N-gram analysis provides a means of probabilistically predicting the next item in a sequence. Due originally to Shannon, it has proven an effective technique for word prediction in natural language processing and for gene sequence analysis. In this paper, we investigate the utility of n-gram analysis in predicting operator sequences in plans. Given a set of sample plans, we perform n-gram analysis to predict the likelihood of subsequent operators, relative to a partial plan. We identify several ways in which this information might be integrated into a planner. In this paper, we investigate one of these directions in further detail. Preliminary results demonstrate the promise of n-gram analysis as a tool for improving planning performance.

Adaptive A* is an incremental version of A* that updates the h-values of the previous A* search to make them more informed and thus future A* searches more focused. In this paper, we show how the A* searches performed by Adaptive A* can reuse part of the path of the previous search and terminate before they expand a goal state, resulting in Path-Adaptive A*. We demonstrate experimentally that Path-Adaptive A* expands fewer states per search and runs faster than Adaptive A* when solving path-planning problems in initially unknown terrain.

Planning systems for real-world applications need the ability to handle concurrency and numeric fluents. Nevertheless, the predominant approach to cope with concurrency followed by the most successful participants in the latest International Planning Competitions (IPC) is still to find a sequential plan that is rescheduled in a post-processing step. We present Temporal Fast Downward (TFD), a planning system for temporal problems that is capable of finding low-makespan plans by performing a heuristic search in a temporal search space. We show how the context-enhanced additive heuristic can be successfully used for temporal planning and how it can be extended to numeric fluents. TFD often produces plans of high quality and, evaluated according to the rating scheme of the last IPC, outperforms all state-of-the-art temporal planning systems.

Symmetry is an important feature of many constraint programs. We show that any symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each symmetry class. We use these observations in two methods for eliminating symmetry from a problem. These methods are designed to have many of the advantages of symmetry breaking methods that post static symmetry breaking constraint without some of the disadvantages. In particular, the two methods prune the search space using fast and efficient propagation of posted constraints, whilst reducing the conflict between symmetry breaking and branching heuristics. Experimental results show that the two methods perform well on some standard benchmarks.

We study novel approaches for solving of hard combinatorial problems by translation to Boolean Satisfiability (SAT). Our focus is on combinatorial problems that can be represented as a permutation of n objects, subject to additional constraints. In the case of the Hamiltonian Cycle Problem (HCP), these constraints are that two adjacent nodes in a permutation should also be neighbors in the original graph for which we search for a Hamiltonian cycle. We use the absolute SAT encoding of permutations, where for each of the n objects and each of its pos- sible positions in a permutation, a predicate is defined to indicate whether the object is placed in that position. For implementation of this predicate, we compare the direct and logarithmic encodings that have been used previously, against 16 hierarchical parameterizable encodings of which we explore 416 instantiations. We propose the use of enumerative adjacency constraints—that enumerate the possible neighbors of a node in a permutation — instead of, or in addition to the exclusivity adjacency constraints — that exclude impossible neighbors, and that have been applied previously. We study 11 heuristics for efficiently choosing the first node in the Hamiltonian cycle, as well as 8 heuristics for static CNF variable ordering. We achieve at least 4 orders of magnitude average speedup on HCP benchmarks from the phase transition region, relative to the previously used encodings for solving of HCPs via SAT, such that the speedup is increasing with the size of the graphs.

Pattern Databases (PDBs) are the most common form of memory-based heuristics, and they have been widely used in a variety of permutation puzzles and other domains. We explore the true-distance heuristics (TDHs) (also appeared in  (Sturtevant et al. 2009)) which are a different form of memory-based heuristics, designed to work in problem states where there isn't a fixed goal state. Unlike PDBs, which build a heuristic based on distances in an abstract state space, TDHs store distances which are computed in the actual state space. We look in detail at how TDHs work, providing both theoretical and experimental motivation for their use.

A problem that often arises in using abstraction is the generation of abstract states, called spurious states, that are—in the abstract space—reachable from some abstract image of a state s, but which have no corresponding state in the original space reachable from s. Spurious states can have a negative effect on pattern database sizes and heuristic quality. We formally define a property—the downward path preserving property (DPP)—that guarantees an abstraction has no spurious states. Analyzing the computational complexity of (i) testing the DPP property for a given state space and abstraction and of (ii) determining whether this property is achievable at all for a given state space, results in strong hardness theorems. On the positive side, we identify formal conditions under which finding DPP abstractions is tractable.

We present two different methods for estimating the cost of solving SAT problems. The methods focus on the online behaviour of the backtracking solver, as well as the structure of the problem. Modern SAT solvers present several challenges to estimate search cost including coping with nonchronological backtracking, learning and restarts. Our first method adapt an existing algorithm for estimating the size of a search tree to deal with these challenges. We then suggest a second method that uses a linear model trained on data gathered online at the start of search. We compare the effectiveness of these two methods using random and structured problems. We also demonstrate that predictions made in early restarts can be used to improve later predictions. We conclude by showing that the cost of solving a set of problems can be reduced by selecting a solver from a portfolio based on such cost estimations.

The article describes the proposition and application of a local search metaheuristic for multi-objective optimization problems. It is based on two main principles of heuristic search, intensification through variable neighborhoods, and diversification through perturbations and successive iterations in favorable regions of the search space. The concept is successfully tested on permutation flow shop scheduling problems under multiple objectives and compared to other local search approaches. While the obtained results are encouraging in terms of their quality, another positive attribute of the approach is its simplicity as it does require the setting of only very few parameters.

The article presents a study of rather simple local search heuristics for the single machine total weighted tardiness problem (SMTWTP), namely hillclimbing and Variable Neighborhood Search. In particular, we revisit these approaches for the SMTWTP as there appears to be a lack of appropriate/challenging benchmark instances in this case. The obtained results are impressive indeed. Only few instances remain unsolved, and even those are approximated within 1% of the optimal/best known solutions. Our experiments support the claim that metaheuristics for the SMTWTP are very likely to lead to good results, and that, before refining search strategies, more work must be done with regard to the proposition of benchmark data. Some recommendations for the construction of such data sets are derived from our investigations.