This paper addresses the Target-Value Search (TVS) problem, which is the problem of finding a path between two nodes in a graph whose cost is as close as possible to a given target value, T. This problem has been previously addressed only for directed acyclic graphs. In this work we develop the theory required to solve this problem optimally for any type of graphs. We modify traditional heuristic search algorithms for this setting, and propose a novel bidirectional search algorithm that is specifically suited for TVS. The benefits of this bidirectional search algorithm are discussed both theoretically and experimentally on several domains.

This paper provides algorithms for predicting the size of the Expanded Search Tree (EST) of Depth-first Branch and Bound algorithms (DFBnB) for optimization tasks. The prediction algorithm is implemented and evaluated in the context of solving combinatorial optimization problems over graphical models such as Bayesian and Markov networks. Our methods extend to DFBnB the approaches provided by Knuth-Chen schemes that were designed and applied for predicting the EST size of backtracking search algorithms. Our empirical results demonstrate good predictions which are superior to competing schemes.

This paper introduces Monte Carlo *-Minimax Search (MCMS), a Monte Carlo search algorithm for turned-based, stochastic, two-player, zero-sum games of perfect information. The algorithm is designed for the class of of densely stochastic games; that is, games where one would rarely expect to sample the same successor state multiple times at any particular chance node. Our approach combines sparse sampling techniques from MDP planning with classic pruning techniques developed for adversarial expectimax planning. We compare and contrast our algorithm to the traditional *-Minimax approaches, as well as MCTS enhanced with the Double Progressive Widening, on four games: Pig, EinStein Wurfelt Nicht!, Can't Stop, and Ra. Our results show that MCMS can be competitive with enhanced MCTS variants in some domains, while consistently outperforming the equivalent classic approaches given the same amount of thinking time.

Constraint propagation is one of the key techniques in constraint programming, and a large body of work has built up around it. Special-purpose constraint propagation algorithms frequently make implicit use of short supports — by examining a subset of the variables, they can infer support (a justification that a variable-value pair still forms part of a solution to the constraint) for all other variables and values and save substantial work. Recently short supports have been used in general purpose propagators, and (when the constraint is amenable to short supports) speed ups of more than three orders of magnitude have been demonstrated. In this paper we present ShortSTR2, a development of the Simple Tabular Reduction algorithm STR2+. We show that ShortSTR2 is complementary to the existing algorithms ShortGAC and HaggisGAC that exploit short supports, while being much simpler. When a constraint is amenable to short supports, the short support set can be exponentially smaller than the full-length support set. Therefore ShortSTR2 can efficiently propagate many constraints that STR2+ cannot even load into memory. We also show that ShortSTR2 can be combined with a simple algorithm to identify short supports from full-length supports, to provide a superior drop-in replacement for STR2+.

Monte-Carlo Tree Search (MCTS) has proved a remarkably effective decision mechanism in many different game domains, including computer Go and general game playing (GGP).  However, in GGP, where many disparate games are played, certain type of games have proved to be particularly problematic for MCTS.  One of the problems are game trees with so-called optimistic moves, that is, bad moves that superficially look good but potentially require much simulation effort to prove otherwise.  Such scenarios can be difficult to identify in real time and can lead to suboptimal or even harmful decisions. In this paper we investigate a selection strategy for MCTS to alleviate this problem. The strategy, called sufficiency threshold, concentrates simulation effort better for resolving potential optimistic move scenarios.  The improved strategy is evaluated empirically in an n-arm-bandit test domain for highlighting its properties as well as in a state-of-the-art GGP agent to demonstrate its effectiveness in practice.  The new strategy shows significant improvements in both domains.

This paper is about transforming constraint networks to accommodate additional constraints in specific ways. The focus is on two intertwined issues. First, we investigate how partial solutions to an initial network can be preserved from the potential impact of additional constraints. Second, we study how more permissive constraints, which are intended to enlarge the set of solutions, can be accommodated in a constraint network. These two problems are studied in the general case and the light is shed on their relationship. A case study is then investigated where a more permissive additional constraint is taken into account through a form of network relaxation, while some previous partial solutions are preserved at the same time.

An extension of the CSP optimization framework tailored to identify fair solutions to instances involving multiple optimization functions is studied. Two settings are considered, based on the maximization of the minimum value over all the given functions (MAX-MIN approach) and on its lexicographical refinement where, over all solutions maximizing the minimum value, those maximizing the second minimum value are preferred, and so on, until all functions are considered (LEXMAX-MIN approach). For both settings, the complexity of computing an optimal solution is analyzed and the tractability frontier is charted for acyclic instances, w.r.t. the number and the domains of the functions to be optimized. Larger islands of tractability are then identified via a novel structural approach, based on a notion of guard that is designed to deal with the interactions among constraint scopes and optimization functions.

Multiobjective Dynamic Programming (MODP) is a general problem solving method used to determine the set of Pareto-optimal solutions in optimization problems involving discrete decision variables and multiple objectives. It applies to combinatorial problems in which Pareto-optimality of a solution extends to all its sub-solutions (Bellman principle). In this paper we focus on the determination of the preferred tradeoffs in the Pareto set where preference is measured by a Choquet integral. This model provides high descriptive possibilities but the associated preferences generally do not meet the Bellman principle, thus preventing any straightforward adaptation of MODP. To overcome this difficulty, we introduce here a general family of dominance rules enabling an early pruning of some Pareto-optimal sub-solutions that cannot lead to a Choquet optimum. Within this family, we identify the most efficient dominance rules and show how they can be incorporated into a MODP algorithm. Then we report numerical tests showing the actual efficiency of this approach to find Choquet-optimal tradeoffs in multiobjective knapsack problems.

Intensification and diversification are the key factors that control the performance of stochastic local search in satisfiability (SAT). Recently, Novelty Walk has become a popular method for improving diversification of the search and so has been integrated in many well-known SAT solvers such as TNM and gNovelty + . In this paper, we introduce new heuristics to improve the effectiveness of Novelty Walk in terms of reducing search stagnation. In particular, we use weights (based on statistical information collected during the search) to focus the diversification phase onto specific areas of interest. With a given probability, we select the most frequently unsatisfied clause instead of a totally random one as Novelty Walk does. Amongst all the variables appearing in the selected clause, we then select the least flipped variable for the next move. Our experimental results show that the new weight-enhanced diversification method significantly improves the performance of gNovelty$^+$ and thus outperforms other local search SAT solvers on a wide range of structured and random satisfiability benchmarks.

A variable elimination rule allows the polynomial-time identification of certain variables whose elimination does not affect the satisfiability of an instance. Variable elimination in the constraint satisfaction problem (CSP) can be used in preprocessing or during search to reduce search space size. We show that there are essentially just four variable elimination rules defined by forbidding generic sub-instances, known as irreducible patterns, in arc-consistent CSP instances. One of these rules is the Broken Triangle Property, whereas the other three are novel.