Problem Solving
Build Order Optimization in StarCraft
Churchill, David (University of Alberta) | Buro, Michael (University of Alberta)
In recent years, real-time strategy (RTS) games have gained interest in the AI research community for their multitude of challenging subproblems โ such as collaborative pathfinding, effective resource allocation and unit targeting, to name a few. In this paper we consider the build order problem in RTS games in which we need to find concurrent action sequences that, constrained by unit dependencies and resource availability, create a certain number of units and structures in the shortest possible time span. We present abstractions and heuristics that speed up the search for approximative solutions considerably in the game of StarCraft, and show the efficacy of our method by comparing its real-time performance with that of professional StarCraft players.
A Sparse Grid Representation for Dynamic Three-Dimensional Worlds
Sturtevant, Nathan R. (University of Denver)
Grid representations offer many advantages for path planning. Lookups in grids are fast, due to the uniform memory layout, and it is easy to modify grids. But, grids often have significant memory requirements, they cannot directly represent more complex surfaces, and path planning is slower due to their high granularity representation of the world. The speed of path planning on grids has been addressed using abstract representations, such as has been documented in work on Dragon Age: Origins. The abstract representation used in this game was compact, preventing permanent changes to the grid. In this paper we introduce a sparse grid representation, where grid cells are only stored where necessary. From this sparse representation we incrementally build an abstract graph which represents possible movement in the world at a high-level of granularity. This sparse representation also allows the representation of three-dimensional worlds. This representation allows the world to be incrementally changed in under a millisecond, reducing the maximum memory required to store a map and abstraction from Dragon Age: Origins by nearly one megabyte. Fundamentally, the representation allows previously allocated but unused memory to be used in ways that result in higher-quality planning and more intelligent agents.
Approaching a Player Model of Game Story Comprehension Through Affordance in Interactive Narrative
Young, R. Michael (North Carolina State University) | Cardona-Rivera, Rogelio (North Carolina State University)
A growing body of work in games research, both generative and analytic, seeks to characterize the relationship between a playerโs understanding of an interactive narrative and her options for action within it. This paper provides several definitions that collectively serve as a basis for a model of the userโs comprehension of an unfolding story in a game. Central to this approach, we define the notion of narrative affordance. In essence, a game provides a narrative affordance for some course of action when a player can imagine that course of action as part of a story that completes their current story experience. To define narrative affordance, we draw links from cognitive models of narrative comprehension and a range of research on affordance, which we couple with planning approaches to story and discourse generation. In our approach, we view the creation of an interactive narrative that provides a high degree of agency as a discourse generation problem. We posit that an interactive narrative system must reason about the content and organization of its communication with a player in order to prompt a playerโs understanding about the gameโs story and her role in it. This paper ends by pointing toward a research direction intended to provide insight into a range of aspects of interactive narrative, including role, genre, choice and agency.
Seven Design Challenges for Fully-realized Experience Management
Roberts, David L. (North Carolina State University)
Drama Managers, a specific type of the more general Experience Manager, have become a common subject of study in the interactive narrative literature. With a range of representational and computational approaches, authors have repeatedly developed techniques that enable computers to generate, reason about, and adapt narratives in an interactive virtual setting. In order to fully realize an experience manager, seven representational and computational problems need to be solved, generally on a case-by-case basis. In other words, the choice to use an Experience Manager is the choice to model the design as, and implement solutions to, seven inter-dependent design problems. We explicitly articulate those design problems and provide a number of examples of methods that both motivate the design problems as well as illustrate a range of approaches to solving them.
Engineering Benchmarks for Planning: the Domains Used in the Deterministic Part of IPC-4
Edelkamp, S., Englert, R., Hoffmann, J., Liporace, F., Thiebaux, S., Trueg, S.
In a field of research about general reasoning mechanisms, it is essential to have appropriate benchmarks. Ideally, the benchmarks should reflect possible applications of the developed technology. In AI Planning, researchers more and more tend to draw their testing examples from the benchmark collections used in the International Planning Competition (IPC). In the organization of (the deterministic part of) the fourth IPC, IPC-4, the authors therefore invested significant effort to create a useful set of benchmarks. They come from five different (potential) real-world applications of planning: airport ground traffic control, oil derivative transportation in pipeline networks, model-checking safety properties, power supply restoration, and UMTS call setup. Adapting and preparing such an application for use as a benchmark in the IPC involves, at the time, inevitable (often drastic) simplifications, as well as careful choice between, and engineering of, domain encodings. For the first time in the IPC, we used compilations to formulate complex domain features in simple languages such as STRIPS, rather than just dropping the more interesting problem constraints in the simpler language subsets. The article explains and discusses the five application domains and their adaptation to form the PDDL test suites used in IPC-4. We summarize known theoretical results on structural properties of the domains, regarding their computational complexity and provable properties of their topology under the h+ function (an idealized version of the relaxed plan heuristic). We present new (empirical) results illuminating properties such as the quality of the most wide-spread heuristic functions (planning graph, serial planning graph, and relaxed plan), the growth of propositional representations over instance size, and the number of actions available to achieve each fact; we discuss these data in conjunction with the best results achieved by the different kinds of planners participating in IPC-4.
The Deterministic Part of IPC-4: An Overview
We provide an overview of the organization and results of the deterministic part of the 4th International Planning Competition, i.e., of the part concerned with evaluating systems doing deterministic planning. IPC-4 attracted even more competing systems than its already large predecessors, and the competition event was revised in several important respects. After giving an introduction to the IPC, we briefly explain the main differences between the deterministic part of IPC-4 and its predecessors. We then introduce formally the language used, called PDDL2.2 that extends PDDL2.1 by derived predicates and timed initial literals. We list the competing systems and overview the results of the competition. The entire set of data is far too large to be presented in full. We provide a detailed summary; the complete data is available in an online appendix. We explain how we awarded the competition prizes.
Improving Heuristics Through Relaxed Search - An Analysis of TP4 and HSP*a in the 2004 Planning Competition
The hm admissible heuristics for (sequential and temporal) regression planning are defined by a parameterized relaxation of the optimal cost function in the regression search space, where the parameter m offers a trade-off between the accuracy and computational cost of theheuristic. Existing methods for computing the hm heuristic require time exponential in m, limiting them to small values (m andlt= 2). The hm heuristic can also be viewed as the optimal cost function in a relaxation of the search space: this paper presents relaxed search, a method for computing this function partially by searching in the relaxed space. The relaxed search method, because it computes hm only partially, is computationally cheaper and therefore usable for higher values of m. The (complete) hm heuristic is combined with partial hm heuristics, for m = 3,..., computed by relaxed search, resulting in a more accurate heuristic. This use of the relaxed search method to improve on the hm heuristic is evaluated by comparing two optimal temporal planners: TP4, which does not use it, and HSP*a, which uses it but is otherwise identical to TP4. The comparison is made on the domains used in the 2004 International Planning Competition, in which both planners participated. Relaxed search is found to be cost effective in some of these domains, but not all. Analysis reveals a characterization of the domains in which relaxed search can be expected to be cost effective, in terms of two measures on the original and relaxed search spaces. In the domains where relaxed search is cost effective, expanding small states is computationally cheaper than expanding large states and small states tend to have small successor states.
Distributed Reasoning in a Peer-to-Peer Setting: Application to the Semantic Web
Adjiman, P., Chatalic, P., Goasdoue, F., Rousset, M. C., Simon, L.
In a peer-to-peer inference system, each peer can reason locally but can also solicit some of its acquaintances, which are peers sharing part of its vocabulary. In this paper, we consider peer-to-peer inference systems in which the local theory of each peer is a set of propositional clauses defined upon a local vocabulary. An important characteristic of peer-to-peer inference systems is that the global theory (the union of all peer theories) is not known (as opposed to partition-based reasoning systems). The main contribution of this paper is to provide the first consequence finding algorithm in a peer-to-peer setting: DeCA. It is anytime and computes consequences gradually from the solicited peer to peers that are more and more distant. We exhibit a sufficient condition on the acquaintance graph of the peer-to-peer inference system for guaranteeing the completeness of this algorithm. Another important contribution is to apply this general distributed reasoning setting to the setting of the Semantic Web through the Somewhere semantic peer-to-peer data management system. The last contribution of this paper is to provide an experimental analysis of the scalability of the peer-to-peer infrastructure that we propose, on large networks of 1000 peers.
Decision-Theoretic Planning with non-Markovian Rewards
Gretton, C., Kabanza, F., Price, D., Slaney, J., Thiebaux, S.
A decision process in which rewards depend on history rather than merely on the current state is called a decision process with non-Markovian rewards (NMRDP). In decision-theoretic planning, where many desirable behaviours are more naturally expressed as properties of execution sequences rather than as properties of states, NMRDPs form a more natural model than the commonly adopted fully Markovian decision process (MDP) model. While the more tractable solution methods developed for MDPs do not directly apply in the presence of non-Markovian rewards, a number of solution methods for NMRDPs have been proposed in the literature. These all exploit a compact specification of the non-Markovian reward function in temporal logic, to automatically translate the NMRDP into an equivalent MDP which is solved using efficient MDP solution methods. This paper presents NMRDPP (Non-Markovian Reward Decision Process Planner), a software platform for the development and experimentation of methods for decision-theoretic planning with non-Markovian rewards. The current version of NMRDPP implements, under a single interface, a family of methods based on existing as well as new approaches which we describe in detail. These include dynamic programming, heuristic search, and structured methods. Using NMRDPP, we compare the methods and identify certain problem features that affect their performance. NMRDPPs treatment of non-Markovian rewards is inspired by the treatment of domain-specific search control knowledge in the TLPlan planner, which it incorporates as a special case. In the First International Probabilistic Planning Competition, NMRDPP was able to compete and perform well in both the domain-independent and hand-coded tracks, using search control knowledge in the latter.
Breaking Instance-Independent Symmetries In Exact Graph Coloring
Aloul, F. A., Markov, I. L., Ramani, A., Sakallah, K. A.
Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature.