Breaking Instance-Independent Symmetries In Exact Graph Coloring

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature

The Configurable SAT Solver Challenge (CSSC)

It is well known that different solution strategies work well for different types of instances of hard combinatorial problems. As a consequence, most solvers for the propositional satisfiability problem (SAT) expose parameters that allow them to be customized to a particular family of instances. In the international SAT competition series, these parameters are ignored: solvers are run using a single default parameter setting (supplied by the authors) for all benchmark instances in a given track. While this competition format rewards solvers with robust default settings, it does not reflect the situation faced by a practitioner who only cares about performance on one particular application and can invest some time into tuning solver parameters for this application. The new Configurable SAT Solver Competition (CSSC) compares solvers in this latter setting, scoring each solver by the performance it achieved after a fully automated configuration step. This article describes the CSSC in more detail, and reports the results obtained in its two instantiations so far, CSSC 2013 and 2014

Evolutionary Computation

This book presents several recent advances on Evolutionary Computation, specially evolution-based optimization methods and hybrid algorithms for several applications, from optimization and learning to pattern recognition and bioinformatics. This book also presents new algorithms based on several analogies and metafores, where one of them is based on philosophy, specifically on the philosophy of praxis and dialectics. In this book it is also presented interesting applications on bioinformatics, specially the use of particle swarms to discover gene expression patterns in DNA microarrays. Therefore, this book features representative work on the field of evolutionary computation and applied sciences. The intended audience is graduate, undergraduate, researchers, and anyone who wishes to become familiar with the latest research work on this field

Analysis of the fitness landscape for the class of combinatorial optimisation problems

Anatomy of the fitness landscape for a group of well known combinatorial optimisation problems is studied in this research and the similarities and the differences between their landscapes are pointed out. In this research we target the analysis of the fitness landscape for MAX-SAT, Graph-Colouring, Travelling Salesman and Quadratic Assignment problems. Belonging to the class of NP-Hard problems, all these problems become exponentially harder as the problem size grows. We study a group of properties of the fitness landscape for these problems and show what properties are shared by different problems and what properties are different. The properties we investigate here include the time it takes for a local search algorithm to find a local optimum, the number of local and global optima, distance between local and global optima, expected cost of found optima, probability of reaching a global optimum and the cost of the best configuration in the search space. The relationship between these properties and the system size and other parameters of the problems are studied, and it is shown how these properties are shared or differ in different problems. We also study the long-range correlation within the search space, including the expected cost in the Hamming sphere around the local and global optima, the basin of attraction of the local and global optima and the probability of finding a local optimum as a function of its cost. We believe these information provide good insight for algorithm designers

SAT and CP: Parallelisation and Applications

This thesis is considered with the parallelisation of solvers which search for either an arbitrary, or an optimum, solution to a problem stated in some formal way. We discuss the parallelisation of two solvers, and their application in three chapters.In the first chapter, we consider SAT, the decision problem of propositional logic, and algorithms for showing the satisfiability or unsatisfiability of propositional formulas. We sketch some proof-theoretic foundations which are related to the strength of different algorithmic approaches. Furthermore, we discuss details of the implementations of SAT solvers, and show how to improve upon existing sequential solvers. Lastly, we discuss the parallelisation of these solvers with a focus on clause exchange, the communication of intermediate results within a parallel solver. The second chapter is concerned with Contraint Programing (CP) with learning. Contrary to classical Constraint Programming techniques, this incorporates learning mechanisms as they are used in the field of SAT solving. We present results from parallelising CHUFFED, a learning CP solver. As this is both a kind of CP and SAT solver, it is not clear which parallelisation approaches work best here. In the final chapter, we will discuss Sorting networks, which are data oblivious sorting algorithms, i. e., the comparisons they perform do not depend on the input data. Their independence of the input data lends them to parallel implementation. We consider the question how many parallel sorting steps are needed to sort some inputs, and present both lower and upper bounds for several cases

Towards hybrid methods for solving hard combinatorial optimization problems

Tesis doctoral leída en la Escuela Politécnica Superior de la Universidad Autónoma de Madrid el 4 de septiembre de 200

Data-driven solutions to enhance planning, operation and design tools in Industry 4.0 context

This thesis proposes three different data-driven solutions to be combined to state-of-the-art solvers and tools in order to primarily enhance their computational performances. The problem of efficiently designing the open sea floating platforms on which wind turbines can be mount on will be tackled, as well as the tuning of a data-driven engine's monitoring tool for maritime transportation. Finally, the activities of SAT and ASP solvers will be thoroughly studied and a deep learning architecture will be proposed to enhance the heuristics-based solving approach adopted by such software. The covered domains are different and the same is true for their respective targets. Nonetheless, the proposed Artificial Intelligence and Machine Learning algorithms are shared as well as the overall picture: promote Industrial AI and meet the constraints imposed by Industry 4.0 vision. The lesser presence of human-in-the-loop, a data-driven approach to discover causalities otherwise ignored, a special attention to the environmental impact of industries' emissions, a real and efficient exploitation of the Big Data available today are just a subset of the latter. Hence, from a broader perspective, the experiments carried out within this thesis are driven towards the aforementioned targets and the resulting outcomes are satisfactory enough to potentially convince the research community and industrialists that they are not just "visions" but they can be actually put into practice. However, it is still an introduction to the topic and the developed models are at what can be defined a "pilot" stage. Nonetheless, the results are promising and they pave the way towards further improvements and the consolidation of the dictates of Industry 4.0