Robert Fourer, David M. Gay, and Brian Kernighan. A modeling language for mathematical programming. Management Science, 36(5):519--554, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Our system may thus serve both as a network planning tool at the strategic level and as a dynamic routing system at the operational level of management. The modelling is reviewed in Section I in order to demonstrate the need for easy reformulation of the initial problem using a modelling language [7]. Our approach involves a hierarchy of design objectives associated with respective network layers which constitutes a set of models with common data. In section 2 we present a current version of the Integrated Network Design System with common data, solvers and graphical user interface (GUI) ....

FOURER, R., GAY, D. AND KERNIGSAN, B. (1990). A modeling language for math- ematical programming. Management Science, 36 519 554.

....search algorithms. The first part of this paper will demonstrate how STRIPS style planning problems extended with costs, resources, and optimality conditions can be represented as an ILP and solved using a LP based branch and bound. For the experiments, use a commercial modeling language (AMPL) (Fourer, Gay, Kernighan 1993) and a mixed integer programming package (ILOG CPLEX) We will argue that specifying a planning problem by a combination of STRIPS operators (to represent logical constraints between actions and their preconditions and effects) and linear inequalities (to represent resource usage and objective ....

Fourer, R.; Gay, D. M.; and Kernighan, B. W. 1993. AMPL, A Modeling Language for Mathematical Programming. Boyd & Fraser publishing Company.

....a structured service model in a Java applet. The paper concludes with a first evaluation of the system. 1 Introduction The Internet gives access to numerous libraries of mathematical models for decision making. For example, NetLib [12] and a Princeton Web server [11] contain about 900 AMPL [4] models. So far these services require installation of the models on the local computer. But Decision support on demand [1] where the model can be used interactively on a remote server, is likely to become widely available in near future. Indeed, application service provision is enjoying a market ....

R. Fourer, D. M. Gay, and B. W. Kernighan. A modeling language for mathematical programming. Management Science, 36(5):519--554, 1990.

....solving. Some guidance is provided to design the right mathematical programming model by means of case studies (see surveys in [Gro93, Wil94] Also there is a growing number of algebraic modelling languages to ease the formulation of LSCO models fed to LP MIP solvers (e.g. GAMS [BM82] AMPL [FGK93] XPRESS MP [Das97] The weak point is the scarcity of work that exists to integrate mathematical programming models with other paradigms like constraint programming, even though they should be seen as complementary. 2.3. The stochastic search paradigm. A third paradigm found to be useful in ....

R. Fourer, D. Gay, and B.W. Kernighan, A modeling language for mathematical programming, The Scientific Press, San Francisco, 1993.

....open up the possibility to include structure speci c propagation into a general solver and are thus extremely important for the e ciency of the solver. Mathematical programming has still not seen the advantage of global constraints to the same extent. Modeling languages for LP IP, such as AMPL [9], do include some constructs to aid the modeler in writing compact and easy tounderstand models. Those constructs, however, have to be transformed into linear inequalities before being sent to an LP IP solver and the structural information is lost in the process. Although the structure may be ....

....hull for such general semi continuous piecewise functions is then a matter of nding the convex hull of a set of points. This is a well known problem in computational geometry and can be done e ciently [5] A simpler syntax for continuous functions could of course be adopted, e.g. as in AMPL [9] and OPL [20] where the functions are assumed to be continuous and starting at the origin, and only the end point and slope of each segment are speci ed. 4. Algorithmic Extensions In CLP, good support for de ning problem speci c search strategies is essential. Strategies derive branching ....

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R. Fourer, D.M. Gay, and B.W. Kernighan. AMPL  A Modeling Language for Mathematical Programming. The Scientic Press, South San Francisco, 1993.

....a given energy system and the formulation of MARKAL is currently written in the GAMS modeling language. In its previous version MARKAL was written in OMNI, a well known matrix generator. Matrix generators are however more and more replaced by algebraic modeling languages such as GAMS [8] or AMPL [18]. Algebraic modeling languages indeed enable to write eoeective mathematical programming problems in a very compact way since the syntax of writing a model in this environment closely resembles the mathematical notation. A new version of MARKAL (also called The Model ) which will include most of ....

....not be done by a non specialist. At the end of 1970 s matrix generators gave way to algebraic modeling languages [7,16] The rst modeling language, GAMS [8] was developed at the World Bank at the end of 1970 s. Nowadays, modelers essentially use Algebraic Modeling Languages (e.g. GAMS [8] AMPL [18], AIMMS [6] to write Mathematical Programming (MP) problems. These AMLs enable modelers to express their problems under a natural mathematical form using equivalent algebraic notations: sets, parameters, indexed variables and constraints. These statements clearly allow to separate the problem ....

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R. Fourer, D. M. Gay, and B. W. Kernighan, AMPL, a Modeling Language For Mathematical Programming, The Scientic Press, 1993.

....variables and iterated operators like and , they provide a convenient way to form expressions such as: i I j ij i y x a I i = AMLs are computer readable equivalents of algebraic notations. They have become very popular in the Operations Research community through languages like AMPL [Fourer et al. 1990] and GAMS [Brooke et al. 1988] More recently, AMLs have also been used in Artificial Intelligence for constraint programming [Michel and van Hentenryck, 1996] AMLs are appropriate in our context because mathematical modelers are familiar with algebraic notations. AMLs are very expressive ....

R. Fourer, D. Gay, and B. Kernighan. A Modeling Language for Mathematical Programming. Management Science, 36, pages 519-554, 1990.

....and or constraints. Allowing indexed expressions, sets, variables and iterated operators like and , they provide a convenient way to form expressions such as: I j ij i y x a I i AMLs have become very popular in the Operations Research community through languages like AMPL (Fourer, Gay and Kernighan 1990) and GAMS (Brooke, Kendrick and Meeraus 1988) More recently, AMLs have also been used in AI for constraint programming (Michel and van Hentenryck 1996) The popularity of AMLs for numerical modeling comes from different factors. First, it is not necessary to be a computer scientist in order to ....

Fourer, R.; Gay, D.; Kernighan, B. 1990. A Modeling Language for Mathematical Programming. Management Science 36 (5), 519-554.

.... variables and expressions, quantifiers and iterated operators like (sum) and (product) in order to build more or less complex algebraic expressions such as, for instance, j J j i x x I i = These languages are mainly used for linear and non linear programming in systems like AMPL [12], for discrete time simulation in AMIA [18] and recently for constraint programming in OPL [28] The success of these languages is due both to their declarativity each equation or constraint forms a corpus of knowledge independent from the others , and to their powerful expressivity that ....

R. Fourer, D. Gay and B. Kernighan, A Modeling Language for Mathematical Programming, Management Science, 36, pp. 519-554, 1990.

....in the best case only one solution is found although there may be several equally optimal ones. In real world situations, the monetary cost of not finding a solution or not finding all equally optimal solutions can be large. Furthermore, traditional mathematical programming techniques and systems [Fourer et al. 1993] do not deal with logical and other non arithmetic constraint that may be present in the problem. As an alternative approach, the idea of constraint programming and solving has emerged in the fields of AI and logic programming [Marriot, Stuckey, 1998] and reliable or interval computing [Interval, ....

....Further research is needed in order to automate such tuning based on problem characteristics, if the algorithm is used for solving other kind of problems. Planned future work includes comparizon of the interval solving approach with traditional mixed integer solvers, such as CPLEX and XLSOLVE [Fourer et al. 1993]. Problems such as the generation rejection problem of this paper are challenging to traditional optimization techniques whose iterative algorithms cannot easily make use of the discrete value domains and constraints. Furthermore, with these systems at most one solution can be found while with ....

Fourer, R., Gay, D., Kernighan, B., AMPL. A modeling language for mathematical programming. Boyd & Freaser Publ. Company, 1993.

....a structured service model in a Java applet. The paper concludes with a first evaluation of the system. 1 Introduction The Internet gives access to numerous libraries of mathematical models for decision making. For example, NetLib [12] and a Princeton Web server [11] contain about 900 AMPL [4] models. So far these services require installation of the models on the local computer. But Decision support on demand [2] where the model can be used interactively on a remote server, is likely to become widely available in near future. Indeed, application service hosting is enjoying a market ....

R. Fourer, D. M. Gay, and B. W. Kernighan. A modeling language for mathematical programming. Management Science, 36(5):519--554, 1990.

....creating new languages or extending old languages much less tedious. Several AD tools have been created with the help of language development tools like Lex and Yacc. The most notable of these AD tools are the FORTRAN precompilers JAKE [Spee80] and PADRE2 [Kubo90] and the modeling language AMPL [Four90]. During the SIAM Workshop on Automatic Differentiation, it became clear that the forces driving AD technology had caused a variety of different tools to be created. Of these various tools, many of them had similar characteristics. Unfortunately, the 3 Final version submitted to the Proceedings ....

....that directly provide automatic differentiation. Several of the earliest AD tools belong to the integral class. The best examples of these are SLANG [Adam69, McCu69, Tham69] and PROSE [Tham75, PROS77, Tham82, Krin84, Pfei87] More recent examples of integral AD tools are the modeling language AMPL [Four90], and the FM FAD [Mazo91] package. J J J J 8 8 8 8 8 8 b b b b b b b ae ae ae ae ae ae ae ae ae ae ae ae ae ae . Computer Algebra Systems Elemental Extensional Integral Operational Symbolic Fig. 1. The relationship among the ....

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R. Fourer, D .M. Gay, and B. W. Kernighan, A Modeling Language for Mathematical Programming, Management Science Vol. 36 no. 5 (1990), pp. 519-554.

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Robert Fourer, David M. Gay, and Brian Kernighan. A modeling language for mathematical programming. Management Science, 36(5):519--554, 1990.

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Robert Fourer, David M. Gay and Brian W. Kernighan, A Modeling Language for Mathematical Programming. Management Science 36 (1990) 519--554.

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R. Fourer, D. M. Gay and B. W. Kernighan, A Modeling Language for Mathematical Programming. Management Science 36 (1990) 519--554.

....optimization jobs and the retrieval of results normally require human intervention. They can be automated only to a limited degree through problem specific programming on the part of the user. This paper describes the new Kestrel interface to the NEOS Server and its application within the AMPL [13, 14] and GAMS [4, 5] modeling systems. A Kestrel client is called by a locally running program, and results are returned to that program. Thus, a modeling system can have much the same access to remote NEOS solvers as to solvers installed locally. As a result, the modeler can consider a wider variety ....

....di#erentiation tools, such as ADIFOR [2] ADIC [3, 20] and ADOL C [17] can be run by the NEOS solver to generate code that computes exact derivatives. High level algebraic formulations describe optimization problems in concise, symbolic formats using modeling languages such as AMPL [13, 14] and GAMS [4, 5] To cope with this variety, the server maintains a data bank, a general framework that enables optimization solvers and their individual needs to be recognized. Each available solver has an entry in the data bank that records solver specific information provided by the solver s ....

R. Fourer, D. M. Gay and B. W. Kernighan, A Modeling Language for Mathematical Programming. Management Science 36 (1990) 519--554.

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R. FOURER, D. M. GAY, AND B. W. KERNIGIAN, A modeling language for mathematical programming, Management Science, 36 (1990), pp. 519-554.

....Thus it is of interest to ask how efficiently we can compute (3) from a suitable symbolic representation of f and c. This paper discusses computing (3) by automatic differentiation (AD) and gives some computational experience with problems expressed symbolically in the AMPL modeling language [11, 12]. For simplicity, the remainder of this paper ignores constraints and just talks about computing 2 f. However, the implementation discussed below is designed to compute (3) which is also relevant when some of the constraints are changed to inequality constraints. Use of AD in Hessian ....

R. Fourer, D. M. Gay, and B. W. Kernighan, "A Modeling Language for Mathematical Programming," Management Science 36 #5 (1990), pp. 519--554.

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R. Fourer, D. Gay and B. Kernighan, A modeling language for mathematical programming, Management Science, 1990, 36(5), 519-554, http://www.ampl.com.

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R. Fourer, D. M. Gay, and B. W. Kernighar. AMPL, A modeling language for mathematical programming. The Scientific Press, 1993.

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R. Fourer, D. M. Gay, and B. W. Kernighar, AMPL, A modeling language for mathematical programming, The Scientific Press, 1993.

No context found.

R. Fourer, D.M. Gay, and B.W. Kernighan, "A modeling language for mathematical programming," Management Science, vol. 36, no. 5, pp. 519--554, 1990.

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R. Fourer, D. M. Gay, and B. W. Kernighar, AMPL, A modeling language for mathematical programming, Boyd & Fraser, Danvers MA, (originally published by The Scientific Press) 1993, pp 291--306.

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R. Fourer, D. M. Gay, B. W. Kernighan: AMPL. A Modeling Language for Mathematical Programming. Scientific Press, 1993. See also: http://www.ampl.com.

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Robert Fourer, David Gay, and Brian Kernighan. A Modeling Language For Mathematical Programming. The Scienti c Press, San Franzisco, 1993.

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