## Constraint and Integer Programming in OPL (2002)

Venue: | INFORMS Journal on Computing |

Citations: | 20 - 6 self |

### BibTeX

@ARTICLE{Hentenryck02constraintand,

author = {Pascal Van Hentenryck},

title = {Constraint and Integer Programming in OPL},

journal = {INFORMS Journal on Computing},

year = {2002},

volume = {14},

pages = {2002}

}

### Years of Citing Articles

### OpenURL

### Abstract

In recent years, it has been increasingly recognized that constraint and integer programming have orthogonal and complementary strengths in stating and solving combinatorial optimization applications. In addition, their integration has become an active research topic. The optimization programming language opl was a first attempt at integrating these technologies both at the language and at the solver levels. In particular, opl is a modeling language integrating the rich language of constraint programming and the ability to specify search procedures at a high level of abstraction. Its implementation includes both constraint and mathematical programming solvers, as well as some cooperation schemes to make them collaborate on a given problem. The purpose of this paper is to illustrate, using opl, the constraint-programming approach to combinatorial optimization and the complementary strengths of constraint and integer programming. (Artificial Intelligence; Computer Science; Integer Programming) 1.

### Citations

785 | Constraint Logic Programming
- Jaffar, Lassez
- 1987
(Show Context)
Citation Context ...natorial optimization, constraint programming systems are generally based on a common set of design principles that stem from their roots in Constraint Logic Programming (CLP) (Colmerauer 1982, 1990; =-=Jaffar and Lassez 1987-=-; Van Hentenryck 1987b). More precisely, the constraint programming approach to combinatorial optimization can be characterized (at this point) by three main features: 1. an expressive language to sta... |

709 | The semantics of predicate logic as a programming language
- Emden, Kowalski
- 1976
(Show Context)
Citation Context ...rogramming framework is essentially languageindependent. Early constraint languages were based on logic programming (Colmerauer et al. 1973, INFORMS Journal on Computing/Vol. 14, No. 4, Fall 2002 353s=-=Kowalski 1974-=-). The embedding of constraints in more traditional languages such as C and C++ was pioneered by Charme which was based on the CHIP implementation. Charme was in fact commercialized by BULL in the lat... |

423 |
Networks of constraints: fundamental properties and application to picture processing
- Montanari
- 1974
(Show Context)
Citation Context ...s et al. 1988, Van Hentenryck 1987b, Van Hentenryck 1989, Van Hentenryck and Dincbas 1986). CHIP included a solver for discrete finite domains based on constraint-satisfaction techniques (Waltz 1972, =-=Montanari 1974-=-, Mackworth 1977). It is important to emphasize that, unlike integer and linear programming, constraint-programming 354 INFORMS Journal on Computing/Vol. 14, No. 4, Fall 2002 C4 C3ssystems may support... |

320 |
A filtering algorithm for constraints of difference in CSPs
- Régin
- 1994
(Show Context)
Citation Context ...artite graph (where one of the set represents the variables and the other set represents their possible values) together with a search for strongly connected components on the same graph (Costa 1994, =-=Régin 1994-=-). Consider now the constraint cardinality(occur,values,all(w in EWeeks & s in Slots) team[p,w,s]); specifies that a team plays exactly twice over the course of the “extended” season. Its first argume... |

289 |
An introduction to Prolog III
- COLMERAUER
- 1990
(Show Context)
Citation Context ... with domain stores that are closely related in general. 3.4. Cooperation in Constraint Programming Cooperating solvers have always been an active research area in constraint programming. Prolog III (=-=Colmerauer 1990-=-) was the pioneering system in that respect. It included a linear-programming solver, a Boolean solver, as well as a constraint solver for equations over lists. These solvers interacted either explici... |

278 |
Integer Programming
- Wolsey
- 1998
(Show Context)
Citation Context ...-programming solvers were part of constraintprogramming systems since their early days. 3.5. Comparison withInteger Programming It is interesting to contrast constraint and integer programming (e.g., =-=Wolsey 1998-=-) and show why they appear complementary for combinatorial optimization. (We only discuss the branch-and-bound approach to integer programming and ignore several other important areas such as Lagrangi... |

260 | Limited discrepancy search
- Harvey, Ginsberg
- 1995
(Show Context)
Citation Context ...neered by Salsa (Laburthe and Caseau 1998) and opl (Van Hentenryck et al. 2000). The language Oz (Schulte 1997) pioneered novel features to express search strategies (e.g., limited discrepancy search =-=Harvey and Ginsberg 1995-=-) in consice ways. Support for search strategies are now available in several modern languages (Perron 1999, Van Hentenryck et al. 2000). Finally, hybrid algorithms, combining systematic and local sea... |

253 | The Constraint Logic Programming Language CHIP - Dincbas, Hentenryck, et al. - 1988 |

204 | The OPL optimization programming language - Hentenryck, Lustig, et al. - 1999 |

195 |
The progamming language aspects of ThingLab, a constraint-oriented simulation laboratory
- Borning
- 1986
(Show Context)
Citation Context ...perations, often in nondeterministic ways, since search is so fundamental in many applications. The constraint-programming framework has been applied to many areas, including computer graphics (e.g., =-=Borning 1981-=-), software engineering (e.g., test generation in Gotlieb et al. 2000), databases (e.g., Kanellakis et al. 1990), hybrid systems (e.g., Kohn et al. 1995), finance (e.g., Berthier 1988, Huynh and Lasse... |

190 |
Concurrent Constraint Programming Languages
- Saraswat
- 1989
(Show Context)
Citation Context ...ing. Once again, the purpose is not to be exhaustive (see, for instance, overviews of constraint programming, or subfields of constraint programming: Jaffar and Maher 1994, Marriott and Stuckey 1999, =-=Saraswat 1989-=-, Van Hentenryck 1991, 1997, Van Hentenryck and Saraswat 1996) but to survey what we consider to be some of the fundamental ideas in this field. 3.1. What Is Constraint Programming? Constraint program... |

170 | Numerica : A Modeling Language for Global Optimization - Hentenryck, Michel, et al. - 1997 |

169 | Older: Applying Interval Arithmetic to Real, Integer and Bolean Constraints - Benhamou, W - 1995 |

163 | Design, implementation, and evaluation of the constraint language cc(fd - Hentenryck, Saraswat, et al. - 1993 |

154 | Generalized arc consistency for global cardinality constraint
- Régin
- 1996
(Show Context)
Citation Context ...he opl implementation achieves arc consistency on this constraint that, in this case, involves the solving of a feasible flow and, once again, a search for connected components in the residual graph (=-=Régin 1996-=-). The VAN HENTENRYCK Constraint and Integer Programming in OPL constraint alldifferent(game); specifies that all games are different, i.e., that each team plays against every other team. Finally, the... |

144 |
Generating semantic descriptions from drawings of scenes with shadows
- Waltz
- 1975
(Show Context)
Citation Context ...stem (Dincbas et al. 1988, Van Hentenryck 1987b, Van Hentenryck 1989, Van Hentenryck and Dincbas 1986). CHIP included a solver for discrete finite domains based on constraint-satisfaction techniques (=-=Waltz 1972-=-, Montanari 1974, Mackworth 1977). It is important to emphasize that, unlike integer and linear programming, constraint-programming 354 INFORMS Journal on Computing/Vol. 14, No. 4, Fall 2002 C4 C3ssys... |

138 | Using constraint programming and local search methods to solve vehicle routing problems
- Shaw
- 1998
(Show Context)
Citation Context ...modern languages (Perron 1999, Van Hentenryck et al. 2000). Finally, hybrid algorithms, combining systematic and local search, were also investigated in (Laburthe and Caseau 1998, Pesant et al. 1997, =-=Shaw 1998-=-). It is also important to stress that the constraintprogramming framework is essentially languageindependent. Early constraint languages were based on logic programming (Colmerauer et al. 1973, INFOR... |

129 |
Logic Semantics for a Class of Committed-Choice Programs
- Maher
- 1987
(Show Context)
Citation Context ...g., Van Hentenryck 1989). As mentioned earlier, much research in constraint programming was devoted to finding ways of expressing search procedures at a high level. Concurrent constraint programming (=-=Maher 1987-=-, Saraswat 1989), which is the foundation of constraint languages such as Oz (Smolka 1995) and cc(FD) (Van Hentenryck et al. 1995), introduced a constraintdriven computation where the programming comp... |

107 |
Programming with Constraints
- Marriott, Stuckey
- 1998
(Show Context)
Citation Context ...view of constraint programming. Once again, the purpose is not to be exhaustive (see, for instance, overviews of constraint programming, or subfields of constraint programming: Jaffar and Maher 1994, =-=Marriott and Stuckey 1999-=-, Saraswat 1989, Van Hentenryck 1991, 1997, Van Hentenryck and Saraswat 1996) but to survey what we consider to be some of the fundamental ideas in this field. 3.1. What Is Constraint Programming? Con... |

73 |
Time and resource constrained scheduling: A constraint satisfaction approach
- Nuijten
- 1994
(Show Context)
Citation Context ...nd to provide a natural way to integrate many algorithms from theoretical computer science, operations research, and numerical analysis (e.g., Beldiceanu and Contejean 1994, Caseau and Laburthe 1997, =-=Nuijten 1994-=-, Regin 1994, Van Hentenryck 1997). A global constraint captures a substructure that arises in many applications and is amenable to efficient pruning algorithms (as described later in this section). I... |

72 | Logic-based methods for optimization combining optimization and constraint satisfaction - Hooker - 2000 |

71 |
Un système de communication homme–machine en français. Technical report, Groupe de Intelligence Artificielle Université de Aix-Marseille
- Colmerauer, Kanoui, et al.
- 1973
(Show Context)
Citation Context ...Pesant et al. 1997, Shaw 1998). It is also important to stress that the constraintprogramming framework is essentially languageindependent. Early constraint languages were based on logic programming (=-=Colmerauer et al. 1973-=-, INFORMS Journal on Computing/Vol. 14, No. 4, Fall 2002 353sKowalski 1974). The embedding of constraints in more traditional languages such as C and C++ was pioneered by Charme which was based on the... |

71 | Probe backtrack search for minimal perturbation in dynamic scheduling - Sakkout, Wallace - 2000 |

63 | Introducing global constraints
- Beldiceanu, Contjean
- 1994
(Show Context)
Citation Context ...ental research topic only in the 1990s when they were found to provide a natural way to integrate many algorithms from theoretical computer science, operations research, and numerical analysis (e.g., =-=Beldiceanu and Contejean 1994-=-, Caseau and Laburthe 1997, Nuijten 1994, Regin 1994, Van Hentenryck 1997). A global constraint captures a substructure that arises in many applications and is amenable to efficient pruning algorithms... |

62 |
On the Development of a General Algebraic Modelling System
- Bisschop, Meeraus
- 1982
(Show Context)
Citation Context ...ntly outside the reach of both technologies. Simultaneously, it has been recognized that mathematical-modeling languages and constraint languages had complementary strengths. Modeling languages (e.g. =-=Bisschop and Meeraus 1982-=-, Fourer et al. 1993) provide high-level set and algebraic notations that may simplify the statement of the problem considerably, while constraint-programming languages feature rich constraint languag... |

60 | Solving the car-sequencing problem in constraint logic programming - Dincbas, Simonis, et al. - 1988 |

49 | Programming constraint inference engines
- Schulte
- 1997
(Show Context)
Citation Context ...aints to, and querying, the constraint store. High-level constructs such as forall and tryall were pioneered by Salsa (Laburthe and Caseau 1998) and opl (Van Hentenryck et al. 2000). The language Oz (=-=Schulte 1997-=-) pioneered novel features to express search strategies (e.g., limited discrepancy search Harvey and Ginsberg 1995) in consice ways. Support for search strategies are now available in several modern l... |

48 | Beyond the Glass Box: Constraints as Objects
- Puget, Leconte
- 1995
(Show Context)
Citation Context ...ther examples of libraries and languages integrating constraints in procedural or object-oriented languages include 2LP(McAloon and Tretkoff 1995), Claire (Laburthe and Caseau 1998), and the library (=-=Puget and Leconte 1995-=-). Note however that declarative, relational, and/or nondeterministic languages provide a more natural vehicle to embed constraint programming because of their conceptual commonalities. One of the des... |

47 | Conjunto: constraint logic programming with finite set domains
- Gervet
- 1994
(Show Context)
Citation Context ...s in many applications and is amenable to efficient pruning algorithms (as described later in this section). In addition, some constraint languages also offer set variables and set constraints (e.g., =-=Gervet 1994-=-). Many of these constraints are illustrated in this paper. The ability to specify a search procedure is another fundamental feature of constraint-programming languages. Once again, this functionality... |

42 | Constraint programming based column generation for crew assignment
- Fahle, Junker, et al.
- 2002
(Show Context)
Citation Context ...bserve that redundant modeling is not the only 360 INFORMS Journal on Computing/Vol. 14, No. 4, Fall 2002sway to integrate the two technologies. Decomposition methods such as column generation (e.g., =-=Junker et al. 1999-=-) and Benders decomposition (e.g., Jain and Grossman 2001) are very interesting alternatives that are not discussed in this paper. 5.1. Bound Cooperation In bound cooperation (e.g., Beringer and De Ba... |

38 | A Language for Search Algorithms
- Laburthe, Caseau, et al.
- 1998
(Show Context)
Citation Context ...where the programming component is a set of agents communicating by adding constraints to, and querying, the constraint store. High-level constructs such as forall and tryall were pioneered by Salsa (=-=Laburthe and Caseau 1998-=-) and opl (Van Hentenryck et al. 2000). The language Oz (Schulte 1997) pioneered novel features to express search strategies (e.g., limited discrepancy search Harvey and Ginsberg 1995) in consice ways... |

36 | Solving Various Weighted Matching Problems with Constraints
- Caseau, Laburthe
- 1997
(Show Context)
Citation Context ...e 1990s when they were found to provide a natural way to integrate many algorithms from theoretical computer science, operations research, and numerical analysis (e.g., Beldiceanu and Contejean 1994, =-=Caseau and Laburthe 1997-=-, Nuijten 1994, Regin 1994, Van Hentenryck 1997). A global constraint captures a substructure that arises in many applications and is amenable to efficient pruning algorithms (as described later in th... |

36 |
LP-based Combinatorial Problem Solving
- Hoffman, Padberg
- 1985
(Show Context)
Citation Context ...se cases, it is possible to add local cuts based on the INFORMS Journal on Computing/Vol. 14, No. 4, Fall 2002 361sdomain store and the current LP solution as is typical in branch-and-cut algorithms (=-=Hoffman and Padberg 1985-=-). Finally, for some global constraints, although a sharp formulation may exist, it may not be desirable because it may represent a poor tradeoff between the time spent pruning and searching. One of t... |

35 | Combinatorial problem solving in constraint logic programming with cooperating solvers - Beringer, Backer - 1995 |

35 | CLP(%2) and some electrical engineering problems
- Heintze, Michaylov, et al.
- 1987
(Show Context)
Citation Context ... in Gotlieb et al. 2000), databases (e.g., Kanellakis et al. 1990), hybrid systems (e.g., Kohn et al. 1995), finance (e.g., Berthier 1988, Huynh and Lassez 1988), engineering (e.g., Graf et al. 1989, =-=Heintze et al. 1987-=-), circuit design (e.g., Simonis and 352 INFORMS Journal on Computing/Vol. 14, No. 4, Fall 2002sDincbas 1987), and, of course, combinatorial optimization. Given the diversity of these application area... |

32 | Search procedures and parallelism in constraint programming
- Perron
- 1999
(Show Context)
Citation Context ...d novel features to express search strategies (e.g., limited discrepancy search Harvey and Ginsberg 1995) in consice ways. Support for search strategies are now available in several modern languages (=-=Perron 1999-=-, Van Hentenryck et al. 2000). Finally, hybrid algorithms, combining systematic and local search, were also investigated in (Laburthe and Caseau 1998, Pesant et al. 1997, Shaw 1998). It is also import... |

31 | A scheme for unifying optimization and constraint satisfaction methods
- Hooker, Ottosson, et al.
(Show Context)
Citation Context ...evel. This recognition has led to increased research activity at the intersection of these two fields (e.g. Bockmayer and Kasper 1998, de Farias et al. 2001, El Sakkout and Wallace 2000, Hooker 2000, =-=Hooker et al. 2001-=-, Refalo 1999). The opl programming language (Van Hentenryck 1999, Van Hentenryck et al. 2000) was a first attempt to support this complementarity at the language and solver levels. From a language st... |

28 |
M.J.: Constraint logic programming: A survey. The journal of logic programming 19
- Jaffar, Maher
- 1994
(Show Context)
Citation Context ...tion gives a brief overview of constraint programming. Once again, the purpose is not to be exhaustive (see, for instance, overviews of constraint programming, or subfields of constraint programming: =-=Jaffar and Maher 1994-=-, Marriott and Stuckey 1999, Saraswat 1989, Van Hentenryck 1991, 1997, Van Hentenryck and Saraswat 1996) but to survey what we consider to be some of the fundamental ideas in this field. 3.1. What Is ... |

27 | Speeding up constraint propagation by redundant modeling - Cheng, Lee, et al. - 1996 |

24 |
Branch and infer: a unifying framework for integer and finite domain constraint programming
- Bockmayr, Kasper
- 1998
(Show Context)
Citation Context ...s feature rich constraint languages and the ability to specify search procedures at a high level. This recognition has led to increased research activity at the intersection of these two fields (e.g. =-=Bockmayer and Kasper 1998-=-, de Farias et al. 2001, El Sakkout and Wallace 2000, Hooker 2000, Hooker et al. 2001, Refalo 1999). The opl programming language (Van Hentenryck 1999, Van Hentenryck et al. 2000) was a first attempt ... |

20 | Tight cooperation and its application in piecewise linear optimization - Refalo - 1999 |

20 | Generality versus Specificity: an Experience with AI and OR Techniques - Hentenryck, Carillon - 1988 |

19 | Sports league scheduling
- McAloon, Tretkoff, et al.
- 1997
(Show Context)
Citation Context ...on for 14 to 30 teams quickly. Both models are based on the constraint programs presented in Régin (1998) (See also Van Hentenryck et al. 1999). 4.1. Problem Description The sport-scheduling problem (=-=McAloon et al. 1997-=-, Régin 1998) is a standard benchmark submitted by Bob Daniel to the well-known MIP library. It consists of scheduling games between n teams over n − 1 weeks. In addition, each week is divided into n/... |

18 |
PrologII: Manuel de référence et modèle théorique. Technical report, Groupe d’Intelligence Artificielle, Faculté de Sciences de Luminy
- Colmerauer
- 1982
(Show Context)
Citation Context ...ting attention to combinatorial optimization, constraint programming systems are generally based on a common set of design principles that stem from their roots in Constraint Logic Programming (CLP) (=-=Colmerauer 1982-=-, 1990; Jaffar and Lassez 1987; Van Hentenryck 1987b). More precisely, the constraint programming approach to combinatorial optimization can be characterized (at this point) by three main features: 1.... |

14 | Algorithmic power from declarative use of redundant constraints - EMDEN - 1999 |

13 | Algorithms for Hybrid MILP/- CLP Models for a Class of Optimization Problems - Jain, Grossmann - 2001 |

11 |
Global Optimization using special ordered sets
- Beale, Forrest
- 1976
(Show Context)
Citation Context ...ure can also be used to design more effective branching schemes, an idea that is at the core of constraintprogramming systems. It is also present in integerprogramming systems (e.g., SOS constraints; =-=Beale and Forrest 1976-=-), but to a lesser extent. Cut cooperation is now an active research topic and may yield significant benefits for some classes of applications. It has only been explored in very limited ways at this p... |

10 | Genius-cp: A Generic Single-Vehicle Routing Algorithm
- Pesant, Gendreau, et al.
- 1997
(Show Context)
Citation Context ...vailable in several modern languages (Perron 1999, Van Hentenryck et al. 2000). Finally, hybrid algorithms, combining systematic and local search, were also investigated in (Laburthe and Caseau 1998, =-=Pesant et al. 1997-=-, Shaw 1998). It is also important to stress that the constraintprogramming framework is essentially languageindependent. Early constraint languages were based on logic programming (Colmerauer et al. ... |

9 |
Persistency in maximum cardinality bipartite matchings
- Costa
- 1994
(Show Context)
Citation Context ...thm on a bipartite graph (where one of the set represents the variables and the other set represents their possible values) together with a search for strongly connected components on the same graph (=-=Costa 1994-=-, Régin 1994). Consider now the constraint cardinality(occur,values,all(w in EWeeks & s in Slots) team[p,w,s]); specifies that a team plays exactly twice over the course of the “extended” season. Its ... |

9 | Branch-and-Cut for Combinatorial Optimization Problems without Auxiliary Binary Variables - Farias, Johnson, et al. - 2001 |