, integer factorization, algebraic curves, projective curves and data dependency in super computers. Importantly, it has been proved that there is no general method to find solutions of such equations. This paper is an attempt to find numerical solutions of Diophantine equations using steepest ascent version of Hill Climbing. The method, which uses tree representation to depict possible solutions of Diophantine equations, adopts a novel methodology to generate successors. The heuristic function used help to make the process of finding solution as a minimization process. The work illustrates the effectiveness of the proposed methodology using a class of Diophantine equations given by a1. x1 p1 + a2. x2 p2 + ...... + an . xn pn = N where ai and N are integers. The experimental results validate that the procedure proposed is successful in finding solutions of Diophantine Equations with sufficiently large powers and large number of variables.

The paper presents a scheme for computing lower and upper bounds on the posterior marginals in Bayesian networks with discrete variables. Its power lies in its ability to use any available scheme that bounds the probability of evidence or posterior marginals and enhance its performance in an anytime manner. The scheme uses the cutset conditioning principle to tighten existing bounding schemes and to facilitate anytime behavior, utilizing a fixed number of cutset tuples. The accuracy of the bounds improves as the number of used cutset tuples increases and so does the computation time. We demonstrate empirically the value of our scheme for bounding posterior marginals and probability of evidence using a variant of the bound propagation algorithm as a plug-in scheme.

Real-time heuristic search algorithms satisfy a constant bound on the amount of planning per action, independent of problem size. As a result, they scale up well as problems become larger. This property would make them well suited for video games where Artificial Intelligence controlled agents must react quickly to user commands and to other agents' actions. On the downside, real-time search algorithms employ learning methods that frequently lead to poor solution quality and cause the agent to appear irrational by re-visiting the same problem states repeatedly. The situation changed recently with a new algorithm, D LRTA*, which attempted to eliminate learning by automatically selecting subgoals. D LRTA* is well poised for video games, except it has a complex and memory-demanding pre-computation phase during which it builds a database of subgoals. In this paper, we propose a simpler and more memory-efficient way of pre-computing subgoals thereby eliminating the main obstacle to applying state-of-the-art real-time search methods in video games. The new algorithm solves a number of randomly chosen problems off-line, compresses the solutions into a series of subgoals and stores them in a database. When presented with a novel problem on-line, it queries the database for the most similar previously solved case and uses its subgoals to solve the problem. In the domain of pathfinding on four large video game maps, the new algorithm delivers solutions eight times better while using 57 times less memory and requiring 14% less pre-computation time.

Narrative, and in particular storytelling, is an important part of the human experience. Consequently, computational systems that can reason about narrative can be more effective communicators, entertainers, educators, and trainers. One of the central challenges in computational narrative reasoning is narrative generation, the automated creation of meaningful event sequences. There are many factors -- logical and aesthetic -- that contribute to the success of a narrative artifact. Central to this success is its understandability. We argue that the following two attributes of narratives are universal: (a) the logical causal progression of plot, and (b) character believability. Character believability is the perception by the audience that the actions performed by characters do not negatively impact the audience's suspension of disbelief. Specifically, characters must be perceived by the audience to be intentional agents. In this article, we explore the use of refinement search as a technique for solving the narrative generation problem -- to find a sound and believable sequence of character actions that transforms an initial world state into a world state in which goal propositions hold. We describe a novel refinement search planning algorithm -- the Intent-based Partial Order Causal Link (IPOCL) planner -- that, in addition to creating causally sound plot progression, reasons about character intentionality by identifying possible character goals that explain their actions and creating plan structures that explain why those characters commit to their goals. We present the results of an empirical evaluation that demonstrates that narrative plans generated by the IPOCL algorithm support audience comprehension of character intentions better than plans generated by conventional partial-order planners.

LAMA is a classical planning system based on heuristic forward search. Its core feature is the use of a pseudo-heuristic derived from landmarks, propositional formulas that must be true in every solution of a planning task. LAMA builds on the Fast Downward planning system, using finite-domain rather than binary state variables and multi-heuristic search. The latter is employed to combine the landmark heuristic with a variant of the well-known FF heuristic. Both heuristics are cost-sensitive, focusing on high-quality solutions in the case where actions have non-uniform cost. A weighted A* search is used with iteratively decreasing weights, so that the planner continues to search for plans of better quality until the search is terminated. LAMA showed best performance among all planners in the sequential satisficing track of the International Planning Competition 2008. In this paper we present the system in detail and investigate which features of LAMA are crucial for its performance. We present individual results for some of the domains used at the competition, demonstrating good and bad cases for the techniques implemented in LAMA. Overall, we find that using landmarks improves performance, whereas the incorporation of action costs into the heuristic estimators proves not to be beneficial. We show that in some domains a search that ignores cost solves far more problems, raising the question of how to deal with action costs more effectively in the future. The iterated weighted A* search greatly improves results, and shows synergy effects with the use of landmarks.

State-space search with explicit abstraction heuristics is at the state of the art of cost-optimal planning. These heuristics are inherently limited, nonetheless, because the size of the abstract space must be bounded by some, even if a very large, constant. Targeting this shortcoming, we introduce the notion of (additive) implicit abstractions, in which the planning task is abstracted by instances of tractable fragments of optimal planning. We then introduce a concrete setting of this framework, called fork-decomposition, that is based on two novel fragments of tractable cost-optimal planning. The induced admissible heuristics are then studied formally and empirically. This study testifies for the accuracy of the fork decomposition heuristics, yet our empirical evaluation also stresses the tradeoff between their accuracy and the runtime complexity of computing them. Indeed, some of the power of the explicit abstraction heuristics comes from precomputing the heuristic function offline and then determining h(s) for each evaluated state s by a very fast lookup in a ``database.'' By contrast, while fork-decomposition heuristics can be calculated in polynomial time, computing them is far from being fast. To address this problem, we show that the time-per-node complexity bottleneck of the fork-decomposition heuristics can be successfully overcome. We demonstrate that an equivalent of the explicit abstraction notion of a ``database'' exists for the fork-decomposition abstractions as well, despite their exponential-size abstract spaces. We then verify empirically that heuristic search with the ``databased" fork-decomposition heuristics favorably competes with the state of the art of cost-optimal planning.

Noisy probabilistic relational rules are a promising world model representation for several reasons. They are compact and generalize over world instantiations. They are usually interpretable and they can be learned effectively from the action experiences in complex worlds. We investigate reasoning with such rules in grounded relational domains. Our algorithms exploit the compactness of rules for efficient and flexible decision-theoretic planning. As a first approach, we combine these rules with the Upper Confidence Bounds applied to Trees (UCT) algorithm based on look-ahead trees. Our second approach converts these rules into a structured dynamic Bayesian network representation and predicts the effects of action sequences using approximate inference and beliefs over world states. We evaluate the effectiveness of our approaches for planning in a simulated complex 3D robot manipulation scenario with an articulated manipulator and realistic physics and in domains of the probabilistic planning competition. Empirical results show that our methods can solve problems where existing methods fail.