Catálogo de publicaciones - libros

An important class of CSP heuristics work by sampling information during search in order to inform subsequent decisions. An example is the use of failures, in the form of constraint weights, to guide variable selection in a weighted degree procedure. The present research analyses the characteristics of the sampling process in this procedure and the manner in which information is used, in order to better understand this type of strategy and to discover further enhancements.

As SAT becomes more popular due to its ability to handle large real-world problems, progress in efficiency appears to have slowed down over the past few years. On the other hand, we now have access to many sophisticated implementations of SAT solvers, sometimes boasting large amounts of code. Although low-level optimizations can help, we argue that the SAT algorithm itself offers opportunities for more significant improvements. Specifically, we start with a no-frills solver implemented in less than 550 lines of code, and show that by focusing on the central aspects of the solver, higher performance can be achieved over some best existing solvers on a large set of benchmarks. This provides motivation for further research into these more important aspects of SAT algorithms, which we hope will lead to future significant advances in SAT.

Local branching is a general purpose heuristic search method successfully used in Mixed Integer Programming (MIP). We propose its integration and extension in Constraint Programming (CP).

The Disjunctive Temporal Problem with Uncertainty (DTPU) is an extension of the Disjunctive Temporal Problem (DTP) that accounts for events not under the control of the executing agent. We investigate the semantics of DTPU constraints, refining the existing notion that they are simply disjunctions of STPU constraints. We then develop the first sound and complete algorithm to determine whether Strong Controllability holds for a DTPU. We analyze the complexity of our algorithm with respect to the number of constraints in different classes, showing that, for several common subclasses of DTPUs, determining Strong Controllability has the same complexity as solving DTPs.

As a first attempt to exploit symmetries in continuous constraint problems, we focus on permutations of the variables consisting of one single cycle. We propose a procedure that takes advantage of these symmetries by interacting with a Branch-and-Prune algorithm without interfering with it. A key concept in this procedure are the classes of symmetric boxes formed by bisecting a -dimensional cube at the same point in all dimensions at the same time. We quantify these classes as a function of . Moreover, we propose a simple algorithm to generate the representatives of all these classes for any number of variables at very high rates. A problem example from the chemical field and a kinematics solver are used to show the performance of the approach in practice.

We introduce a definition of constraint symmetry for soft CSPs, based on the definition of constraint symmetry for classical CSPs. We show that the constraint symmetry group of a soft CSP is a subgroup of that of an associated classical CSP instance. Where it is smaller, we can successfully exploit the additional symmetries using conditional symmetry breaking. We demonstrate, in a case-study of graph colouring, that eliminating the symmetry of the soft CSP combined with conditional symmetry breaking can lead to huge reductions in the search effort to find an optimal solution to the soft CSP.

One common type of symmetry is when values are symmetric. For example, if we are assigning colours (values) to nodes (variables) in a graph colouring problem then we can uniformly interchange the colours throughout a colouring. For a problem with value symmetries, all symmetric solutions can be eliminated in polynomial time [1,2]. However, as we show here, both static and dynamic methods to deal with symmetry have computational limitations. With static methods, pruning all symmetric values is NP-hard in general.With dynamic methods, we can take exponential time on problems which static methods solve without search.