Incremental search algorithms reuse information from previous searches to speed up the current search and are thus often able to find shortest paths for series of similar search problems faster than by solving each search problem independently from scratch. However, they do poorly on moving target search problems, where both the start and goal cells change over time. In this paper, we thus develop Fringe-Retrieving A* (FRA*), an incremental version of A* that repeatedly finds shortest paths for moving target search in known gridworlds. We demonstrate experimentally that it runs up to one order of magnitude faster than a variety of state-of-the-art incremental search algorithms applied to moving target search in known gridworlds.

In many scenarios, quickly solving a relatively small search problem with an arbitrary start and arbitrary goal state is important (e.g., GPS navigation). In order to speed this process, we introduce a new class of memory-based heuristics, called true distance heuristics, that store true distances between some pairs of states in the original state space can be used for a heuristic between any pair of states. We provide a number of techniques for using and improving true distance heuristics such that most of the benefits of the all-pairs shortest-path computation can be gained with less than 1% of the memory. Experimental results on a number of domains show a 6-14 fold improvement in search speed compared to traditional heuristics.

Optimization in graphical models is an important problem which has been studied in many AI frameworks such as weighted CSP, maximum satisfiability or probabilistic networks. By identifying conditionally independent subproblems, which are solved independently and whose optimum is cached, recent Branch and Bound algorithms offer better asymptotic time complexity. But the locality of bounds induced by decomposition often hampers the practical effects of this result because subproblems are often uselessly solved to optimality. Following the Russian Doll Search (RDS) algorithm, a possible approach to overcome this weakness is to (inductively) solve a relaxation of each subproblem to strengthen bounds. The algorithm obtained generalizes both RDS and tree-decomposition based algorithms such as BTD or AND-OR Branch and Bound. We study its efficiency on different problems, closing a very hard frequency assignment instance which has been open for more than 10 years.

We present a new algorithm for computing upper bounds for an optimization version of the EMAJSAT problem called functional E-MAJSAT. The algorithm utilizes the compilation language d- DNNF which underlies several state-of-the-art algorithms for solving related problems. This bound computation can be used in a branch-and-bound solver for solving functional E-MAJSAT. We then present a technique for pruning values from the branch-and-bound search tree based on the information available after each bound computation. We evaluated the proposed techniques in a MAP solver and a probabilistic conformant planner. In both cases, our experiments showed that the new techniques improved the efficiency of state-of-the-art solvers by orders of magnitude.

Moving target search (MTS) or the game of cops and robbers has a broad field of application reaching from law enforcement to computer games. Within the recent years research has focused on computing move policies for one or multiple pursuers (cops). The present work motivates to extend this perspective to both sides, thus developing algorithms for the target (robber). We investigate the game with perfect information for both players and propose two new methods, named TrailMax and Dynamic Abstract Trailmax, to compute move policies for the target. Experiments are conducted by simulating games on 20 maps of the commercial computer game Baldur's Gate and measuring survival time and computational complexity. We test seven algorithms: Cover, Dynamic Abstract Minimax, minimax, hill climbing with distance heuristic, a random beacon algorithm, TrailMax and DATrailMax. Analysis shows that our methods outperform all the other algorithms in quality, achieving up to 98% optimality, while meeting modern computer game computation time constraints.

Systematic search and local search paradigms for combinatorial problems are generally believed to have complementary strengths. Nevertheless, attempts to combine the power of the two paradigms have had limited success, due in part to the expensive information communication overhead involved. We propose a hybrid strategy based on shared memory, ideally suited for multi-core processor architectures. This method enables continuous information exchange between two solvers without slowing down either of the two. Such a hybrid search strategy is surprisingly effective, leading to substantially better quality solutions to many challenging Maximum Satisfiability (MaxSAT) instances than what the current best exact or heuristic methods yield, and it often achieves this within seconds. This hybrid approach is naturally best suited to MaxSAT instances for which proving unsatisfiability is already hard; otherwise the method falls back to pure local search.

Branch and bound is an effective technique for solving constraint optimization problems (COP’s). However, its search space expands very rapidly as the domain sizes of the problem variables grow. In this paper, we present an algorithm that clusters the values of a variable’s domain into sets. Branch and bound can then branch on these sets of values rather than on individual values, thereby reducing the branching factor of its search space. The aim of our clustering algorithm is to construct a collection of sets such that branching on these sets will still allow effective bounding. In conjunction with the reduced branching factor, the size of the explored search space is thus significantly reduced. We test our method and show empirically that it can yield significant performance gains over existing stateof- the-art techniques.

Decomposition is an effective technique for solving discrete Constraint Optimization Problems (COPs) with low tree-width. On problems with high treewidth, however, existing decomposition algorithms offer little advantage over branch and bound search (B&B). In this paper we propose a method for exploiting decomposition on problems with high treewidth. Our technique involves modifying B&B to detect and exploit decomposition on a selected subset of the problem’s objectives. Decompositions over this subset, generated during search, are exploited to compute tighter bounds allowing B&B to prune more of its search space. We present a heuristic for selecting an appropriate subset of objectives—one that readily decomposes during search and yet can still provide good bounds. We demonstrate empirically that our approach can significantly improve B&B’s performance and outperform standard decomposition algorithms on a variety of high tree-width problems.

Designing high-performance algorithms for computationally hard problems is a difficult and often time-consuming task. In this work, we demonstrate that this task can be automated in the context of stochastic local search (SLS) solvers for the propositional satisfiability problem (SAT). We first introduce a generalised, highly parameterised solver framework, dubbed SATenstein, that includes components gleaned from or inspired by existing high-performance SLS algorithms for SAT. The parameters of SATenstein control the selection of components used in any specific instantiation and the behaviour of these components. SATenstein can be configured to instantiate a broad range of existing high-performance SLSbased SAT solvers, and also billions of novel algorithms. We used an automated algorithm configuration procedure to find instantiations of SATenstein that perform well on several well-known, challenging distributions of SAT instances. Overall, we consistently obtained significant improvements over the previously best-performing SLS algorithms, despite expending minimal manual effort.

The rectangle packing problem consists of finding an enclosing rectangle of smallest area that can contain a given set of rectangles without overlap. Our algorithm picks the x-coordinates of all the rectangles before picking any of the y-coordinates. For the x-coordinates, we present a dynamic variable ordering heuristic and an adaptation of a pruning algorithm used in previous solvers. We then transform the rectangle packing problem into a perfect packing problem that has no empty space, and present inference rules to reduce the instance size. For the y-coordinates we search a space that models empty positions as variables and rectangles as values. Our solver is over 19 times faster than the previous state-of-the-art on the largest problem solved to date, allowing us to extend the known solutions for a consecutive-square packing benchmark from N=27 to N=32.