Karen E. Petrie

Symmetry in Constraint Programming

Publisher Summary This chapter reviews that symmetry in constraints has always been important but in recent years has become a major research area in its own right. A key problem in constraint programming has long been recognised: search can revisit equivalent states over and over again. In principle this problem has been solved, with a number of different techniques. It discusses that research remains active for two reasons. First, there are many difficulties in the practical application of the techniques that are known for symmetry exclusion, and overcoming these remain important research problems. Second, the successes achieved in the area so far have encouraged researchers to find new ways to exploit symmetry. The chapter covers both these issues, and the details of the symmetry exclusion methods that have been conceived. It also explores the most important application of symmetry in constraint programming to reduce search: “symmetry breaking”. The goal of symmetry breaking is never to explore two search states which are symmetric to each other, as the result in both cases must be the same.

Implementing logical connectives in constraint programming

Combining constraints using logical connectives such as disjunction is ubiquitous in constraint programming, because it adds considerable expressive power to a constraint language. We explore the solver architecture needed to propagate such combinations of constraints efficiently. In particular we describe two new features named satisfying sets and constraint trees. We also make use of movable triggers (Gent et al., 2006) [1], and with these three complementary features we are able to make considerable efficiency gains. A key reason for the success of Boolean Satisfiability (SAT) solvers is their ability to propagate Or constraints efficiently, making use of movable triggers. We successfully generalise this approach to an Or of an arbitrary set of constraints, maintaining the crucial property that at most two constraints are active at any time, and no computation at all is done on the others. We also give an And propagator within our framework, which may be embedded within the Or. Using this approach, we demonstrate speedups of over 10,000 times in some cases, compared to traditional constraint programming approaches. We also prove that the Or algorithm enforces generalised arc consistency (GAC) when all its child constraints have a GAC propagator, and no variables are shared between children. By extending the Or propagator, we present a propagator for AtLeastK, which expresses that at least k of its child constraints are satisfied in any solution. Some logical expressions (e.g. exclusive-or) cannot be compactly expressed using And, Or and AtLeastK. Therefore we investigate reification of constraints. We present a fast generic algorithm for reification using satisfying sets and movable triggers.

A case study of Facebook use: Outlining a multi-layer strategy for higher education

Many students are looking to appropriate social networking sites, amongst them, Facebook, to enhance their learning experience. A growing body of literature reports on the motivation of students and staff to engage with Facebook as a learning platform as well as mapping such activities to pedagogy and curricula. This paper presents student opinions of the use of a Facebook strategy within higher education through the use of focus groups. Results show that the Facebook strategy is useful in promoting collaborative learning alongside the face-to-face delivery of content. Participants rebuked the perceived blurring of educational and social purposes, which is prevalent in the literature, with the current structure allowing a clear divide between their different uses of the site. The development of further guidelines for the use of Facebook for education is encouraged and recommendations are provided.

Automatic generation of constraints for partial symmetry breaking

Constraint Satisfaction Problems (CSPs) are often highly symmetric. Symmetries can give rise to redundant search, since subtrees may be explored which are symmetric to subtrees already explored. To avoid this redundant search, constraint programmers have designed methods, which try to exclude all but one in each equivalence class of solutions. One problem with many of the symmetry breaking methods that eliminate all the symmetry is that they can have a large running overhead. To counter this flaw many CP practitioners have looked for methods that only eliminate a subset of the symmetries, so called partial symmetry breaking methods, but do so in an efficient manner. Partial symmetry breaking methods often work only when the problem is of a certain type. In this paper, we introduce a new method of finding a small set of constraints which provide very efficient partial symmetry breaking. This method works with all problem classes and modelling techniques.

Same-relation constraints

The ALLDIFFERENT constraint was one of the first global constraints [17] and it enforces the conjunction of one binary constraint, the not-equal constraint, for every pair of variables. By looking at the set of all pairwise not-equal relations at the same time, AllDifferent offers greater filtering power. The natural question arises whether we can generally leverage the knowledge that sets of pairs of variables all share the same relation. This paper studies exactly this question. We study in particular special constraint graphs like cliques, complete bipartite graphs, and directed acyclic graphs, whereby we always assume that the same constraint is enforced on all edges in the graph. In particular, we study whether there exists a tractable GAC propagator for these global Same-Relation constraints and show that AllDifferent is a huge exception: most Same-Relation Constraints pose NP-hard filtering problems. We present algorithms, based on AC-4 and AC-6, for one family of Same-Relation Constraints, which do not achieve GAC propagation but outperform propagating each constraint individually in both theory and practice.

Self-Learning Genetic Algorithm For Constrains Satisfaction Problems

The efficient choice of a preprocessing level can reduce the search time of a constraint solver to find a solution to a constraint problem. Currently the parameters in constraint solver are often picked by hand by experts in the field. Genetic algorithms are a robust machine learning technology for problem optimization such as function optimization. Self-learning Genetic Algorithm are a strategy which suggests or predicts the suitable preprocessing method for large scale problems by learning from the same class of small scale problems. In this paper Self-learning Genetic Algorithms are used to create an automatic preprocessing selection mechanism for solving various constraint problems. The experiments in the paper are a proof of concept for the idea of combining genetic algorithm self-learning ability with constraint programming to aid in the parameter selection issue.

Combination: automated generation of puzzles with constraints

Constraint Programming offers a powerful means of solving a wide variety of combinatorial problems. We have used this powerful paradigm to create a successful computer game called Combination. Combination is an application for the iPhone and iPod touch. It has been on sale internationally through the iTunes store since December, 2008 and received a number of positive reviews. In this paper we explain how all the levels of Combination were generated, checked for correctness and rated for difficulty completely automatically through the use of constraints. We go on to evaluate this method of creation with the use of a human evaluation. This showed that fun, immersing computer games can be created with constraint programming.

Real-time processing of proteomics data: The internet of things and the connected laboratory

Processing data from life sciences experiments presents many challenges, these include the volume of data to be processed and the complexity of the processing needed in order to present meaningful results back to the experimenters. This is particularly evident in the field of proteomics where the complex datasets provided by mass spectrometers require extensive preprocessing and the use of search algorithms before they can be used effectively. Many tools currently exist to carry out this processing but they are focused on batch based workloads where the mass spectrometer finishes its analysis and then the data is processed on a file by file basis. Usually this work is carried out on local PC hardware, which can also cause a data management problem. The research described in this paper leads to a distributed cluster-based architecture designed to process the mass spectrometer output in a real-time streaming fashion. In this way the mass spectrometers in a laboratory together with a central computing platform constitute an internet of things problem which can be solved using modern open-source technology and cloud computing.

Using Self-learning and Automatic Tuning to Improve the Performance of Sexual Genetic Algorithms for Constraint Satisfaction Problems.

Currently the parameters in a constraint solver are often selected by hand by experts in the field; these parameters might include the level of preprocessing to be used and the variable ordering heuristic. The efficient and automatic choice of a preprocessing level for a constraint solver is a step towards making constraint programming a more widely accessible technology. Self-learning sexual genetic algorithms are a new approach combining a self-learning mechanism with sexual genetic algorithms in order to suggest or predict a suitable solver configuration for large scale problems by learning from the same class of small scale problems. In this paper, Self-learning Sexual genetic algorithms are applied to create an automatic solver configuration mechanism for solving various constraint problems. The starting population of self-learning sexual genetic algorithms will be trained through experience on small instances. The experiments in this paper are a proof-of-concept for the idea of combining sexual genetic algorithms with a self-learning strategy to aid in parameter selection for constraint programming.

Constraint Programming to Solve Maximal Density Still Life

The Maximum Density Still Life problem fills a finite Game of Life board with a stable pattern of cells that has as many live cells as possible. Although simple to state, this problem is computationally challenging for any but the smallest sizes of board. Especially difficult is to prove that the maximum number of live cells has been found. Various approaches have been employed. The most successful are approaches based on Constraint Programming (CP). We describe the Maximum Density Still Life problem, introduce the concept of constraint programming, give an overview on how the problem can be modelled and solved with CP, and report on best-known results for the problem.