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Interfaces, 2001
Arising from research in the computer science community, constraint programming is a fairly new technique for solving optimization problems. For those familiar with mathematical programming, a number of language barriers make it difficult to understand the concepts of constraint programming. In this short tutorial on constraint programming, we explain how it relates to familiar mathematical programming concepts and how constraint programming and mathematical programming technologies are complementary. We assume a minimal background in linear and integer programming.
On the Relatedness and Nestedness of Constraints
Sports Medicine - Open
The purpose of this opinion paper is providing a platform for explaining and discussing the relatedness and nestedness of constraints on the basis of four claims: (a) task constraints are distributed between the person and the environment and hence are relational variables, (b) being relational, task constraints are also emergent properties of the organism/environment system, (c) constraints are nested in timescales, and (d) a vast set of constraints are correlated through circular causality. Theoretical implications for improving the understanding of the constraints-led approach and practical applications for enhancing the manipulation of constraints in learning and training settings are proposed.
Zeitschrift für Operations Research, 1979
In his book "Linear Programming" 11964] Llewellyn devoted a chapter to simplifications and reductions of a linear programming problem by means of algebraic rules. These rules are claimed to be rather general. Here we give some counterexamples, where the rules of Ltewellyn do not hold. Furthermore we give some general rules to identify redundant constraints in the case LleweUyn considers and show that the original rules of Llewellyn together with an extra condition are a variant of these general rules. Finally we consider the question whether or not the rules of Llewellyn should be used tO identify redundant constraints. Zusammenfassung: Bereits 1964 hat si'ch Llewellyn in seinem Buch ,,Linear Programming" mR der Vereinfachung yon linearen Programmen durch Ermittlung redundanter Nebenbedingungen be-sch~iftigt. Der von ihm fOx seine Regeln erhobene Ansprueh der Allgemeingiiltigkeit wird in diesem Beitrag durch Gegenbeispiele widerlegt. Ferner werden allgemeine Regeln zur Identifikation redundanter Nebenbedingungen hergeleitet und gezeigt, daf~ diese die Regeln yon Llewellyn, sofern man sic um eine zus~itzliche Bedingung erweitert, umfassen.
Twenty Years of Constraint Programming (CP) Research
Constraints
Around twenty years ago, the research community working on constraint satisfaction, optimization and contraint programming was moving the first steps toward a more organized structure. Indeed the first events on the subject, often colocated with major AI conferences, date back to almost thirty years ago. In 1995, after a successful series of two workshops on the subject (PPCP'93 and PPCP'94), the first Conference on Principles and Practice of Constraint Programming was organized in Cassis. One year later, the first number of the Constraints Journal was issued. The Editor in Chief was Eugene Freuder, whose paper opens this special issue with a very clear and lucid analysis on the advances obtained in twenty years of research and on open research perspectives. Constraint programming has its roots in the Artificial Intelligence area of constraint satisfaction, but along the years many cross-fertilizations with related disciplines have been studied. Logic programming is the first obvious intersection, as the first constraint languages were based on logic. The integration of operations research techniques in constraint programming has been extremely successful, as wittnessed by the long series of CPAIOR conferences. Problem solving in the precence of uncertainty has received a lot of attention in the last decade resulting in stochastic constraint languages. Techniques based on SAT have been succesfully integrated into constraint programming solvers and obtained state of the art results in many combinatorial problems. More recently also machine learning has been succesfully integrated in CP to ease the modeling activity, to acquire constraints and to exploit existing solutions of similar problems. These cross-fertilizations have been made possible thanks to CP flexibility, one of the main features of constraint programming languages. Constraint programming global constraints are in fact, a very powerful modeling tool, but also enable the embedding of sophisticated algorithms inherited by other disciplines.
A Study of Encodings of Constraint Satisfaction
Many constraint satisfaction problems (csp's) are formulated with 0/1 variables. Sometimes this is a natural encoding, sometimes it is as a result of a reformulation of the problem, other times 0/1 variables make up only a part of the problem. Frequently we have constraints that restrict the sum of the values of variables. This can be encoded as a simple summation of the variables. However, since variables can only take 0/1 values we can also use an occurrence constraint, e.g. the number of occurrences of 1 must be k. Would this make a difference? Similarly, problems may use channelling constraints and encode these as a biconditional such as P ↔ Q (i.e. P if and only if Q). This can also be encoded in a number of ways. Might this make a difference as well? We attempt to answer these questions, using a variety of problems and two constraint programming toolkits. We show that even minor changes to the formulation of a constraint can have a profound effect on the run time of a constraint program and that these effects are not consistent across constraint programming toolkits. This leads us to a cautionary note for constraint programmers: take note of how you encode constraints, and don't assume computational behaviour is toolkit independent.
Chapter 11. Constraints constrained
Neglected Aspects of Motion-Event Description, 2022
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IFSR International Series on Systems Science and Engineering, 2017
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