
Analyzing Search Topology Without Running Any Search: On the Connection Between Causal Graphs and h+
The ignoring delete lists relaxation is of paramount importance for both...
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Engineering Benchmarks for Planning: the Domains Used in the Deterministic Part of IPC4
In a field of research about general reasoning mechanisms, it is essenti...
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The MetricFF Planning System: Translating "Ignoring Delete Lists" to Numeric State Variables
Planning with numeric state variables has been a challenge for many year...
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A Formal Characterization of the Local Search Topology of the Gap Heuristic
The pancake puzzle is a classic optimization problem that has become a s...
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Improved local search for graph edit distance
Graph Edit Distance (GED) measures the dissimilarity between two graphs ...
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Homotopic Convex Transformation: A New Method to Smooth the Landscape of the Traveling Salesman Problem
This paper proposes a novel landscape smoothing method for the symmetric...
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The Complexity of Plan Existence and Evaluation in Probabilistic Domains
We examine the computational complexity of testing and finding small pla...
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Where 'Ignoring Delete Lists' Works: Local Search Topology in Planning Benchmarks
Between 1998 and 2004, the planning community has seen vast progress in terms of the sizes of benchmark examples that domainindependent 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 NPhard to compute. We identify several key characteristics of the topology under h^+, concerning the existence/nonexistence of unrecognized dead ends, as well as the existence/nonexistence 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 typicalcase 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.
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