DOCSLIB.ORG

A Satisfiability Modulo Theories Approach to Constraint Programming

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Satisfiability Modulo Theories Approach to Constraint Programming A SATISFIABILITY MODULO THEORIES APPROACH TO CONSTRAINT PROGRAMMING Josep SUY FRANCH Dipòsit legal: GI. 150-2013 http://hdl.handle.net/10803/98302 A satisfiability modulo theories approach to constraint programming està subjecte a una llicència de Reconeixement 3.0 No adaptada de Creative Commons ©2013, Josep Suy Franch PHDTHESIS A Satisfiability Modulo Theories Approach to Constraint Programming Author: Josep SUY FRANCH 2012 Programa de Doctorat en Tecnologia Advisors: Dr. Miquel BOFILL ARASA Dr. Mateu VILLARET AUSELLE Memoria` presentada per optar al t´ıtol de doctor per la Universitat de Girona Abstract Satisfiability Modulo Theories (SMT) is an active research area mainly focused on for- mal verification of software and hardware. The SMT problem is the problem of deter- mining the satisfiability of ground logical formulas with respect to background theories expressed in classical first-order logic with equality. Examples of theories include linear real or integer arithmetic, arrays, bit vectors, uninterpreted functions, etc., or combina- tions of them. Modern SMT solvers integrate a Boolean satisfiability (SAT) solver with specialized solvers for a set of literals belonging to each theory. On the other hand, Constraint Programming (CP) is a programming paradigm de- voted to solve Constraint Satisfaction Problems (CSP). In a CSP, relations between vari- ables are stated in the form of constraints. Each constraint restricts the combination of values that a set of variables may take simultaneously. The constraints are stated over specific domains, typically: Booleans, integers, rationals, reals, finite domains, or com- binations of them. The problem consists in finding an assignment to the variables that satisfy all constraints. Many CP solving algorithms are based on systematic search, but in the last years there have been many other successful approaches to solve CSPs: SAT, Mixed Integer Linear Programming (MILP), Lazy Clause Generation (Lazy fd), genetic algorithms, tabu search, . In this thesis we focus on solving CSPs using SMT. Essentially, what we do is reformulating CSPs into SMT. There are already promising results in this direction, but there does not exist a generic approach and there are no available tools to extensively explore the adequacy of this approach. We intend to fill this gap with a complete encoding of an standard CP language. We provide extensive performance comparisons between state-of-the-art SMT solvers and most of the available CP solvers on a large collection of problems. The obtained results allow us to conclude that state-of-the-art SMT solvers are a robust tool to solve CSPs. We tackle not only decisional CSPs, but also Constraint Optimization Problems (COP), where the objective is to find a solution that is optimal with respect to some given objective function. We also address the Weighted Constraint Satisfiability Prob- lem (WCSP), where there are constraints with an associated weight (cost) and where the goal is to minimize the sum of the costs of the unsatisfied constraints. For solving COP i ii and WCSP we have used SMT in conjunction with appropriated algorithms: search algo- rithms and UNSAT core based algorithms borrowed from the MaxSAT area. We have developed the fzn2smt system for encoding instances of the MINIZINC standard (CSP and COP) specification language into SMT. With this system we have obtained the golden medal in the par division and the silver medal in the free division of the MINIZINC challenge 2010, and the silver medal in the same divisions of the MINIZINC challenge 2011. We have also developed a new specification language, called Simply, and its ex- tension WSimply, for programming in the three CP paradigms (CSP, COP and WCSP), and a compiler from this language to SMT. WSimply provides support for meta-constraints that is, constraints on constraints. Meta-constraints can be very helpful in the modelling process, since they allow us to abstract to a higher level, expressing, e.g., priorities be- tween a set of soft constraints, different levels of preference (multi-objective optimiza- tion), etc. As far as we know, WSimply is the first declarative CP language allowing to model WCSP instances intensionally and supporting meta-constraints. Once seen that SMT is a very good approximation for CP, we have tried to test whether algorithms built on top of an SMT solver can have equal or better performance than ad hoc programs designed specifically for a given problem, based on other ap- proaches. We concentrate on scheduling problems. Scheduling problems consist in de- ciding how to commit resources and time of execution to a set of activities. They are well suited to SMT because have a strong Boolean component and also an important arith- metic component. To test our approach we have chosen the resource-constrained project scheduling problem (RCPSP), and its generalizations RPCPSP/max and MRCPSP, since this is the most widely studied scheduling problem in the literature. We provide exten- sive performance comparisons between our approach and state-of-the-art RCPSP solvers. We remark that our system outperforms all other approaches described in the literature to solve MRCPSP and it is competitive in RCPSP and RCPSP/max. Resum La Satisfactibilitat Modul` Teories (SMT) es´ una area` de recerca activa centrada principal- ment en la verificacio´ formal de programari i maquinari. Un problema SMT consisteix en determinar la satisfactibilitat de formules´ logiques` sense quantificadors, respecte a teories de fons expressades en logica` classica` de primer ordre amb igualtat. Alguns exemples d’aquestes teories son:´ l’aritmetica` lineal real o entera, les matrius, els vectors de bits, les funcions no interpretades, . , o combinacions d’elles. Els solucionadors SMT moderns integren un solucionador de Satisfactibilitat Booleana (SAT) amb solucionadors especial- itzats per al conjunt de literals que pertanyen a cada teoria. D’altra banda, la Programacio´ amb Restriccions (CP) es´ un paradigma de progra- macio´ dedicat a resoldre els problemes de satisfaccio´ de restriccions (CSP). En un CSP, les relacions entre les variables s’expressen en forma de restriccions. Cada restriccio´ limita la combinacio´ de valors que poden prendre a la vegada un conjunt de variables. Les restriccions s’expressen a traves´ de dominis espec´ıfics com ara: Booleans, enters, racionals, reals, dominis finits, o combinacions d’aquests. Aquest problema consisteix en trobar una assignacio´ a les variables que satisfaci totes les restriccions. Molts algorismes de resolucio´ de CSPs es basen en la cerca sistematica,` tot i que en els ultims´ anys han aparegut molts altres metodes` per resoldre CSPs amb exit:` SAT, Mixed Integer Linear Programming (MILP), Lazy Clause Generation (Lazy fd ), algorismes genetics,` recerca tabu,´ . Aquesta tesi es centra en la resolucio´ de CSPs utilitzant SMT. En esencia,` es re- formulen els CSPs a formules´ SMT. Ja existeixen alguns resultats prometedors en aquest sentit, pero` sense un enfocament generic.` Tampoc existeixen eines disponibles per explo- rar exhaustivament la idone¨ıtat d’aquest enfocament. Es preten omplir aquest buit amb una codificacio´ completa d’un llenguatge estandard` de CP. Tambe´ es proporcionen com- paracions exhaustives de rendiment entre els millors solucionadors actuals d’SMT i la majoria dels solucionadors de CP disponibles en una amplia` col·leccio´ de problemes. Els resultats obtinguts permeten concloure que els millors solucionadors actuals d’SMT son´ una eina solida` per a resoldre CSPs. No nomes´ s’aborden els CSP decisionals, sino´ tambe´ problemes d’optimitzacio´ de restriccions (COP), on l’objectiu es´ trobar una solucio´ que sigui optima` respecte a una iii iv funcio´ objectiu donada. Tambe´ tractem el problema de restriccions de satisfacibilitat amb pesos (WCSP), on hi ha restriccions amb un pes associat (cost) i on l’objectiu es´ minim- itzar la suma dels costos de les restriccions insatisfetes. Per a resoldre COP i WCSP s’ha utilitzat SMT juntament amb els algorismes apropiats: algorismes de cerca i algorismes basats en nuclis d’insatisfactibilitat provinents de l’area` de MaxSAT. S’ha desenvolupat el sistema fzn2smt per a la codificacio´ de les instancies` del llenguatge d’especificacio´ estandard MINIZINC a SMT. Amb aquest sistema s’ha obtingut la medalla d’or en la divisio´ “par” i la medalla de plata en la divisio´ “free” de la MINIZINC Challenge 2010, i la medalla de plata en les mateixes divisions de la MINIZINC Challenge 2011. Tambe´ s’ha desenvolupat un nou llenguatge d’especificacio,´ anomenat Simply, i la seva extensio´ WSimply, per a la programacio´ dels tres paradigmes de CP (CSP, COP i WCSP), i un compilador d’aquests llenguatges a SMT. WSimply dona´ suport a meta- restriccions, es´ a dir, restriccions sobre restriccions. Les meta-restriccions poden ser de gran ajuda en el proces´ de modelatge, ates` que ens permeten abstreure’ns a un nivell superior, per expressar, per exemple, les prioritats entre un conjunt de restriccions amb pes, diferents nivells de preferencia` (optimitzacio´ multiobjectiu), etc. Pel que sabem, WSimply es´ el primer llenguatge declaratiu de CP que permet modelar WCSPs inten- sionalment i alhora donar suport a meta-restriccions. Un cop comprovat que SMT es´ una molt bona aproximacio´ per a CP, s’ha trac- tat de comprovar si els algorismes basats en SMT (amb ajuda d’un solucionador SMT directament o utilitzant-lo com un oracle) poden tenir un rendiment igual o millor que els programes dissenyats espec´ıficament per a un problema donat, desenvolupats so- bre la base d’altres enfocaments. Ens concentrem en els problemes de programacio´ d’activitats (scheduling). Els problemes de programacio´ d’activitats consisteixen en de- cidir com assignar recursos i temps d’execucio´ a un conjunt d’activitats. Aquest prob- lemes s’adapten be´ a SMT ja que tenen una forta component Booleana i tambe´ una compo- nent aritmetica` important. Per comprovar el nostre enfocament s’ha escollit el Problema del Projecte de Programacio´ amb Recursos Limitats (RCPSP), i les seves generalitzacions RPCPSP/max i MRCPSP, ates` que aquest es´ el problema de programacio´ d’activitats mes´ ampliament` estudiat en la literatura.
Load more

Recommended publications
  • Constraint Programming
    Constraint Programming Mikael Z. Lagerkvist Tomologic October 2015 Mikael Z. Lagerkvist (Tomologic) Constraint Programming October 2015 1 / 42 [flickr.com/photos/santos/] Who am I? Mikael Zayenz Lagerkvist Basic education at KTH 2000-2005 I Datateknik PhD studies at KTH 2005-2010 I Research in constraint programming systems I One of three core developers for Gecode, fast and well-known Constraint Programming (CP) system. http://www.gecode.org Senior developer R&D at Tomologic I Optimization systems for sheet metal cutting I Constraint programming for some tasks Mikael Z. Lagerkvist (Tomologic) Constraint Programming October 2015 3 / 42 Mikael Z. Lagerkvist (Tomologic) Constraint Programming October 2015 4 / 42 Mikael Z. Lagerkvist (Tomologic) Constraint Programming October 2015 5 / 42 Tomologic Mostly custom algorithms and heuristics Part of system implemented using CP at one point I Laser Cutting Path Planning Using CP Principles and Practice of Constraint Programming 2013 M. Z. Lagerkvist, M. Nordkvist, M. Rattfeldt Some sub-problems solved using CP I Ordering problems with side constraints I Some covering problems Mikael Z. Lagerkvist (Tomologic) Constraint Programming October 2015 6 / 42 1 Introduction 2 Sudoku example 3 Solving Sudoku with CP 4 Constraint programming basics 5 Constraint programming in perspective Constraint programming evaluation Constraint programming alternatives 6 Summary Mikael Z. Lagerkvist (Tomologic) Constraint Programming October 2015 7 / 42 Sudoku - The Rules Each square gets one value between 1 and 9 Each row has all values different Each column has all values different Each square has all values different Mikael Z. Lagerkvist (Tomologic) Constraint Programming October 2015 7 / 42 Sudoku - Example 3 6 1 9 7 5 8 9 2 8 7 4 3 6 1 2 8 9 4 5 1 Mikael Z.
    [Show full text]
  • A Stochastic Continuous Optimization Backend for Minizinc with Applications to Geometrical Placement Problems Thierry Martinez, François Fages, Abder Aggoun
    A Stochastic Continuous Optimization Backend for MiniZinc with Applications to Geometrical Placement Problems Thierry Martinez, François Fages, Abder Aggoun To cite this version: Thierry Martinez, François Fages, Abder Aggoun. A Stochastic Continuous Optimization Backend for MiniZinc with Applications to Geometrical Placement Problems. Proceedings of the 13th International Conference on Integration of Artificial Intelligence and Operations Research Techniques in Constraint Programming, CPAIOR’16, May 2016, Banff, Canada. pp.262-278, 10.1007/978-3-319-33954-2_19. hal-01378468 HAL Id: hal-01378468 https://hal.archives-ouvertes.fr/hal-01378468 Submitted on 30 Nov 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. A Stochastic Continuous Optimization Backend for MiniZinc with Applications to Geometrical Placement Problems Thierry Martinez1 and Fran¸cois Fages1 and Abder Aggoun2 1 Inria Paris-Rocquencourt, Team Lifeware, France 2 KLS-Optim, France Abstract. MiniZinc is a solver-independent constraint modeling lan- guage which is increasingly used in the constraint programming com- munity. It can be used to compare different solvers which are currently based on either Constraint Programming, Boolean satisfiability, Mixed Integer Linear Programming, and recently Local Search. In this paper we present a stochastic continuous optimization backend for MiniZinc mod- els over real numbers.
    [Show full text]
  • Model-Based Optimization for Effective and Reliable Decision-Making
    Model-Based Optimization for Effective and Reliable Decision-Making Robert Fourer [email protected] AMPL Optimization Inc. www.ampl.com — +1 773-336-2675 DecisionCAMP Bolzano, Italy — 18 September 2019 Model-Based Optimization DecisionCAMP — 18 September 2019 1 Model-Based Optimization for Effective and Reliable Decision-Making Optimization originated as an advanced between the human modeler’s formulation mathematical technique, but it has become an and the solver software’s needs. This talk accessible and widely used decision-making introduces model-based optimization by tool. A key factor in the spread of successful contrasting it to a method-based approach optimization applications has been the that relies on customized implementation of adoption of a model-based approach: A rules and algorithms. Model-based domain expert or operations analyst focuses implementations are illustrated using the on modeling the problem of interest, while AMPL modeling language and popular the computation of a solution is left to solvers. The presentation concludes by general-purpose, off-the-shelf solvers; surveying the variety of modeling languages powerful yet intuitive modeling software and solvers available for model-based manages the difficulties of translating optimization today. Dr. Fourer has over 40 years’ experience in institutes, and corporations worldwide; he is studying, creating, and applying large-scale also author of a popular book on AMPL. optimization software. In collaboration with Additionally, he has been a key contributor to the colleagues in Computing Science Research at NEOS Server project and other efforts to make Bell Laboratories, he initiated the design and optimization services available over the Internet, development of AMPL, which has become one and has supported development of open-source of the most widely used software systems for software for operations research through his modeling and analyzing optimization problems, service on the board of the COIN-OR with users in hundreds of universities, research Foundation.
    [Show full text]
  • Theory and Practice of Constraint Programming September 24-28, 2012
    Association for Constraint Programming ACP Summer School 2012 Theory and Practice of Constraint Programming September 24-28, 2012 Institute of Computer Science University of Wrocław Poland Association for Constraint Programming ACP Summer School 2012 Theory and Practice of Constraint Programming September 24-28, 2012 Institute of Computer Science University of Wrocław Poland Table of contents Introduction to constraint programming Willem-Jan van Hoeve Operations Research Techniques in Constraint Programming Willem-Jan van Hoewe Constraint Programming and Biology Agostino Dovier Constraints and Complexity Peter Jeavons Set Constraints Witold Charatonik Constraints: Counting and Approximation Andrei Bulatov Introduction to Constraint Programming Willem-Jan van Hoeve Tepper School of Business, Carnegie Mellon University ACP Summer School on Theory and Practice of Constraint Programming September 24-28, 2012, Wrocław, Poland Outline Constraint Programming Overview General introduction • Successful applications Artificial Operations Computer Intelligence Research Science • Modeling • Solving • CP software optimization search algorithms data structures Basic concepts logical inference formal languages • Search Constraint • Constraint propagation Programming • Complexity Evolution events of CP Successful applications 1970s: Image processing applications in AI; Search+qualitative inference 1980s: Logic Programming (Prolog); Search + logical inference 1989: CHIP System; Constraint Logic Programming 1990s: Constraint Programming; Industrial Solvers
    [Show full text]
  • Introduction to Constraint Programming Outline Constraint
    Introduction to Constraint Programming Willem-Jan van Hoeve Tepper School of Business, Carnegie Mellon University ACP Summer School on Theory and Practice of Constraint Programming September 24-28, 2012, Wrocław, Poland Outline General introduction • Successful applications • Modeling • Solving • CP software Basic concepts • Search • Constraint propagation • Complexity Constraint Programming Overview Artificial Operations Computer Intelligence Research Science optimization search algorithms data structures logical inference formal languages Constraint Programming 1 Evolution events of CP 1970s: Image processing applications in AI; Search+qualitative inference 1980s: Logic Programming (Prolog); Search + logical inference 1989: CHIP System; Constraint Logic Programming 1990s: Constraint Programming; Industrial Solvers (ILOG, Eclipse,…) 1994: Advanced inference for alldifferent and resource scheduling 2000s: Global constraints; integrated methods; modeling languages 2006: CISCO Systems acquires Eclipse CLP solver 2009: IBM acquires ILOG CP Solver & Cplex Successful applications Sport Scheduling Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Period 1 0 vs1 0 vs2 4 vs7 3 vs6 3 vs 7 1 vs 5 2 vs4 Period 2 2 vs3 1 vs7 0 vs3 5 vs7 1 vs4 0 vs6 5 vs 6 Period 3 4 vs 5 3 vs 5 1 vs6 0 vs4 2 vs6 2 vs7 0 vs7 Period 4 6 vs 7 4 vs 6 2 vs 5 1 vs 2 0 vs 5 3 vs 4 1 vs 3 Schedule of 1997/1998 ACC basketball league (9 teams) • various complicated side constraints • all 179 solutions were found in 24h using enumeration and integer linear programming [Nemhauser
    [Show full text]
  • Constraint Programming
    Constraint Programming Justin Pearson Uppsala University 1st July 2016 Special thanks to Pierre Flener, Joseph Scott and Jun He CP MiniZinc Strings Other Final Outline 1 Introduction to Constraint Programming (CP) 2 Introduction to MiniZinc 3 Constraint Programming with Strings 4 Some recent, and not so Recent Advances 5 Final Thoughts Uppsala University Justin Pearson Constraint Programming CP MiniZinc Strings Other Final Constraint Programming in a Nutshell Slogan of CP Constraint Program = Model [ + Search ] CP provides: high level declarative modelling abstractions, a framework to separate search from from modelling. Search proceeds by intelligent backtracking with intelligent inference called propagation that is guided by high-level modelling constructs called global constraints. Uppsala University Justin Pearson Constraint Programming CP MiniZinc Strings Other Final Outline 1 Introduction to Constraint Programming (CP) Modelling Propagation Systematic Search History of CP 2 Introduction to MiniZinc 3 Constraint Programming with Strings 4 Some recent, and not so Recent Advances 5 Final Thoughts Uppsala University Justin Pearson Constraint Programming CP MiniZinc Strings Other Final Constraint-Based Modelling Example (Port tasting, PT) Alva Dan Eva Jim Leo Mia Ulla 2011 2003 2000 1994 1977 1970 1966 Constraints to be satisfied: Equal jury size: Every wine is evaluated by 3 judges. Equal drinking load: Every judge evaluates 3 wines. Fairness: Every port pair has 1 judge in common. Uppsala University Justin Pearson Constraint Programming CP MiniZinc Strings Other Final Constraint-Based Modelling Example (Port tasting, PT) Alva Dan Eva Jim Leo Mia Ulla 2011 3 3 3 2003 3 3 3 2000 3 3 3 1994 3 3 3 1977 3 3 3 1970 3 3 3 1966 3 3 3 Constraints to be satisfied: Equal jury size: Every wine is evaluated by 3 judges.
    [Show full text]
  • A GPU Implementation of Large Neighborhood Search for Solving Constraint Optimization Problems
    A GPU Implementation of Large Neighborhood Search for Solving Constraint Optimization Problems F. Campeotto and A. Dovier and F. Fioretto and E. Pontelli 1 Abstract. Constraint programming has gained prominence as an Processing Units—GPGPUs). Several libraries and programming en- effective and declarative paradigm for modeling and solving com- vironments (e.g., the Compute Unified Device Architecture (CUDA) plex combinatorial problems. In particular, techniques based on lo- created by NVIDIA) have been made available to allow programmers cal search have proved practical to solve real-world problems, pro- to access GPGPUs and exploit their computational power. viding a good compromise between optimality and efficiency. In In this paper, we propose the design and implementation of a spite of the natural presence of concurrency, there has been rela- novel constraint solver that exploits parallel Local Search (LS) us- tively limited effort to use novel massively parallel architectures— ing GPGPU architectures to solve constraint optimization problems. such as those found in modern Graphical Processing Units (GPUs)— The optimization process is performed in parallel on multiple large to speedup constraint programming algorithms, in general, and local promising regions of the search space, with the aim of improving the search methods, in particular. This paper describes a novel frame- quality of the current solution. The local search model pursued is a work which exploits parallelism from a popular local search method variant of Large Neighborhood Search (LNS) [18, 3]. LNS is a local (the Large Neighborhood Search method), using GPUs. search techniques characterized by an alternation of destroy and re- pair methods—used to destroy and repair part of a solution of a prob- lem.
    [Show full text]
  • Y Su Aplicación a Problemas Reales De La Industria
    MejorA DE LA EfiCIENCIA DE resolución DEL SISTEMA TOY(FD) Y SU aplicación A PROBLEMAS REALES DE LA INDUSTRIA TESIS DoctorAL Ignacio CastiñeirAS Pérez Directores Fernando Sáenz Pérez FrANCISCO Javier López FrAGUAS Universidad Complutense DE Madrid Facultad DE Informática Departamento DE Sistemas Informáticos Y Computación Madrid, MARZO DE 2014 Improving THE Solving EffiCIENCY OF TOY(FD) AND ITS Application TO Real-Life Problems PhD Thesis Ignacio CastiñeirAS Pérez Advisors Fernando Sáenz Pérez FrANCISCO Javier López FrAGUAS Complutense Univesity OF Madrid Faculty OF Information TECHNOLOGY AND Computer Science Departament OF Information Systems AND Computing Madrid, March OF 2014 MejorA DE LA EfiCIENCIA DE resolución DEL SISTEMA TOY(FD) Y SU aplicación A PROBLEMAS REALES DE LA INDUSTRIA Improving THE Solving EffiCIENCY OF TOY(FD) AND ITS Application TO Real-Life Problems Ignacio CastiñeirAS Pérez TESIS DOCTORal, CON título “MejorA DE LA EfiCIENCIA DE resolución DEL SISTEMA TOY(FD) Y SU aplicación A PROBLEMAS REALES DE LA INDUSTRIA”, PRESENTADA POR Ignacio CastiñeirAS Pérez PARA LA obtención DEL título DE Doctor POR LA Universi- DAD Complutense DE Madrid. Título: MejorA DE LA EfiCIENCIA DE resolución DEL SISTEMA TOY(FD) Y SU aplicación A PROBLEMAS REALES DE LA INDUSTRIA Autor: Ignacio CastiñeirAS Pérez ([email protected]) Directores: Fernando Sáenz Pérez ([email protected]) FrANCISCO Javier López FrAGUAS ([email protected]) Universidad Complutense DE Madrid, Facultad DE Informática, Departamento DE Sistemas Informáticos Y Computación Madrid, MARZO DE 2014 PhD Thesis, WITH TITLE “Improving THE Solving EffiCIENCY OF TOY(FD) AND ITS Ap- PLICATION TO Real-Life Problems”, PRESENTED BY Ignacio CastiñeirAS Pérez FOR ob- TAINING A PhD AT THE Complutense University OF Madrid.
    [Show full text]
  • Constraint Modelling and Solving of Some Verification Problems Anicet Bart
    Constraint modelling and solving of some verification problems Anicet Bart To cite this version: Anicet Bart. Constraint modelling and solving of some verification problems. Programming Languages [cs.PL]. Ecole nationale supérieure Mines-Télécom Atlantique, 2017. English. NNT : 2017IMTA0031. tel-01743851 HAL Id: tel-01743851 https://tel.archives-ouvertes.fr/tel-01743851 Submitted on 26 Mar 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Thèse de Doctorat Anicet BART Mémoire présenté en vue de l’obtention du grade de Docteur de l’École nationale supérieure Mines-Télécom Atlantique Bretagne-Pays de la Loire sous le sceau de l’Université Bretagne Loire École doctorale : Mathématiques et STIC (MathSTIC) Discipline : Informatique, section CNU 27 Unité de recherche : Laboratoire des Sciences du Numérique de Nantes (LS2N) Soutenue le 17 octobre 2017 Thèse n°: 2017IMTA0031 Constraint Modelling and Solving of some Verification Problems JURY Présidente : Mme Béatrice BÉRARD, Professeur, Université Pierre et Marie Curie, Paris-VI Rapporteurs : M. Salvador ABREU, Professeur, Universidade de Évora, Portugal Mme Béatrice BÉRARD, Professeur, Université Pierre et Marie Curie, Paris-VI Examinateurs : M. Nicolas BELDICEANU, Professeur, Institut Mines-Télécom Atlantique, Nantes M. Philippe CODOGNET, Professeur, Université Pierre et Marie Curie, Paris-VI Invité : M.
    [Show full text]
  • What Is Constraint Programming (CP)?
    ConstraintProgramming Extensions.jl An MOI/JuMP extension for constraint programming Thibaut Cuvelier — CentraleSupélec (université Paris-Saclay) What is constraint programming (CP)? ▪ Way of formulating combinatorial problems ▪ CP doesn’t really work for continuous problems (exception: Ibex, e.g.) ▪ Initial focus in CP was on feasibility, but optimisation is also possible ▪ Quite different from mathematical optimisation: ▪ No duality, no convexity, no linear/continuous relaxation, no differentiability at all ▪ More generic set of constraints, not just equations and inequalities ▪ Real focus on discrete aspect of the problem ▪ Mathematical optimisation’s support for combinatorial problems is more an afterthought ▪ CP has had many successes in operational research: ▪ Scheduling, time tabling, resource allocation An example of CP model: solving Sudokus ▪ Variables: ▪ 푑푖푗: digit for cell 푖, 푗 , a number between 1 and 9 ▪ Constraints: ▪ Known digits (hints) ▪ Each digit appears once in each row: alldifferent 푑푖푗 ∀푗 , ∀푖 ▪ Each digit appears once in each column: alldifferent 푑푖푗 ∀푖 , ∀푗 ▪ Each digit appears once in each block: 푑3푠,3푡 푑3푠,3푡+1 푑3푠,3푡+2 alldifferent 푑3푠+1,3푡 푑3푠+1,3푡+1 푑3푠+1,3푡+2 , 푠 ∈ 0,1,2 , 푡 ∈ 0,1,2 푑3푠+1,3푡 푑3푠+1,3푡+1 푑3푠+1,3푡+2 ▪ What about your typical MIP model ? ConstraintProgrammingExtensions.jl • What is the state of CP in Julia? • What is the state of the package? • What comes next? • What is missing in Julia/MOI/JuMP? • What is enabled with this package? What is the state of CP in Julia? ▪ Quite a few CP solvers
    [Show full text]
  • Thesis Structure
    UvA-DARE (Digital Academic Repository) Enabling framework for service-oriented collaborative networks Sargolzaei, M. Publication date 2018 Document Version Final published version License Other Link to publication Citation for published version (APA): Sargolzaei, M. (2018). Enabling framework for service-oriented collaborative networks. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl) Download date:23 Sep 2021 Enabling Framework for Service-oriented Collaborative Networks Mahdi Sargolzaei Enabling Framework for Service-oriented Collaborative Networks Mahdi Sargolzaei Enabling Framework for Service-oriented Collaborative Networks Mahdi Sargolzaei Enabling Framework for Service-oriented Collaborative Networks Academisch Proefschrift ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magnificus prof.dr. ir. K.I.J. Maex ten overstaan van een door het College voor Promoties ingestelde commissie, in het openbaar te verdedigen in de Agnietenkapel op dinsdag 15 mei 2018, te 10.00 uur door Mahdi Sargolzaei geboren te Mashhad, Iran.
    [Show full text]
  • The First Constraint-Based Local Search Backend for Minizinc
    IT 14 066 Examensarbete 15 hp Oktober 2014 The First Constraint-Based Local Search Backend for MiniZinc Gustav Björdal Institutionen för informationsteknologi Department of Information Technology Abstract The First Constraint-Based Local Search Backend for MiniZinc Gustav Björdal Teknisk- naturvetenskaplig fakultet UTH-enheten MiniZinc is a modelling language used to model combinatorial optimisation and satisfaction problems, which can then be solved in a backend solver. There are many Besöksadress: different backend solvers based on different technologies such as constraint Ångströmlaboratoriet Lägerhyddsvägen 1 programming, mathematical programming, or Boolean satisfiability solving. However, Hus 4, Plan 0 there is currently no constraint-based local search (CBLS) backend. This thesis gives an overview of the design of the first CBLS backend for MiniZinc. Experimental Postadress: results show that for some relevant MiniZinc models, the CBLS backend is able to Box 536 751 21 Uppsala give high-quality results. Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student Handledare: Jean-Noël Monette Ämnesgranskare: Pierre Flener Examinator: Olle Gällmo IT 14 066 Tryckt av: Reprocentralen ITC Acknowledgements I would like to thank my supervisor Dr. Jean-No¨elMonette for the fruitful discussions throughout this project and for all of your help and feedback. I would also like to thank my reviewer Professor Pierre Flener for initially introducing me to the world of constraint programming and for being the most thorough proofreader I have ever met, all of your feedback has been greatly appreciated. Finally, I would like to thank the ASTRA group for entrusting me with this thesis project, it has been both challenging and educational, and more importantly, fun.
    [Show full text]