Recent real-time heuristic search algorithms have demonstrated outstanding performance in video-game pathfinding. However, their applications have been thus far limited to that domain. We proceed with the aim of facilitating wider applications of real-time search by fostering a greater understanding of the performance of recent algorithms. We first introduce eight algorithm-independent complexity measures for search spaces and correlate their values with algorithm performance. The complexity measures are statistically shown to be significant predictors of algorithm performance across a set of commercial video-game maps. We then extend this analysis to a wider variety of search spaces in the first application of database-driven real-time search to domains outside of video-game pathfinding. In doing so, we gain insight into algorithm performance and possible enhancement as well as into search space complexity.
More recently, Hoffman extended a similar study of heuristic topology The terms topography and topology are used interchangeably in the literature when discussing heuristic functions. to general planning @cite_32 @cite_12 . On a set of @math well-established planning benchmarks, he enumerated topological heuristic features and domain properties to sort the benchmarks into a complexity taxonomy. This is similar to our ranking of search spaces based on complexity in Sections and , although Hoffman does not compute empirical correlations to performance. Hoffman concluded that the benchmark taxonomy would shed insight on the levels of success of heuristic search planning in these benchmarks. He also claimed that it could inform subsequent improvement of heuristic functions, allow prediction of planning performance and assist in developing more challenging benchmark sets.
@cite_32 @cite_12
2170377262 2167963482 146911184 2071853901 2146674345 174354460 2122054842 2220999736 2099752828 2161414194 2623510711 2146607065 1965973321 2088866137 2107218456 2406763882 2033896831 2606507580 1992432622 2001622826
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 FF’s 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. Many state-of-the-art heuristic planners derive their heuristic function by relaxing the planning task at hand, where the relaxation is to assume that all delete lists are empty. The success of such planners on many of the current benchmarks suggests that in those task's state spaces relaxed goal distances yield a heuristic function of high quality. Recent work has revealed empirical evidence confirming this intuition, stating several hypotheses about the local search topology of the current benchmarks, concerning the non-existence of dead ends and of local minima, as well as a limited maximal distance to exits on benches. Investigating a large range of planning domains, we prove that the above hypotheses do in fact hold true for the majority of the current benchmarks. This explains the recent success of heuristic planners. Specifically, it follows that FF's search algorithm, using an idealized heuristic function, is polynomial in (at least) eight commonly used benchmark domains. Our proof methods shed light on what the structural reasons are behind the topological phenomena, giving hints on how these phenomena might be automatically recognizable. Many state-of-the-art heuristic planners derive their heuristic function by relaxing the planning task at hand, where the relaxation is to assume that all delete lists are empty. Looking at a collection of planning benchmarks, we measure topological properties of state spaces with respect to that relaxation. The results suggest that, given the heuristic based on the relaxation, many planning benchmarks are simple in structure. This sheds light on the recent success of heuristic planners employing local search. Evolutionary algorithms integrating various niching techniques have been widely used to find multiple optima of an optimization problem. In recent years, an increasing amount of research has been focused on the design and application of speciation-based niching techniques. These techniques rely on speciation to partition a population into subpopulations (species) such that each occupies a different region of attraction (niche) on the fitness landscape. Existing speciation methods are either distance-based or topology-based. Topology-based methods are more flexible and have fewer assumptions than distance-based methods. However, existing topology-based methods all require sampling and evaluating new individuals in order to capture the landscape topography. This incurs additional fitness evaluations (FEs), which is a drawback, especially when the FE budget is limited. In this paper, a new topology-based speciation method named history-based topological speciation (HTS) is proposed. It relies exclusively on search history to capture the landscape topography and, therefore, does not require any additional FEs to be performed. To the best of our knowledge, HTS is the only parameter-free speciation method at the moment. Both theoretical and empirical analyses have been conducted. Theoretical analysis shows that HTS incurs acceptable computational overhead. In the experimental study, HTS outperformed existing topology-based methods on benchmark functions in up to 32-D space and with as many as 50 optima, and the time overhead was practically negligible if a single FE took seconds. Topology optimization is the process of determining the optimal layout of material and connectivity inside a design domain. This paper surveys topology optimization of continuum structures from the year 2000 to 2012. It focuses on new developments, improvements, and applications of finite element-based topology optimization, which include a maturation of classical methods, a broadening in the scope of the field, and the introduction of new methods for multiphysics problems. Four different types of topology optimization are reviewed: (1) density-based methods, which include the popular Solid Isotropic Material with Penalization (SIMP) technique, (2) hard-kill methods, including Evolutionary Structural Optimization (ESO), (3) boundary variation methods (level set and phase field), and (4) a new biologically inspired method based on cellular division rules. We hope that this survey will provide an update of the recent advances and novel applications of popular methods, provide exposure to lesser known, yet promising, techniques, and serve as a resource for those new to the field. The presentation of each method's focuses on new developments and novel applications. We present a novel approach to learning heuristic functions for AI planning domains. Given a state, we view a relaxed plan (RP) found from that state as a relational database, which includes the current state and goal facts, the actions in the RP, and the actions' add and delete lists. We represent heuristic functions as linear combinations of generic features of the database, selecting features and weights using training data from solved problems in the target planning domain. Many recent competitive planners use RP-based heuristics, but focus exclusively on the length of the RP, ignoring other RP features. Since RP construction ignores delete lists, for many domains, RP length dramatically under-estimates the distance to a goal, providing poor guidance. By using features that depend on deleted facts and other RP properties, our learned heuristics can potentially capture patterns that describe where such under-estimation occurs. Experiments in the STRIPS domains of IPC 3 and 4 show that best-first search using the learned heuristic can outperform FF (Hoffmann & Nebel 2001), which provided our training data, and frequently outperforms the top performances in IPC 4. In the AIPS98 Planning Contest, the HSP planner showed that heuristic search planners can be competitive with state-of-the-art Graphplan and SAT planners. Heuristic search planners like HSP transform planning problems into problems of heuristic search by automatically extracting heuristics from Strips encodings. They differ from specialized problem solvers such as those developed for the 24-Puzzle and Rubik’s Cube in that they use a general declarative language for stating problems and a general mechanism for extracting heuristics from these representations. In this paper, we study a family of heuristic search planners that are based on a simple and general heuristic that assumes that action preconditions are independent. The heuristic is then used in the context of best-first and hill-climbing search algorithms, and is tested over a large collection of domains. We then consider variations and extensions such as reversing the direction of the search for speeding node evaluation, and extracting information about propositional invariants for avoiding dead-ends. We analyze the resulting planners, evaluate their performance, and explain when they do best. We also compare the performance of these planners with two state-of-the-art planners, and show that the simplest planner based on a pure best-first search yields the most solid performance over a large set of problems. We also discuss the strengths and limitations of this approach, establish a correspondence between heuristic search planning and Graphplan, and briefly survey recent ideas that can reduce the current gap in performance between general heuristic search planners and specialized solvers.  2001 Elsevier Science B.V. All rights reserved. Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsoe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary” and several others. The paper gives an overview, comparison and critical review of the different approaches, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research. Many real-world planning domains, including those used in common benchmark problems, are based on multiagent scenarios. It has long been recognised that breaking down such problems into sub-problems for individual agents may help reduce overall planning complexity. This kind of approach is especially effective in domains where interaction between agents is limited. In this paper we present a fully centralised, offline, sequential, total-order planning algorithm for solving classical planning problems based on this idea. This algorithm consists of an automated decomposition process and a heuristic search method designed specifically for decomposed domains. The decomposition method is part of a preprocessing step and can be used to determine the "multiagent nature" of a planning problem prior to actual plan search. The heuristic search strategy is shown to effectively exploit any decompositions that are found and performs significantly better than current approaches on loosely coupled domains. Fast Downward is a classical planning system based on heuristic search. It can deal with general deterministic planning problems encoded in the propositional fragment of PDDL2.2, including advanced features like ADL conditions and effects and derived predicates (axioms). Like other well-known planners such as HSP and FF, Fast Downward is a progression planner, searching the space of world states of a planning task in the forward direction. However, unlike other PDDL planning systems, Fast Downward does not use the propositional PDDL representation of a planning task directly. Instead, the input is first translated into an alternative representation called multivalued planning tasks, which makes many of the implicit constraints of a propositional planning task explicit. Exploiting this alternative representation, Fast Downward uses hierarchical decompositions of planning tasks for computing its heuristic function, called the causal graph heuristic, which is very different from traditional HSP-like heuristics based on ignoring negative interactions of operators. In this article, we give a full account of Fast Downward's approach to solving multivalued planning tasks. We extend our earlier discussion of the causal graph heuristic to tasks involving axioms and conditional effects and present some novel techniques for search control that are used within Fast Downward's best-first search algorithm: preferred operators transfer the idea of helpful actions from local search to global best-first search, deferred evaluation of heuristic functions mitigates the negative effect of large branching factors on search performance, and multiheuristic best-first search combines several heuristic evaluation functions within a single search algorithm in an orthogonal way. We also describe efficient data structures for fast state expansion (successor generators and axiom evaluators) and present a new non-heuristic search algorithm called focused iterative-broadening search, which utilizes the information encoded in causal graphs in a novel way. Fast Downward has proven remarkably successful: It won the "classical" (i. e., propositional, non-optimising) track of the 4th International Planning Competition at ICAPS 2004, following in the footsteps of planners such as FF and LPG. Our experiments show that it also performs very well on the benchmarks of the earlier planning competitions and provide some insights about the usefulness of the new search enhancements. In this paper, we propose a novel appearance-based approach for topological mapping based on a hierarchical decomposition of the environment. In our map, images with similar visual properties are grouped together in nodes, which are represented by means of an average global descriptor and an index of binary features based on a bag-of-words online approach. Each image is represented by means of a global descriptor and a set of local features, and this information is used in a two-level loop closure approach, where first global descriptors are employed to obtain the most likely nodes of the map and then binary image features are used to retrieve the most likely images inside these nodes. This hierarchical scheme enables us to reduce the search space when recognizing places, maintaining high accuracy when creating a map. Our approach is validated using several public datasets and compared against several state-of-the-art techniques. The accuracy and the sparsity of the generated maps are also discussed. Comparing graphs to determine the level of underlying structural similarity between them is a widely encountered problem in computer science. It is particularly relevant to the study of Internet topologies, such as the generation of synthetic topologies to represent the Internet's AS topology. We derive a new metric that enables exactly such a structural comparison: the weighted spectral distribution. We then apply this metric to three aspects of the study of the Internet's AS topology. i) We use it to quantify the effect of changing the mixing properties of a simple synthetic network generator. ii) We use this quantitative understanding to examine the evolution of the Internet's AS topology over approximately seven years, finding that the distinction between the Internet core and periphery has blurred over time. iii) We use the metric to derive optimal parameterizations of several widely used AS topology generators with respect to a large-scale measurement of the real AS topology. In a time of information glut, observations about complex systems and phenomena of interest are available in several applications areas, such as biology and text. As a consequence, scientists have started searching for patterns that involve interactions among the objects of analysis, to the effect that research on models and algorithms for network analysis has become a central theme for knowledge discovery and data mining (KDD). The intuitions behind the plethora of approaches rely upon few basic types of networks, identified by specific local and global topological properties, which we term "pure" topology types.In this paper, (1) we survey pure topology types along with existing sampling algorithms that generate them, (2) we introduce novel algorithms that enhance the diversity of samples, and address the case of cellular topologies, (3) we perform statistical studies of the stability of the properties of pure types to alternative generative algorithms, and a joint study of the separability of pure types, in terms of their embedding in a space of metrics for network analysis, widely adopted in the social and physical sciences.We conclude with a word of caution to the practitioners, who sample pure topology types to assess the "statistical significance" of their findings, e.g., the p-value of the clustering coefficient is sensitive to the sampling algorithm used. We find that different pure types share similar topological properties. Further, real world networks hardly present the variability profile of a single pure type. We suggest the assumption of "mixtures of types" as an alternative starting point for developing models and algorithms for network analysis. This article improves recent methods for large scale image search. We first analyze the bag-of-features approach in the framework of approximate nearest neighbor search. This leads us to derive a more precise representation based on Hamming embedding (HE) and weak geometric consistency constraints (WGC). HE provides binary signatures that refine the matching based on visual words. WGC filters matching descriptors that are not consistent in terms of angle and scale. HE and WGC are integrated within an inverted file and are efficiently exploited for all images in the dataset. We then introduce a graph-structured quantizer which significantly speeds up the assignment of the descriptors to visual words. A comparison with the state of the art shows the interest of our approach when high accuracy is needed. Experiments performed on three reference datasets and a dataset of one million of images show a significant improvement due to the binary signature and the weak geometric consistency constraints, as well as their efficiency. Estimation of the full geometric transformation, i.e., a re-ranking step on a short-list of images, is shown to be complementary to our weak geometric consistency constraints. Our approach is shown to outperform the state-of-the-art on the three datasets. A number of today's state-of-the-art planners are based on forward state-space search. The impressive performance can be attributed to progress in computing domain independent heuristics that perform well across many domains. However, it is easy to find domains where such heuristics provide poor guidance, leading to planning failure. Motivated by such failures, the focus of this paper is to investigate mechanisms for learning domain-specific knowledge to better control forward search in a given domain. While there has been a large body of work on inductive learning of control knowledge for AI planning, there is a void of work aimed at forward-state-space search. One reason for this may be that it is challenging to specify a knowledge representation for compactly representing important concepts across a wide range of domains. One of the main contributions of this work is to introduce a novel feature space for representing such control knowledge. The key idea is to define features in terms of information computed via relaxed plan extraction, which has been a major source of success for non-learning planners. This gives a new way of leveraging relaxed planning techniques in the context of learning. Using this feature space, we describe three forms of control knowledge---reactive policies (decision list rules and measures of progress) and linear heuristics---and show how to learn them and incorporate them into forward state-space search. Our empirical results show that our approaches are able to surpass state-of-the-art non-learning planners across a wide range of planning competition domains. The ignoring delete lists relaxation is of paramount importance for both satisficing and optimal planning. In earlier work (Hoffmann 2005), it was observed that the optimal relaxation heuristic h+ has amazing qualities in many classical planning benchmarks, in particular pertaining to the complete absence of local minima. The proofs of this are hand-made, raising the question whether such proofs can be lead automatically by domain analysis techniques. In contrast to earlier disappointing results (Hoffmann 2005) - the analysis method has exponential runtime and succeeds only in two extremely simple benchmark domains - we herein answer this question in the affirmative. We establish connections between causal graph structure and h+ topology. This results in low-order polynomial time analysis methods, implemented in a tool we call TorchLight. Of the 12 domains where the absence of local minima has been proved, TorchLight gives strong success guarantees in 8 domains. Empirically, its analysis exhibits strong performance in a further 2 of these domains, plus in 4 more domains where local minima may exist but are rare. In this way, TorchLight can distinguish "easy" domains from "hard" ones. By summarizing structural reasons for analysis failure, TorchLight also provides diagnostic output indicating domain aspects that may cause local minima. We explore computational topology for clustering.We focus on time series and spatial data.Shape features are extracted based on n-dimensional holes.We run experiments with synthetic and real-world data.Results show improvements when compared to traditional clustering. Topology is the branch of mathematics that studies how objects relate to one another for their qualitative structural properties, such as connectivity and shape. In this paper, we present an approach for data clustering based on topological features computed over the persistence diagram, estimated using the theory of persistent homology. The features indicate topological properties such as Betti numbers, i.e., the number of n-dimensional holes in the discretized data space. The main contribution of our approach is enabling the clustering of time series that have similar recurrent behavior characterized by their attractors in phase space and spatial data that have similar scale-invariant spatial distributions, as traditional clustering techniques ignore that information as they rely on point-to-point dissimilarity measures such as Euclidean distance or elastic measures. We present experiments that confirm the usefulness of our approach with time series and spatial data applications in the fields of biology, medicine and ecology. A landmark based heuristic is investigated for reducing query phase run-time of the probabilistic roadmap (PRM) motion planning method. The heuristic is generated by storing minimum spanning trees from a small number of vertices within the PRM graph and using these trees to approximate the cost of a shortest path between any two vertices of the graph. The intermediate step of preprocessing the graph increases the time and memory requirements of the classical motion planning technique in exchange for speeding up individual queries making the method advantageous in multi-query applications. This paper investigates these trade-offs on PRM graphs constructed in randomized environments as well as a practical manipulator simulation. We conclude that the method is preferable to Dijkstra's algorithm or the A∗ algorithm with conventional heuristics in multi-query applications. The steadily increasing number of nodes in high-performance computing systems and the technology and power constraints lead to sparse network topologies. Efficient mapping of application communication patterns to the network topology gains importance as systems grow to petascale and beyond. Such mapping is supported in parallel programming frameworks such as MPI, but is often not well implemented. We show that the topology mapping problem is NP-complete and analyze and compare different practical topology mapping heuristics. We demonstrate an efficient and fast new heuristic which is based on graph similarity and show its utility with application communication patterns on real topologies. Our mapping strategies support heterogeneous networks and show significant reduction of congestion on torus, fat-tree, and the PERCS network topologies, for irregular communication patterns. We also demonstrate that the benefit of topology mapping grows with the network size and show how our algorithms can be used in a practical setting to optimize communication performance. Our efficient topology mapping strategies are shown to reduce network congestion by up to 80 , reduce average dilation by up to 50 , and improve benchmarked communication performance by 18 . We consider the problem of inferring the topology of an M-by-N network by sending probes between M sources and N receivers. Prior work has shown that this problem can be decomposed into two parts: first, infer smaller subnetwork components (i.e., 1-by-N's or 2-by-2's) and then merge these components to identify the M-by-N topology. In this paper, we focus on the second part. In particular, we assume that a 1by-N topology is given and that all 2-by-2 components can be queried and learned using end-to-end probes. The problem is which 2-by-2's to query and how to merge them with the 1-byN, so as to exactly identify the 2-by-N topology, and optimize a number of performance metrics including measurement traffic, time complexity, and memory usage. We provide a lower bound, ⌈N 2⌉, on the number of 2-by-2's required by any active learning algorithm and we also propose a greedy algorithm that is nearoptimal and efficient in practice. It follows a bottom-up approach: at every step, it selects two receivers, queries the corresponding 2-by-2, and merges it with the given 1-by-N. The algorithm requires exactly N - 1 steps, which is much less than all (N:2) possible 2-by-2's, and it correctly identifies the 2-by-N topology.