Improvement and Integration of Counting-Based Search Heuristics in Constraint Programming

Ce mémoire s’intéresse à la programmation par contraintes, un paradigme pour résoudre des problèmes combinatoires. Pour la plupart des problèmes, trouver une solution n’est pas possible si on se limite à des mécanismes d’inférence logique; l’exploration d’un espace des solutions à l’aide d’heuristiques de recherche est nécessaire. Des nombreuses heuristiques existantes, les heuristiques de branchement basées sur le dénombrement seront au centre de ce mémoire. Cette approche repose sur l’utilisation d’algorithmes pour estimer le nombre de solutions des contraintes individuelles d’un problème de satisfaction de contraintes. Notre contribution se résume principalement à l’amélioration de deux algorithmes de dénombrement pour les contraintes alldifferent et spanningTree; ces contraintes peuvent exprimer de nombreux problèmes de satisfaction, et sont par le fait même essentielles à nos heuristiques de branchement. Notre travail fait également l’objet d’une contribution à un solveur de programmation par contraintes open-source. Ainsi, l’ensemble de ce mémoire est motivé par cette considération pratique; nos algorithmes doivent être accessibles et performants. Finalement, nous explorons deux techniques applicables à l’ensemble de nos heuristiques: une technique qui réutilise des calculs précédemment faits dans l’arbre de recherche ainsi qu’une manière d’apprendre de nouvelles heuristiques de branchement pour un problème.=----------ABSTRACT: This thesis concerns constraint programming, a paradigm for solving combinatorial problems. The focus is on the mechanism involved in making hypotheses and exploring the solution space towards satisfying solutions: search heuristics. Of interest to us is a specific family called counting-based search, an approach that uses algorithms to estimate the number of solutions of individual constraints in constraint satisfaction problems to guide search. The improvements of two existing counting algorithms and the integration of counting-based search in a constraint programming solver are the two main contributions of this thesis. The first counting algorithm concerns the alldifferent constraint; the second one, the spanningTree constraint. Both constraints are useful for expressing many constraint satisfaction problems and thus are essential for counting-based search. Practical matters are also central to this work; we integrated counting-based search in an open-source constraint programming solver called Gecode. In doing so, we bring this family of search heuristics to a wider audience; everything in this thesis is built upon this contribution. Lastly, we also look at more general improvements to counting-based search with a method for trading computation time for accuracy, and a method for learning new counting-based search heuristics from past experiments

Dynamically weakened constraints in bounded search for constraint optimisation problems

Combinatorial optimisation problems, where the goal is to an optimal solution from the set of solutions of a problem involving resources, constraints on how these resources can be used, and a ranking of solutions are of both theoretical and practical interest. Many real world problems (such as routing vehicles or planning timetables) can be modelled as constraint optimisation problems, and solved via a variety of solver technologies which rely on differing algorithms for search and inference. The starting point for the work presented in this thesis is two existing approaches to solving constraint optimisation problems: constraint programming and decision diagram branch and bound search. Constraint programming models problems using variables which have domains of values and valid value assignments to variables are restricted by constraints. Constraint programming is a mature approach to solving optimisation problems, and typically relies on backtracking search algorithms combined with constraint propagators (which infer from incomplete solutions which values can be removed from the domains of variables which are yet to be assigned a value). Decision diagram branch and bound search is a less mature approach which solves problems modelled as dynamic programming models using width restricted decision diagrams to provide bounds during search. The main contribution of this thesis is adapting decision diagram branch and bound to be the search scheme in a general purpose constraint solver. To achieve this we propose a method in which we introduce a new algorithm for each constraint that we wish to include in our solver and these new algorithms weaken individual constraints, so that they respect the problem relaxations introduced while using decision diagram branch and bound as the search algorithm in our solver. Constraints are weakened during search based on the problem relaxations imposed by the search algorithm: before search begins there is no way of telling which relaxations will be introduced. We attempt to provide weakening algorithms which require little to no changes to existing propagation algorithms. We provide weakening algorithms for a number of built-in constraints in the Flatzinc specifi- cation, as well as for global constraints and symmetry reduction constraints. We implement a solver in Go and empirically verify the competitiveness of our approach. We show that our solver can be parallelised using Goroutines and channels and that our approach scales well. Finally, we also provide an implementation of our approach in a solver which is tailored towards solving extremal graph problems. We use the forbidden subgraph problem to show that our approach of using decision diagram branch and bound as a search scheme in a constraint solver can be paired with canonical search. Canonical search is a technique for graph search which ensures that no two isomorphic graphs are returned during search. We pair our solver with the Nauty graph isomorphism algorithm to achieve this, and explore the relationship between branch and bound and canonical search

Solving hard industrial combinatorial problems with SAT

The topic of this thesis is the development of SAT-based techniques and tools for solving industrial combinatorial problems. First, it describes the architecture of state-of-the-art SAT and SMT Solvers based on the classical DPLL procedure. These systems can be used as black boxes for solving combinatorial problems. However, sometimes we can increase their efficiency with slight modifications of the basic algorithm. Therefore, the study and development of techniques for adjusting SAT Solvers to specific combinatorial problems is the first goal of this thesis. Namely, SAT Solvers can only deal with propositional logic. For solving general combinatorial problems, two different approaches are possible: - Reducing the complex constraints into propositional clauses. - Enriching the SAT Solver language. The first approach corresponds to encoding the constraint into SAT. The second one corresponds to using propagators, the basis for SMT Solvers. Regarding the first approach, in this document we improve the encoding of two of the most important combinatorial constraints: cardinality constraints and pseudo-Boolean constraints. After that, we present a new mixed approach, called lazy decomposition, which combines the advantages of encodings and propagators. The other part of the thesis uses these theoretical improvements in industrial combinatorial problems. We give a method for efficiently scheduling some professional sport leagues with SAT. The results are promising and show that a SAT approach is valid for these problems. However, the chaotical behavior of CDCL-based SAT Solvers due to VSIDS heuristics makes it difficult to obtain a similar solution for two similar problems. This may be inconvenient in real-world problems, since a user expects similar solutions when it makes slight modifications to the problem specification. In order to overcome this limitation, we have studied and solved the close solution problem, i.e., the problem of quickly finding a close solution when a similar problem is considered

Development of hybrid metaheuristics based on instance reduction for combinatorial optimization problems

113 p.La tesis presentada describe el desarrollo de algoritmos metaheurísticos híbridos, basados en reducción de instancias de problema. Éstos son enfocados en la resolución de problemas de optimización combinatorial. La motivación original de la investigación radicó en lograr, a través de la reducción de instancias de problemas, el uso efectivo de modelos de programación lineal entera (ILP) sobre problemas que dado su tamaño no admiten el uso directo con esta técnica exacta. En este contexto se presenta entre otros desarrollos el framework Construct, Merge, Solve & Adapt (CMSA) para resolución de problemas de optimización combinatorial en general, el cual posteriormente fue adaptado para mejorar el desempeño de otras metaheurísticas sin el uso de modelos ILP. Los algoritmos presentados mostraron resultados que compiten o superan el estado del arte sobre los problemas Minimum Common String Partition (MCSP), Minimum Covering Arborescence (MCA) y Weighted Independent Domination (WID)

Sound Probabilistic #SAT with Projection

We present an improved method for a sound probabilistic estimation of the model count of a boolean formula under projection. The problem solved can be used to encode a variety of quantitative program analyses, such as concerning security of resource consumption. We implement the technique and discuss its application to quantifying information flow in programs.Comment: In Proceedings QAPL'16, arXiv:1610.0769

LOGIC AND CONSTRAINT PROGRAMMING FOR COMPUTATIONAL SUSTAINABILITY

Computational Sustainability is an interdisciplinary field that aims to develop computational and mathematical models and methods for decision making concerning the management and allocation of resources in order to help solve environmental problems. This thesis deals with a broad spectrum of such problems (energy efficiency, water management, limiting greenhouse gas emissions and fuel consumption) giving a contribution towards their solution by means of Logic Programming (LP) and Constraint Programming (CP), declarative paradigms from Artificial Intelligence of proven solidity. The problems described in this thesis were proposed by experts of the respective domains and tested on the real data instances they provided. The results are encouraging and show the aptness of the chosen methodologies and approaches. The overall aim of this work is twofold: both to address real world problems in order to achieve practical results and to get, from the application of LP and CP technologies to complex scenarios, feedback and directions useful for their improvement

Development of hybrid metaheuristics based on instance reduction for combinatorial optimization problems

113 p.La tesis presentada describe el desarrollo de algoritmos metaheurísticos híbridos, basados en reducción de instancias de problema. Éstos son enfocados en la resolución de problemas de optimización combinatorial. La motivación original de la investigación radicó en lograr, a través de la reducción de instancias de problemas, el uso efectivo de modelos de programación lineal entera (ILP) sobre problemas que dado su tamaño no admiten el uso directo con esta técnica exacta. En este contexto se presenta entre otros desarrollos el framework Construct, Merge, Solve & Adapt (CMSA) para resolución de problemas de optimización combinatorial en general, el cual posteriormente fue adaptado para mejorar el desempeño de otras metaheurísticas sin el uso de modelos ILP. Los algoritmos presentados mostraron resultados que compiten o superan el estado del arte sobre los problemas Minimum Common String Partition (MCSP), Minimum Covering Arborescence (MCA) y Weighted Independent Domination (WID)

Empirical Hardness of Finding Optimal Bayesian Network Structures: Algorithm Selection and Runtime Prediction

Various algorithms have been proposed for finding a Bayesian network structure that is guaranteed to maximize a given scoring function. Implementations of state-of-the-art algorithms, solvers, for this Bayesian network structure learning problem rely on adaptive search strategies, such as branch-and-bound and integer linear programming techniques. Thus, the time requirements of the solvers are not well characterized by simple functions of the instance size. Furthermore, no single solver dominates the others in speed. Given a problem instance, it is thus a priori unclear which solver will perform best and how fast it will solve the instance. We show that for a given solver the hardness of a problem instance can be efficiently predicted based on a collection of non-trivial features which go beyond the basic parameters of instance size. Specifically, we train and test statistical models on empirical data, based on the largest evaluation of state-of-the-art exact solvers to date. We demonstrate that we can predict the runtimes to a reasonable degree of accuracy. These predictions enable effective selection of solvers that perform well in terms of runtimes on a particular instance. Thus, this work contributes a highly efficient portfolio solver that makes use of several individual solvers.Peer reviewe

Capping methods for the automatic configuration of optimization algorithms

Automatic configuration techniques are widely and successfully used to find good parameter settings for optimization algorithms. Configuration is costly, because it is necessary to evaluate many configurations on different instances. For decision problems, when the objective is to minimize the running time of the algorithm, many configurators implement capping methods to discard poor configurations early. Such methods are not directly applicable to optimization problems, when the objective is to optimize the cost of the best solution found, given a predefined running time limit. We propose new capping methods for the automatic configuration of optimization algorithms. They use the previous executions to determine a performance envelope, which is used to evaluate new executions and cap those that do not satisfy the envelope conditions. We integrate the capping methods into the irace configurator and evaluate them on different optimization scenarios. Our results show that the proposed methods can save from about 5% to 78% of the configuration effort, while finding configurations of the same quality. Based on the computational analysis, we identify two conservative and two aggressive methods, that save an average of about 20% and 45% of the configuration effort, respectively. We also provide evidence that capping can help to better use the available budget in scenarios with a configuration time limit.This research has been supported by Coordenação de Aperfeiçoa-mento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code001. M. de Souza acknowledges the support of the Santa Catarina State University, Brasil. M. Ritt acknowledges the support of CNPq, Brasil (grant 437859/2018-5) and Google Research Latin America (grant25111). M. López-Ibáñez is a ‘‘Beatriz Galindo’’ Senior Distinguished Researcher (BEAGAL 18/00053) funded by the Spanish Ministry of Science and Innovation (MICINN). This research is partially funded by TAILOR ICT-48 Network (No 952215) funded by EU Horizon 2020 research and innovation programme. Funding for open access charge: Universidad de Málaga / CBU