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.

In this paper we approach the problem of reasoning with quantified Boolean formulas (QBFs) by combining search and resolution, and by switching between them according to structural properties of QBFs. We provide empirical evidence that QBFs which cannot be solved by search or resolution alone, can be solved by combining them, and that our approach makes a proof-of-concept implementation competitive with current QBF solvers.

But this premature paving is not very useful if the searchtree is explored depth-first (DFS) or breadth-first (BFS): DFS When applied to numerical CSPs, the branch and quickly converges to ɛ-boxes that are too close to one another prune algorithm (BPA) computes a sharp covering to be representative of the solution set (see the left part of of the solution set. The BPA is therefore impractical Figure 1); BFS computes a homogeneous paving but finds no when the solution set is large, typically when ɛ-box at all if stopped too early (see the center graphic of Figure it has a dimension larger than four or five which is 1; note that such a sharp paving cannot be computed for often met in underconstrained problems. The purpose larger solution sets, making BFS useless in such cases). of this paper is to present a new search tree The search strategy used in an anytime BPA should quickly exploration strategy for BPA that hybridizes depthfirst find ɛ-boxes that are representative of the solution set: ɛ- and breadth-first searches. This search strategy boxes should be discovered uniformly on a continuous connected allows the BPA discovering potential solutions component in the solution set, while every connected in different areas of the search space in early stages components should be reached by some ɛ-boxes in early of the exploration, hence allowing an anytime usage stages of the search. Two such strategies are introduced in of the BPA. The merits of the proposed search the present paper. The most distant-first strategy (MDFS) strategy are experimentally evaluated.

In this paper we address the problem of generating preferred plans by combining the procedural control knowledge specified by Hierarchical Task Networks (HTNs) with rich user preferences. To this end, we extend the popular Planning Domain Definition Language, PDDL3, to support specification of simple and temporally extended preferences over HTN constructs. To compute preferred HTN plans, we propose a branch-and-bound algorithm, together with a set of heuristics that, leveraging HTN structure, measure progress towards satisfaction of preferences. Our preference-based planner, HTNPLAN-P, is implemented as an extension of the SHOP2 planner. We compared our planner with SGPLAN5 and HPLAN-P — the top performers in the 2006 International Planning Competition preference tracks. HTNPLAN-P generated plans that in all but a few cases equalled or exceeded the quality of plans returned by HPLAN-P and SGPLAN5. While our implementation builds on SHOP2, the language and techniques proposed here are relevant to a broad range of HTN planners.

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.

This paper studies the solving of finite-domain action planning problems with discrete action costs and soft constraints. For sequential optimal planning, a symbolic perimeter database heuristic is addressed in a bucket implementation of A*. For computing net-benefits, we propose symbolic branch-and-bound search together with some search refinements. The net-benefit we optimize is the total benefit of satisfying the goals, minus the total action cost to achieve them. This results in an objective function to be minimized that is a linear expression over the violation of the preferences added to the action cost total.

In Bayesian networks, a most probable explanation (MPE) is a most likely instantiation of all network variables given a piece of evidence. Solving (the decision version of) an MPE query is NP-hard. Recent work proposed a branch-and-bound search algorithm that finds exact solutions to MPE queries, where bounds are computed on a relaxed network obtained by a technique known as node splitting. In this work we study the impact of variable and value ordering on such a search algorithm. We study several heuristics based on the entropies of variables and on the notion of  nogoods, and propose a new meta-heuristic that combines their strengths. Experiments indicate that search efficiency is significantly improved, allowing many hard problems to be solved for the first time.

There are two basic approaches to generalize the propagation mechanism of the two-player Minimax search algorithm to multi-player (3 or more) games: the MaxN algorithm and the Paranoid algorithm. The main shortcoming of these approaches is that their strategy is fixed. In this paper we suggest a new approach (called MP-Mix) that dynamically changes the propagation strategy based on the players' relative strengths between MaxN, Paranoid and a newly presented  offensive strategy. In addition, we introduce the Opponent Impact factor for multi-player games, which measures the players' ability to impact their opponents' score, and show its relation to the relative performance of our new MP-Mix strategy. Experimental results show that MP-Mix outperforms all other approaches under most circumstances.

Fourier-based learning algorithms rely on being able to efficiently find the large coefficients of a function's spectral representation. In this paper, we introduce and analyze techniques for finding large coefficients. We show how a previously introduced search technique can be generalized from the Boolean case to the real-valued case, and we apply it in branch-and-bound and beam search algorithms that have significant advantages over the best-first algorithm in which the technique was originally introduced.