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Journal articles on the topic 'Constraint programming'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 November 2024

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1

APT, KRZYSZTOF R., and ERIC MONFROY. "Constraint programming viewed as rule-based programming." Theory and Practice of Logic Programming 1, no. 6 (November 2001): 713–50. http://dx.doi.org/10.1017/s1471068401000072.

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We study here a natural situation when constraint programming can be entirely reduced to rule-based programming. To this end we explain first how one can compute on constraint satisfaction problems using rules represented by simple first-order formulas. Then we consider constraint satisfaction problems that are based on predefined, explicitly given constraints. To solve them we first derive rules from these explicitly given constraints and limit the computation process to a repeated application of these rules, combined with labeling. We consider two types of rule here. The first type, that we call equality rules, leads to a new notion of local consistency, called rule consistency that turns out to be weaker than arc consistency for constraints of arbitrary arity (called hyper-arc consistency in Marriott & Stuckey (1998)). For Boolean constraints rule consistency coincides with the closure under the well-known propagation rules for Boolean constraints. The second type of rules, that we call membership rules, yields a rule-based characterization of arc consistency. To show feasibility of this rule-based approach to constraint programming, we show how both types of rules can be automatically generated, as CHR rules of Frühwirth (1995). This yields an implementation of this approach to programming by means of constraint logic programming. We illustrate the usefulness of this approach to constraint programming by discussing various examples, including Boolean constraints, two typical examples of many valued logics, constraints dealing with Waltz's language for describing polyhedral scenes, and Allen's qualitative approach to temporal logic.

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Van Hentenryck, Pascal, Laurent Michel, and Frédéric Benhamou. "Constraint programming over nonlinear constraints." Science of Computer Programming 30, no. 1-2 (January 1998): 83–118. http://dx.doi.org/10.1016/s0167-6423(97)00008-7.

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3

O'Sullivan, Barry. "Automated Modelling and Solving in Constraint Programming." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (July 5, 2010): 1493–97. http://dx.doi.org/10.1609/aaai.v24i1.7530.

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Constraint programming can be divided very crudely into modeling and solving. Modeling defines the problem, in terms of variables that can take on different values, subject to restrictions (constraints) on which combinations of variables are allowed. Solving finds values for all the variables that simultaneously satisfy all the constraints. However, the impact of constraint programming has been constrained by a lack of "user-friendliness''. Constraint programming has a major "declarative" aspect, in that a problem model can be handed off for solution to a variety of standard solving methods. These methods are embedded in algorithms, libraries, or specialized constraint programming languages. To fully exploit this declarative opportunity however, we must provide more assistance and automation in the modeling process, as well as in the design of application-specific problem solvers. Automated modelling and solving in constraint programming presents a major challenge for the artificial intelligence community. Artificial intelligence, and in particular machine learning, is a natural field in which to explore opportunities for moving more of the burden of constraint programming from the user to the machine. This paper presents technical challenges in the areas of constraint model acquisition, formulation and reformulation, synthesis of filtering algorithms for global constraints, and automated solving. We also present the metrics by which success and progress can be measured.

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Dao, Thi-Bich-Hanh, Khanh-Chuong Duong, and Christel Vrain. "Constrained clustering by constraint programming." Artificial Intelligence 244 (March 2017): 70–94. http://dx.doi.org/10.1016/j.artint.2015.05.006.

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SCHRIJVERS, TOM, PETER STUCKEY, and PHILIP WADLER. "Monadic constraint programming." Journal of Functional Programming 19, no. 6 (August 14, 2009): 663–97. http://dx.doi.org/10.1017/s0956796809990086.

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AbstractA constraint programming system combines two essential components: a constraint solver and a search engine. The constraint solver reasons about satisfiability of conjunctions of constraints, and the search engine controls the search for solutions by iteratively exploring a disjunctive search tree defined by the constraint program. In this paper we give a monadic definition of constraint programming in which the solver is defined as a monad threaded through the monadic search tree. We are then able to define search and search strategies as first-class objects that can themselves be built or extended by composable search transformers. Search transformers give a powerful and unifying approach to viewing search in constraint programming, and the resulting constraint programming system is first class and extremely flexible.

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Mattenet, Alex, Ian Davidson, Siegfried Nijssen, and Pierre Schaus. "Generic Constraint-based Block Modeling using Constraint Programming." Journal of Artificial Intelligence Research 70 (February 9, 2021): 597–630. http://dx.doi.org/10.1613/jair.1.12280.

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Block modeling has been used extensively in many domains including social science, spatial temporal data analysis and even medical imaging. Original formulations of the problem modeled it as a mixed integer programming problem, but were not scalable. Subsequent work relaxed the discrete optimization requirement, and showed that adding constraints is not straightforward in existing approaches. In this work, we present a new approach based on constraint programming, allowing discrete optimization of block modeling in a manner that is not only scalable, but also allows the easy incorporation of constraints. We introduce a new constraint filtering algorithm that outperforms earlier approaches, in both constrained and unconstrained settings, for an exhaustive search and for a type of local search called Large Neighborhood Search. We show its use in the analysis of real datasets. Finally, we show an application of the CP framework for model selection using the Minimum Description Length principle.

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Dincbas, M. "Constraint programming." ACM Computing Surveys 28, no. 4es (December 1996): 62. http://dx.doi.org/10.1145/242224.242303.

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Van Hentenryck, Pascal. "Constraint programming." ACM SIGSOFT Software Engineering Notes 25, no. 1 (January 2000): 89–90. http://dx.doi.org/10.1145/340855.341036.

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Van Hentenryck, Pascal. "Constraint Programming." Revue Ouverte d'Intelligence Artificielle 5, no. 2-3 (September 26, 2024): 139–59. http://dx.doi.org/10.5802/roia.76.

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Booth, Kyle E. C., Bryan O'Gorman, Jeffrey Marshall, Stuart Hadfield, and Eleanor Rieffel. "Quantum-accelerated constraint programming." Quantum 5 (September 28, 2021): 550. http://dx.doi.org/10.22331/q-2021-09-28-550.

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Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems. In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking tree search augmented with logical inference. In this paper, we show how quantum algorithms can accelerate CP, at both the levels of inference and search. Leveraging existing quantum algorithms, we introduce a quantum-accelerated filtering algorithm for the alldifferent global constraint and discuss its applicability to a broader family of global constraints with similar structure. We propose frameworks for the integration of quantum filtering algorithms within both classical and quantum backtracking search schemes, including a novel hybrid classical-quantum backtracking search method. This work suggests that CP is a promising candidate application for early fault-tolerant quantum computers and beyond.

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ARIAS, JOAQUIN, MANUEL CARRO, ELMER SALAZAR, KYLE MARPLE, and GOPAL GUPTA. "Constraint Answer Set Programming without Grounding." Theory and Practice of Logic Programming 18, no. 3-4 (July 2018): 337–54. http://dx.doi.org/10.1017/s1471068418000285.

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AbstractExtending ASP with constraints (CASP) enhances its expressiveness and performance. This extension is not straightforward as the grounding phase, present in most ASP systems, removes variables and the links among them, and also causes a combinatorial explosion in the size of the program. Several methods to overcome this issue have been devised: restricting the constraint domains (e.g., discrete instead of dense), or the type (or number) of models that can be returned. In this paper we propose to incorporate constraints into s(ASP), a goal-directed, top-down execution model which implements ASP while retaining logical variables both during execution and in the answer sets. The resulting model, s(CASP), can constrain variables that, as in CLP, are kept during the execution and in the answer sets. s(CASP) inherits and generalizes the execution model of s(ASP) and is parametric w.r.t. the constraint solver. We describe this novel execution model and show through several examples the enhanced expressiveness of s(CASP) w.r.t. ASP, CLP, and other CASP systems. We also report improved performance w.r.t. other very mature, highly optimized ASP systems in some benchmarks.

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PUGET, JEAN-FRANÇOIS, and IRVIN LUSTIG. "Constraint programming and maths programming." Knowledge Engineering Review 16, no. 1 (March 2001): 5–23. http://dx.doi.org/10.1017/s0269888901000042.

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Maths programming (MP) and constraint programming (CP) are two techniques that are able to solve difficult industrial optimisation problems. The purpose of this paper is to compare them from an algorithmic and a modelling point of view. Algorithmic principles of each approach are described and contrasted. Some ways of combining both techniques are also introduced.

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Sitek, Pawel, and Jaroslaw Wikarek. "A Hybrid Method for the Modelling and Optimisation of Constrained Search Problems." Foundations of Management 5, no. 3 (August 21, 2014): 7–22. http://dx.doi.org/10.2478/fman-2014-0016.

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AbstractThe paper presents a concept and the outline of the implementation of a hybrid approach to modelling and solving constrained problems. Two environments of mathematical programming (in particular, integer programming) and declarative programming (in particular, constraint logic programming) were integrated. The strengths of integer programming and constraint logic programming, in which constraints are treated in a different way and different methods are implemented, were combined to use the strengths of both. The hybrid method is not worse than either of its components used independently. The proposed approach is particularly important for the decision models with an objective function and many discrete decision variables added up in multiple constraints. To validate the proposed approach, two illustrative examples are presented and solved. The first example is the authors’ original model of cost optimisation in the supply chain with multimodal transportation. The second one is the two-echelon variant of the well-known capacitated vehicle routing problem.

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Milano, Michela, Greger Ottosson, Philippe Refalo, and Erlendur S. Thorsteinsson. "The Role of Integer Programming Techniques in Constraint Programming's Global Constraints." INFORMS Journal on Computing 14, no. 4 (November 2002): 387–402. http://dx.doi.org/10.1287/ijoc.14.4.387.2830.

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Oleynik, Yu A., and A. A. Zuenko. "Global constraints in modeling and solving problems within the Constraint Programming paradigm." Transaction Kola Science Centre 11, no. 8-2020 (December 16, 2020): 67–83. http://dx.doi.org/10.37614/2307-5252.2020.8.11.006.

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At the moment, constraint programming technology is a powerful tool for solving combinatorial search and combinatorial optimization problems. To use this technology, any task must be formulated as a task of satisfying constraints. The role of the concept of global constraints in modeling and solving applied problems within the framework of the constraint programming paradigm can hardly be overestimated. The procedures that implement the algorithms of filtering global constraints are the elementary “building blocks” from which the model of a specific applied problem is built. Algorithms for filtering global constraints, as a rule, are supported by the corresponding developed theories that allow organizing high-performance computing. The choice of a particular software library is primarily determined by the extent to which the set and method of implementing global constraints corresponds tothe level of modern research in this area. The main focus of this article is focused on an overview of global constraints that are implemented within the most popular constraint programming libraries: Choco, GeCode, JaCoP, MiniZinc.

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Baykasoğlu, Adil, Şeyda Topaloğlu, and Filiz Şenyüzlüler. "Manufacturing cell formation with flexible processing capabilities and worker assignment: Comparison of constraint programming and integer programming approaches." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 232, no. 11 (January 5, 2017): 2054–68. http://dx.doi.org/10.1177/0954405416682281.

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Cell formation deals with grouping of machines and parts in manufacturing systems according to their compatibility. Manufacturing processes are surrounded with an abundance of complex constraints which should be considered carefully and represented clearly for obtaining high efficiency and productivity. Constraint programming is a new approach to combinatorial optimization and provides a rich language to represent complex constraints easily. However, the cell formation problems are well suited to be solved by constraint programming approach since the problem has many constraints such as part-machine requirements, availabilities in the system in terms of capacity, machine and worker abilities. In this study, the cell formation problem is modeled using machine, part processing and worker flexibilities via resource element–based representation. Resource elements define the processing requirements of parts and processing capabilities of machines and workers, which are resource-independent capability units. A total of 12 case problems are generated, and different search phases of constraint programming are defined for the solution procedure. The cell formation problem is modeled in both constraint programming and integer programming, and a comparative analysis of constraint programming and integer programming model solutions is done. The results indicate that both the models are effective and efficient in the solution of the cell formation problem.

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Kjenstad, Dag. "Concurrent Constraint Programming." AI Communications 8, no. 2 (1995): 102–3. http://dx.doi.org/10.3233/aic-1995-8206.

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18

Jaffar, J., and R. Yap. "Constraint programming 2000." ACM Computing Surveys 28, no. 4es (December 1996): 65. http://dx.doi.org/10.1145/242224.242307.

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19

McAloon, Ken. "Constraint-based programming." ACM Computing Surveys 28, no. 4es (December 1996): 69. http://dx.doi.org/10.1145/242224.242313.

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Van Hentenryck, Pascal. "Constraint logic programming." Knowledge Engineering Review 6, no. 3 (September 1991): 151–94. http://dx.doi.org/10.1017/s0269888900005798.

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AbstractConstraint logic programming (CLP) is a generalization of logic programming (LP) where unification, the basic operation of LP languages, is replaced by constraint handling in a constraint system. The resulting languages combine the advantages of LP (declarative semantics, nondeterminism, relational form) with the efficiency of constraint-solving algorithms. For some classes of combinatorial search problems, they shorten the development time significantly while preserving most of the efficiency of imperative languages. This paper surveys this new class of programming languages from their underlying theory, to their constraint systems, and to their applications to combinatorial problems.

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21

Faltings, Boi, and Santiago Macho-Gonzalez. "Open constraint programming." Artificial Intelligence 161, no. 1-2 (January 2005): 181–208. http://dx.doi.org/10.1016/j.artint.2004.10.005.

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22

DUNDUA, BESIK, MÁRIO FLORIDO, TEMUR KUTSIA, and MIRCEA MARIN. "CLP(H):Constraint logic programming for hedges." Theory and Practice of Logic Programming 16, no. 2 (April 16, 2015): 141–62. http://dx.doi.org/10.1017/s1471068415000071.

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AbstractCLP(H) is an instantiation of the general constraint logic programming scheme with the constraint domain of hedges. Hedges are finite sequences of unranked terms, built over variadic function symbols and three kinds of variables: for terms, for hedges, and for function symbols. Constraints involve equations between unranked terms and atoms for regular hedge language membership. We study algebraic semantics of CLP(H) programs, define a sound, terminating, and incomplete constraint solver, investigate two fragments of constraints for which the solver returns a complete set of solutions, and describe classes of programs that generate such constraints.

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23

Van Hentenryck, Pascal, Helmut Simonis, and Mehmet Dincbas. "Constraint satisfaction using constraint logic programming." Artificial Intelligence 58, no. 1-3 (December 1992): 113–59. http://dx.doi.org/10.1016/0004-3702(92)90006-j.

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24

Cohen, Jacques. "Logic programming and constraint logic programming." ACM Computing Surveys 28, no. 1 (March 1996): 257–59. http://dx.doi.org/10.1145/234313.234416.

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MAHER, MICHAEL J. "Contractibility for open global constraints." Theory and Practice of Logic Programming 17, no. 4 (June 27, 2017): 365–407. http://dx.doi.org/10.1017/s1471068417000126.

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AbstractOpen forms of global constraints allow the addition of new variables to an argument during the execution of a constraint program. Such forms are needed for difficult constraint programming problems, where problem construction and problem solving are interleaved, and fit naturally within constraint logic programming. However, in general, filtering that is sound for a global constraint can be unsound when the constraint is open. This paper provides a simple characterization, called contractibility, of the constraints, where filtering remains sound when the constraint is open. With this characterization, we can easily determine whether a constraint has this property or not. In the latter case, we can use it to derive a contractible approximation to the constraint. We demonstrate this work on both hard and soft constraints. In the process, we formulate two general classes of soft constraints.

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Yu, Chun-Mei, Dang-Jun Zhao, and Ye Yang. "Efficient Convex Optimization of Reentry Trajectory via the Chebyshev Pseudospectral Method." International Journal of Aerospace Engineering 2019 (May 2, 2019): 1–9. http://dx.doi.org/10.1155/2019/1414279.

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A novel sequential convex (SCvx) optimization scheme via the Chebyshev pseudospectral method is proposed for efficiently solving the hypersonic reentry trajectory optimization problem which is highly constrained by heat flux, dynamic pressure, normal load, and multiple no-fly zones. The Chebyshev-Gauss Legend (CGL) node points are used to transcribe the original dynamic constraint into algebraic equality constraint; therefore, a nonlinear programming (NLP) problem is concave and time-consuming to be solved. The iterative linearization and convexification techniques are proposed to convert the concave constraints into convex constraints; therefore, a sequential convex programming problem can be efficiently solved by convex algorithms. Numerical results and a comparison study reveal that the proposed method is efficient and effective to solve the problem of reentry trajectory optimization with multiple constraints.

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FIERBINTEANU, CRISTINA. "CONSTRAINT LOGIC PROGRAMMING APPROACH OF NETWORK FLOW PROBLEMS WITHIN A DECISION SUPPORT SYSTEMS GENERATOR FOR TRANSPORTATION PLANNIG." International Journal on Artificial Intelligence Tools 07, no. 04 (December 1998): 453–62. http://dx.doi.org/10.1142/s0218213098000214.

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In this paper we propose a model of a decision support systems (DSS) generator for unstructured problems. The model is developed within the constraint logic programming (CLP) paradigm. At the center of the generator there is an ontology defining the concepts and relationships necessary and sufficient to describe the domain to be reasoned about, in a manner suitable for a particular class of tasks. The constraint solver of the constraint logic programming host language has to be extended with constraints which are relevant to the domain studied, but can not be found among the general constraints provided by the constraint solver. The domain of transportation planning was chosen to illustrate the proposed concept of DSS generator for ustructured problems. In this case we need to extend the constraint solver with constraint manipulation techniques specific to network flow problems. This paper presents in detail our constraint logic programming approach of network flow problems.

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ZHANG, YUANLIN, and ROLAND H. C. YAP. "Solving functional constraints by variable substitution." Theory and Practice of Logic Programming 11, no. 2-3 (February 4, 2011): 297–322. http://dx.doi.org/10.1017/s1471068410000591.

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AbstractFunctional constraints and bi-functional constraints are an important constraint class in Constraint Programming (CP) systems, in particular for Constraint Logic Programming (CLP) systems. CP systems with finite domain constraints usually employ Constraint Satisfaction Problem(s)-based solvers which use local consistency, for example, arc consistency. We introduce a new approach which is based instead on variable substitution. We obtain efficient algorithms for reducing systems involving functional and bi-functional constraints together with other nonfunctional constraints. It also solves globally any CSP where there exists a variable such that any other variable is reachable from it through a sequence of functional constraints. Our experiments on random problems show that variable elimination can significantly improve the efficiency of solving problems with functional constraints.

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Peng, Yunfang, Dandan Lu, and Yarong Chen. "A Constraint Programming Method for Advanced Planning and Scheduling System with Multilevel Structured Products." Discrete Dynamics in Nature and Society 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/917685.

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This paper deals with the advanced planning and scheduling (APS) problem with multilevel structured products. A constraint programming model is constructed for the problem with the consideration of precedence constraints, capacity constraints, release time and due date. A new constraint programming (CP) method is proposed to minimize the total cost. This method is based on iterative solving via branch and bound. And, at each node, the constraint propagation technique is adapted for domain filtering and consistency check. Three branching strategies are compared to improve the search speed. The results of computational study show that the proposed CP method performs better than the traditional mixed integer programming (MIP) method. And the binary constraint heuristic branching strategy is more effective than the other two branching strategies.

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FAGES, FRANÇOIS, and EMMANUEL COQUERY. "Typing constraint logic programs." Theory and Practice of Logic Programming 1, no. 6 (November 2001): 751–77. http://dx.doi.org/10.1017/s1471068401001120.

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We present a prescriptive type system with parametric polymorphism and subtyping for constraint logic programs. The aim of this type system is to detect programming errors statically. It introduces a type discipline for constraint logic programs and modules, while maintaining the capabilities of performing the usual coercions between constraint domains, and of typing meta-programming predicates, thanks to the exibility of subtyping. The property of subject reduction expresses the consistency of a prescriptive type system w.r.t. the execution model: if a program is ‘well-typed’, then all derivations starting from a ‘well-typed’ goal are again ‘well-typed’. That property is proved w.r.t. the abstract execution model of constraint programming which proceeds by accumulation of constraints only, and w.r.t. an enriched execution model with type constraints for substitutions. We describe our implementation of the system for type checking and type inference. We report our experimental results on type checking ISO-Prolog, the (constraint) libraries of Sicstus Prolog and other Prolog programs.

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Yin, Minghao, Tingting Zou, and Wenxiang Gu. "Reverse Bridge Theorem under Constraint Partition." Mathematical Problems in Engineering 2010 (2010): 1–18. http://dx.doi.org/10.1155/2010/617398.

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Reverse bridge theorem (RBTH) has been proved to be both a necessary and sufficient condition for solving Nonlinear programming problems. In this paper, we first propose three algorithms for finding constraint minimum points of continuous, discrete, and mixed-integer nonlinear programming problems based on the reverse bridge theorem. Moreover, we prove that RBTH under constraint partition is also a necessary and sufficient condition for solving nonlinear programming problems. This property can help us to develop an algorithm using RBTH under constraints. Specifically, the algorithm first partitions mixed-integer nonlinear programming problems (MINLPs) by their constraints into some subproblems in similar forms, then solves each subproblem by using RBTH directly, and finally resolves those unsatisfied global constraints by choosing appropriate penalties. Finally, we prove the soundness and completeness of our algorithm. Experimental results also show that our algorithm is effective and sound.

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Huang, Y. Q., S. L. Nie, and H. Ji. "Identification of Contamination Control Strategy for Fluid Power System Using an Inexact Chance-Constrained Integer Program." Journal of Applied Mathematics 2014 (2014): 1–19. http://dx.doi.org/10.1155/2014/146413.

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An inexact chance-constrained integer programming (ICIP) method is developed for planning contamination control of fluid power system (FPS). The ICIP is derived by incorporating chance-constrained programming (CCP) within an interval mixed integer linear programming (IMILP) framework, such that uncertainties presented in terms of probability distributions and discrete intervals can be handled. It can also help examine the reliability of satisfying (or risk of violating) system constraints under uncertainty. The developed method is applied to a case of contamination control planning for one typical FPS. Interval solutions associated with risk levels of constraint violation are obtained. They can be used for generating decision alternatives and thus help designers identify desired strategies under various environmental, economic, and system reliability constraints. Generally, willingness to take a higher risk of constraint violation will guarantee a lower system cost; a strong desire to acquire a lower risk will run into a higher system cost. Thus, the method provides not only decision variable solutions presented as stable intervals but also the associated risk levels in violating the system constraints. It can therefore support an in-depth analysis of the tradeoff between system cost and system-failure risk.

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MANCARELLA, PAOLO, GIACOMO TERRENI, FARIBA SADRI, FRANCESCA TONI, and ULLE ENDRISS. "The CIFF proof procedure for abductive logic programming with constraints: Theory, implementation and experiments." Theory and Practice of Logic Programming 9, no. 6 (August 14, 2009): 691–750. http://dx.doi.org/10.1017/s1471068409990093.

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AbstractWe present the CIFF proof procedure for abductive logic programming with constraints, and we prove its correctness. CIFF is an extension of the IFF proof procedure for abductive logic programming, relaxing the original restrictions over variable quantification (allowedness conditions) and incorporating a constraint solver to deal with numerical constraints as in constraint logic programming. Finally, we describe the CIFF system, comparing it with state-of-the-art abductive systems and answer set solvers and showing how to use it to program some applications.

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ZHOU, NENG-FA. "Programming finite-domain constraint propagators in Action Rules." Theory and Practice of Logic Programming 6, no. 5 (August 2, 2006): 483–507. http://dx.doi.org/10.1017/s1471068405002590.

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In this paper, we propose a new language, called AR (Action Rules), and describe how various propagators for finite-domain constraints can be implemented in it. An action rule specifies a pattern for agents, an action that the agents can carry out, and an event pattern for events that can activate the agents. AR combines the goal-oriented execution model of logic programming with the event-driven execution model. This hybrid execution model facilitates programming constraint propagators. A propagator for a constraint is an agent that maintains the consistency of the constraint and is activated by the updates of the domain variables in the constraint. AR has a much stronger descriptive power than indexicals, the language widely used in the current finite-domain constraint systems, and is flexible for implementing not only interval-consistency but also arc-consistency algorithms. As examples, we present a weak arc-consistency propagator for the all_distinct constraint and a hybrid algorithm for n-ary linear equality constraints. B-Prolog has been extended to accommodate action rules. Benchmarking shows that B-Prolog as a CLP(FD) system significantly outperforms other CLP(FD) systems.

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Finkel, Raphael, Victor W. Marek, and Miros?aw Truszczy?ski. "Constraint Lingo: towards high-level constraint programming." Software: Practice and Experience 34, no. 15 (2004): 1481–504. http://dx.doi.org/10.1002/spe.623.

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Ram, Balasubramanian, and A. J. G. Babu. "Reduction of dimensionality in dynamic programming-based solution methods for nonlinear integer programming." International Journal of Mathematics and Mathematical Sciences 11, no. 4 (1988): 811–14. http://dx.doi.org/10.1155/s0161171288000985.

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This paper suggests a method of formulating any nonlinear integer programming problem, with any number of constraints, as an equivalent single constraint problem, thus reducing the dimensionality of the associated dynamic programming problem.

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Barnier, Nicolas, and Cyril Allignol. "Trajectory deconfliction with constraint programming." Knowledge Engineering Review 27, no. 3 (July 26, 2012): 291–307. http://dx.doi.org/10.1017/s0269888912000227.

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AbstractAs acknowledged by the SESAR (Single European Sky ATM (Air Traffic Management) Research) program, current Air Traffic Control (ATC) systems must be drastically improved to accommodate the predicted traffic growth in Europe. In this context, the Episode 3 project aims at assessing the performance of new ATM concepts, like 4D-trajectory planning and strategic deconfliction.One of the bottlenecks impeding ATC performances is the hourly capacity constraints defined on each en-route ATC sector to limit the rate of aircraft. Previous works were mainly focused on optimizing the current ground holding slot allocation process devised to satisfy these constraints. We propose to estimate the cost of directly solving all conflicts in the upper airspace with ground holding, provided that aircraft were able to follow their trajectories accurately.We present a Constraint Programming model of this large-scale combinatorial optimization problem and the results obtained with the FaCiLe (Functional Constraint Library). We study the effect of uncertainties on the departure time and estimate the cost of improving the robustness of our solutions with the Complete Air Traffic Simulator (CATS). Encouraging results were obtained without uncertainty but the costs of robust solutions are prohibitive. Our approach may however be improved, for example, with a prior flight level allocation and the dynamic resolution of remaining conflicts with one of CATS’ modules.

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Aoga, John O. R., Tias Guns, and Pierre Schaus. "Mining Time-constrained Sequential Patterns with Constraint Programming." Constraints 22, no. 4 (June 7, 2017): 548–70. http://dx.doi.org/10.1007/s10601-017-9272-3.

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Kirchner, Claude, and Christophe Ringeissen. "Rule-Based Constraint Programming." Fundamenta Informaticae 34, no. 3 (1998): 225–62. http://dx.doi.org/10.3233/fi-1998-34302.

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Réty, Jean-Hugues. "Distributed Concurrent Constraint Programming." Fundamenta Informaticae 34, no. 3 (1998): 323–46. http://dx.doi.org/10.3233/fi-1998-34305.

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Montanari, Ugo, and Francesca Rossi. "Constraint solving and programming." ACM Computing Surveys 28, no. 4es (December 1996): 70. http://dx.doi.org/10.1145/242224.242314.

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Puget, Jean-Francois. "Future of constraint programming." ACM Computing Surveys 28, no. 4es (December 1996): 72. http://dx.doi.org/10.1145/242224.242317.

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Cohen, Jacques. "Constraint logic programming languages." Communications of the ACM 33, no. 7 (July 1990): 52–68. http://dx.doi.org/10.1145/79204.79209.

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Gupta, V., R. Jagadeesan, and V. A. Saraswat. "Truly concurrent constraint programming." Theoretical Computer Science 278, no. 1-2 (May 2002): 223–55. http://dx.doi.org/10.1016/s0304-3975(00)00337-6.

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Olarte, Carlos, Elaine Pimentel, and Vivek Nigam. "Subexponential concurrent constraint programming." Theoretical Computer Science 606 (November 2015): 98–120. http://dx.doi.org/10.1016/j.tcs.2015.06.031.

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Flener, Pierre, Mats Carlsson, and Christian Schulte. "Constraint Programming in Sweden." IEEE Intelligent Systems 24, no. 2 (March 2009): 87–89. http://dx.doi.org/10.1109/mis.2009.25.

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Pesant, Gilles. "A constraint programming primer." EURO Journal on Computational Optimization 2, no. 3 (July 22, 2014): 89–97. http://dx.doi.org/10.1007/s13675-014-0026-3.

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Bistarelli, Stefano, Ugo Montanari, and Francesca Rossi. "Soft concurrent constraint programming." ACM Transactions on Computational Logic 7, no. 3 (July 2006): 563–89. http://dx.doi.org/10.1145/1149114.1149118.

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Wilson, Molly, and Alan Borning. "Hierarchical constraint logic programming." Journal of Logic Programming 16, no. 3-4 (July 1993): 277–318. http://dx.doi.org/10.1016/0743-1066(93)90046-j.

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Bortolussi, Luca. "Stochastic Concurrent Constraint Programming." Electronic Notes in Theoretical Computer Science 164, no. 3 (October 2006): 65–80. http://dx.doi.org/10.1016/j.entcs.2006.07.012.

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