In this work we demonstrate that CSE has similar benefits when the reformulated constraint model is encoded to SAT and solved using a state-of-the-art SAT solver. Common Subexpression Elimination (CSE) is a family of techniques to improve automatically the formulation of constraint satisfaction problems, which are often highly beneficial when using a conventional constraint solver. Our approach is different: rather than reformulate the SAT representation directly, we apply automated reformulations to a higher level representation (a constraint model) of the original problem. Preprocessing and inprocessing are highly effective in extending the reach of SAT solvers, however they necessarily operate on the lowest level representation of the problem, the raw SAT clauses, where higher-level patterns are difficult and/or costly to identify. This has motivated research on preprocessing, and inprocessing techniques where reformulation of a SAT instance is interleaved with solving. The formulation of a Propositional Satisfiability (SAT) problem instance is vital to efficient solving. Our tests reveal that the new algorithm significantly outperforms all the others in several classes of BCSP instances. The performance of the new algorithm is compared against two SAT-based solvers and three general purpose CP solvers. We carry out an extensive computational campaign on a benchmark of almost 2000 instances which encompasses numerous real and synthetic problems from the literature.
In addition, the algorithm initialization phase performs a reordering of the microstructure graph vertices which produces an often easier reformulation to solve. Our filtering phases are based on coloring techniques and on heuristically solving an associated boolean satisfiability (SAT) problem. Our new algorithm exploits the cutting-edge branching scheme of the state-of-the-art maximum clique algorithms combined with two filtering phases in which the domains of the variables are reduced. In this work, we develop a new exact algorithm which effectively solves the BCSP by reformulating it as a k-clique problem on the underlying microstructure graph representation. The BCSP is a cornerstone problem in Constraint Programming (CP), appearing in a very wide range of real-world applications.
The problem is called binary because the constraints involve only pairs of variables. We conclude by arguing that AI planning could benefit from a richer modelling language.Ī binary constraint satisfaction problem (BCSP) consist in determining an assignment of values to variables which is compatible with a set of constraints. We also discuss the difficulties and inefficiencies of modelling Plotting in PDDL, the standard language used for input to specialised AI planners. We present and evaluate a constraint model of the Plotting problem that captures this complexity.
A single shot can affect multiple tiles directly, and the grid is affected by gravity so numerous other tiles can be affected indirectly. The key difficulty in modelling Plotting is in capturing the way the puzzle state changes after each shot. Plotting is an example of a planning problem: given a model of the environment, a planning problem asks us to find a sequence of actions that can lead from an initial state of the environment to a given goal state while respecting some constraints. This is achieved by the avatar character repeatedly shooting the block it holds into the grid. Its objective is to reduce a given grid of coloured blocks down to a goal number or fewer. Plotting is a tile-matching puzzle video game published by Taito in 1989.
0 kommentar(er)
