Restarts and Nogood Recording in Qualitative Constraint-based Reasoning

This paper introduces restart and nogood recording techniques in the domain of qualitative spatial and temporal reasoning. Nogoods and restarts can be applied orthogonally to usual methods for solving qualitative constraint satisfaction problems. In particular, we propose a more general definition of nogoods that allows for exploiting information about nogoods and tractable subclasses during backtracking search. First evaluations of the proposed techniques show promising results

An Extensive Evaluation of Portfolio Approaches for Constraint Satisfaction Problems

In the context of Constraint Programming, a portfolio approach exploits the complementary strengths of a portfolio of different constraint solvers. The goal is to predict and run the best solver(s) of the portfolio for solving a new, unseen problem. In this work we reproduce, simulate, and evaluate the performance of different portfolio approaches on extensive benchmarks of Constraint Satisfaction Problems. Empirical results clearly show the benefits of portfolio solvers in terms of both solved instances and solving time

Symmetry-reinforced Nogood Recording from Restarts

dans le cadre de CP'11International audienceNogood recording from restarts is a form of lightweight learn- ing that combines nogood recording with a restart strategy. At the end of each run, nogoods are extracted from the current (rightmost) branch of the search tree. These nogoods can be used to prevent parts of the search space from being explored more than once. In this paper, we propose to reinforce nogood recording (from restarts) by exploiting symmetries: every time the solver has to be restarted, not only the nogoods that are extracted from the current branch are recorded, but also some additional nogoods that can be computed by means of the previously identi ed problem symmetries. This mechanism of computing symmetric nogoods can be iterated until a xed-point is reached, and controlled (if necessary) by limiting the number and/or the size of recorded nogoods

An Extensive Evaluation of Portfolio Approaches for Constraint Satisfaction Problems

International audienceIn the context of Constraint Programming, a portfolio approach exploits the complementary strengths of a portfolio of different constraint solvers. The goal is to predict and run the best solver(s) of the portfolio for solving a new, unseen problem. In this work we reproduce, simulate, and evaluate the performance of different portfolio approaches on extensive benchmarks of Constraint Satisfaction Problems. Empirical results clearly show the benefits of portfolio solvers in terms of both solved instances and solving time

Reasoning from Last Conflict(s) in Constraint Programming

International audienceConstraint programming is a popular paradigm to deal with combinatorial problems in arti cial intelligence. Backtracking algorithms, applied to constraint networks, are commonly used but su er from thrashing, i.e. the fact of repeatedly exploring similar subtrees during search. An extensive literature has been devoted to prevent thrashing, often classi ed 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 conicts and, as a side e ect, to obtain a behavior similar to a backjumping technique. The principle is the following: after each conict, 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 conict. Experiments over a wide range of benchmarks demonstrate the e ectiveness of this approach in both constraint satisfaction and automated arti cial intelligence planning

Symmetry Breaking for Answer Set Programming

In the context of answer set programming, this work investigates symmetry detection and symmetry breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We contribute a reduction of symmetry detection to a graph automorphism problem which allows to extract symmetries of a logic program from the symmetries of the constructed coloured graph. We also propose an encoding of symmetry-breaking constraints in terms of permutation cycles and use only generators in this process which implicitly represent symmetries and always with exponential compression. These ideas are formulated as preprocessing and implemented in a completely automated flow that first detects symmetries from a given answer set program, adds symmetry-breaking constraints, and can be applied to any existing answer set solver. We demonstrate computational impact on benchmarks versus direct application of the solver. Furthermore, we explore symmetry breaking for answer set programming in two domains: first, constraint answer set programming as a novel approach to represent and solve constraint satisfaction problems, and second, distributed nonmonotonic multi-context systems. In particular, we formulate a translation-based approach to constraint answer set solving which allows for the application of our symmetry detection and symmetry breaking methods. To compare their performance with a-priori symmetry breaking techniques, we also contribute a decomposition of the global value precedence constraint that enforces domain consistency on the original constraint via the unit-propagation of an answer set solver. We evaluate both options in an empirical analysis. In the context of distributed nonmonotonic multi-context system, we develop an algorithm for distributed symmetry detection and also carry over symmetry-breaking constraints for distributed answer set programming.Comment: Diploma thesis. Vienna University of Technology, August 201

Local Rapid Learning for Integer Programs

Conflict learning algorithms are an important component of modern MIP and CP solvers. But strong conflict information is typically gained by depth-first search. While this is the natural mode for CP solving, it is not for MIP solving. Rapid Learning is a hybrid CP/MIP approach where CP search is applied at the root to learn information to support the remaining MIP solve. This has been demonstrated to be beneficial for binary programs. In this paper, we extend the idea of Rapid Learning to integer programs, where not all variables are restricted to the domain {0,1}, and rather than just running a rapid CP search at the root, we will apply it repeatedly at local search nodes within the MIP search tree. To do so efficiently, we present six heuristic criteria to predict the chance for local \rapidlearning to be successful. Our computational experiments indicate that our extended Rapid Learning algorithm significantly speeds up MIP search and is particularly beneficial on highly dual degenerate problems