Sébastien Tabary

Reasoning from last conflict(s) in constraint programming

Constraint programming is a popular paradigm to deal with combinatorial problems in artificial intelligence. Backtracking algorithms, applied to constraint networks, are commonly used but suffer from thrashing, i.e. the fact of repeatedly exploring similar subtrees during search. An extensive literature has been devoted to prevent thrashing, often classified into look-ahead (constraint propagation and search heuristics) and look-back (intelligent backtracking and learning) approaches. In this paper, we present an original look-ahead approach that allows to guide backtrack search toward sources of conflicts and, as a side effect, to obtain a behavior similar to a backjumping technique. The principle is the following: after each conflict, the last assigned variable is selected in priority, so long as the constraint network cannot be made consistent. This allows us to find, following the current partial instantiation from the leaf to the root of the search tree, the culprit decision that prevents the last variable from being assigned. This way of reasoning can easily be grafted to many variations of backtracking algorithms and represents an original mechanism to reduce thrashing. Moreover, we show that this approach can be generalized so as to collect a (small) set of incompatible variables that are together responsible for the last conflict. Experiments over a wide range of benchmarks demonstrate the effectiveness of this approach in both constraint satisfaction and automated artificial intelligence planning.

Exploiting past and future: pruning by inconsistent partial state dominance

It has recently been shown, for the Constraint Satisfaction Problem (CSP), that the state associated with a node of the search tree built by a backtracking algorithm can be exploited, using a transposition table, to prevent the exploration of similar nodes. This technique is commonly used in game search algorithms, heuristic search or planning. Its application is made possible in CSP by computing a partial state - a set of meaningful variables and their associated domains - preserving relevant information. We go further in this paper by providing two new powerful operators dedicated to the extraction of inconsistent partial states. The first one eliminates any variable whose current domain can be deduced from the partial state, and the second one extracts the variables involved in the inconsistency proof of the subtree rooted by the current node. Interestingly, we show these two operators can be safely combined, and that the pruning capabilities of the recorded partial states can be improved by a dominance detection approach (using lazy data structures).

An Adaptive Parallel SAT Solver

We present and evaluate AmPharoS, a new parallel SAT solver based on the divide and conquer paradigm. This solver, designed to work on a great number of cores, runs workers on sub-formulas restricted to cubes. In addition to classical clause sharing, it also exchange extra information associated to the cubes. Furthermore, we propose a new criterion to dynamically adapt both the amount of shared clauses and the number of cubes. Experiments show that, in general, AmPharoS correctly adjusts its strategy to the nature of the problem. Thus, we show that our new parallel approach works well and opens a broad range of possibilities to boost parallel SAT solver performances.

Lightweight Detection of Variable Symmetries for Constraint Satisfaction

In this paper, we propose to automatically detect variable symmetries of CSP instances by computing for each constraint scope a partition exhibiting locally symmetric variables. From this local information obtained in polynomial time, we can build a so-called lsv-graph whose automorphisms correspond to (global) variable symmetries. Interestingly enough, our approach allows us to disregard the representation (extension, intension, global) of constraints. Besides, the size of the lsv-graph is linear with respect to the number of constraints (and their arity).

Solving WCSP by Extraction of Minimal Unsatisfiable Cores

Usual techniques to solve WCSP are based on cost transfer operations coupled with a branch and bound algorithm. In this paper, we focus on an approach integrating extraction and relaxation of Minimal Unsatisfiable Cores in order to solve this problem. We derive our approach in two ways: an incomplete, greedy, algorithm and a complete one.

Propagating soft table constraints

WCSP is a framework that has attracted a lot of attention during the last decade. In particular, many filtering approaches have been developed on the concept of equivalence-preserving transformations (cost transfer operations), using the definition of soft local consistencies such as, for example, node consistency, arc consistency, full directional arc consistency, and existential directional arc consistency. Almost all algorithms related to these properties have been introduced for binary weighted constraint networks, and most of the conducted experiments typically include networks with binary and ternary constraints only. In this paper, we focus on extensional soft constraints (of large arity), so-called soft table constraints. We propose an algorithm to enforce a soft version of generalized arc consistency (GAC) on such constraints, by combining both the techniques of cost transfer and simple tabular reduction, the latter dynamically maintaining the list of allowed tuples in constraint tables. On various series of problem instances containing soft table constraints of large arity, we show the practical interest of our approach.

A Distributed Version of Syrup

A portfolio SAT solver has to share clauses in order to be efficient. In a distributed environment, such sharing implies additional problems: more information has to be exchanged and communications among solvers can be time consuming. In this paper, we propose a new version of the state-of-the-art SAT solver Syrup that is now able to run on distributed architectures. We analyze and compare different programming models of communication. We show that, using a dedicated approach, it is possible to share many clauses without penalizing the solvers. Experiments conducted on SAT 2016 benchmarks with up to 256 cores show that our solver is very effective and outperforms other approaches. This opens a broad range of possibilities to boost parallel solvers needing to share many data.

Constraint-Based Symmetry Detection in General Game Playing

Symmetry detection is a promising approach for reducing the search tree of games. In General Game Playing (GGP), where any game is compactly represented by a set of rules in the Game Description Language (GDL), the state-of-the-art methods for symmetry detection rely on a rule graph associated with the GDL description of the game. Though such rule-based symmetry detection methods can be applied to various tree search algorithms, they cover only a limited number of symmetries which are apparent in the GDL description. In this paper, we develop an alternative approach to symmetry detection in stochastic games that exploits constraint programming techniques. The minimax optimization problem in a GDL game is cast as a stochastic constraint satisfaction problem (SCSP), which can be viewed as a sequence of one-stage SCSPs. Minimax symmetries are inferred according to the microstructure complement of these one-stage constraint networks. Based on a theoretical analysis of this approach, we experimentally show on various games that the recent stochastic constraint solver MAC-UCB, coupled with constraint-based symmetry detection, significantly outperforms the standard Monte Carlo Tree Search algorithms, coupled with rule-based symmetry detection. This constraint-driven approach is also validated by the excellent results obtained by our player during the last GGP competition.

General game playing with stochastic CSP

The challenge of General Game Playing (GGP) is to devise game playing programs that take as input the rules of any strategic game, described in the Game Description Language (GDL), and that effectively play without human intervention. The aim of this paper is to address the GGP challenge by casting GDL games (potentially with chance events) into the Stochastic Constraint Satisfaction Problem (SCSP). The stochastic constraint network of a game is decomposed into a sequence of µSCSPs (also know as one-stage SCSP), each associated with a game round. Winning strategies are searched by coupling the MAC (Maintaining Arc Consistency) algorithm, used to solve each µSCSP in turn, together with the UCB (Upper Confidence Bound) policy for approximating the values of those strategies obtained by the last µSCSP in the sequence. Extensive experiments conducted on various GDL games with different deliberation times per round, demonstrate that the MAC-UCB algorithm significantly outperforms the state-of-the-art UCT (Upper Confidence bounds for Trees) algorithm.