In this paper, we are considering advanced pathplanning problems that feature finding paths for multiple units subject to rich path constraints. Examples of richer constraints are the following of other units or to stay out of sight of a specific unit. Little attention has so far been given to richer pathplanning problem where the objective is more than reaching a specific destination from a starting point such that the path length is minimized. Richer pathplanning problems occur in many complex real-world scenarios, ranging from computer games to military movement planning. In this paper, a novel way to formally specify such problems and a new local-search strategy to solve such problems are proposed and demonstrated by a prototype implementation. Among the design goals are real-time computability as well as extendibility for new constraints and search heuristics.

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.

We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in R^D given a noisy sample from the manifold. We assume that the manifold satisfies a smoothness condition and that the noise distribution has compact support. We show that the optimal rate of convergence is n^{-2/(2+d)}. Thus, the minimax rate depends only on the dimension of the manifold, not on the dimension of the space in which M is embedded.

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.

Between 1998 and 2004, the planning community has seen vast progress in terms of the sizes of benchmark examples that domain-independent planners can tackle successfully. The key technique behind this progress is the use of heuristic functions based on relaxing the planning task at hand, where the relaxation is to assume that all delete lists are empty. The unprecedented success of such methods, in many commonly used benchmark examples, calls for an understanding of what classes of domains these methods are well suited for. In the investigation at hand, we derive a formal background to such an understanding. We perform a case study covering a range of 30 commonly used STRIPS and ADL benchmark domains, including all examples used in the first four international planning competitions. We *prove* connections between domain structure and local search topology -- heuristic cost surface properties -- under an idealized version of the heuristic functions used in modern planners. The idealized heuristic function is called h^+, and differs from the practically used functions in that it returns the length of an *optimal* relaxed plan, which is NP-hard to compute. We identify several key characteristics of the topology under h^+, concerning the existence/non-existence of unrecognized dead ends, as well as the existence/non-existence of constant upper bounds on the difficulty of escaping local minima and benches. These distinctions divide the (set of all) planning domains into a taxonomy of classes of varying h^+ topology. As it turns out, many of the 30 investigated domains lie in classes with a relatively easy topology. Most particularly, 12 of the domains lie in classes where FFs search algorithm, provided with h^+, is a polynomial solving mechanism. We also present results relating h^+ to its approximation as implemented in FF. The behavior regarding dead ends is provably the same. We summarize the results of an empirical investigation showing that, in many domains, the topological qualities of h^+ are largely inherited by the approximation. The overall investigation gives a rare example of a successful analysis of the connections between typical-case problem structure, and search performance. The theoretical investigation also gives hints on how the topological phenomena might be automatically recognizable by domain analysis techniques. We outline some preliminary steps we made into that direction.

Real-time search methods are suited for tasks in which the agent is interacting with an initially unknown environment in real time. In such simultaneous planning and learning problems, the agent has to select its actions in a limited amount of time, while sensing only a local part of the environment centered at the agents current location. Real-time heuristic search agents select actions using a limited lookahead search and evaluating the frontier states with a heuristic function. Over repeated experiences, they refine heuristic values of states to avoid infinite loops and to converge to better solutions. The wide spread of such settings in autonomous software and hardware agents has led to an explosion of real-time search algorithms over the last two decades. Not only is a potential user confronted with a hodgepodge of algorithms, but he also faces the choice of control parameters they use. In this paper we address both problems. The first contribution is an introduction of a simple three-parameter framework (named LRTS) which extracts the core ideas behind many existing algorithms. We then prove that LRTA*, epsilon-LRTA*, SLA*, and gamma-Trap algorithms are special cases of our framework. Thus, they are unified and extended with additional features. Second, we prove completeness and convergence of any algorithm covered by the LRTS framework. Third, we prove several upper-bounds relating the control parameters and solution quality. Finally, we analyze the influence of the three control parameters empirically in the realistic scalable domains of real-time navigation on initially unknown maps from a commercial role-playing game as well as routing in ad hoc sensor networks.

In this paper, we introduce DLS-MC, a new stochastic local search algorithm for the maximum clique problem. DLS-MC alternates between phases of iterative improvement, during which suitable vertices are added to the current clique, and plateau search, during which vertices of the current clique are swapped with vertices not contained in the current clique. The selection of vertices is solely based on vertex penalties that are dynamically adjusted during the search, and a perturbation mechanism is used to overcome search stagnation. The behaviour of DLS-MC is controlled by a single parameter, penalty delay, which controls the frequency at which vertex penalties are reduced. We show empirically that DLS-MC achieves substantial performance improvements over state-of-the-art algorithms for the maximum clique problem over a large range of the commonly used DIMACS benchmark instances.

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.

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.

Tabu search is one of the most effective heuristics for locating high-quality solutions to a diverse array of NP-hard combinatorial optimization problems. Despite the widespread success of tabu search, researchers have a poor understanding of many key theoretical aspects of this algorithm, including models of the high-level run-time dynamics and identification of those search space features that influence problem difficulty. We consider these questions in the context of the job-shop scheduling problem (JSP), a domain where tabu search algorithms have been shown to be remarkably effective. Previously, we demonstrated that the mean distance between random local optima and the nearest optimal solution is highly correlated with problem difficulty for a well-known tabu search algorithm for the JSP introduced by Taillard. In this paper, we discuss various shortcomings of this measure and develop a new model of problem difficulty that corrects these deficiencies. We show that Taillards algorithm can be modeled with high fidelity as a simple variant of a straightforward random walk. The random walk model accounts for nearly all of the variability in the cost required to locate both optimal and sub-optimal solutions to random JSPs, and provides an explanation for differences in the difficulty of random versus structured JSPs. Finally, we discuss and empirically substantiate two novel predictions regarding tabu search algorithm behavior. First, the method for constructing the initial solution is highly unlikely to impact the performance of tabu search. Second, tabu tenure should be selected to be as small as possible while simultaneously avoiding search stagnation; values larger than necessary lead to significant degradations in performance.