AMPL

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AMPL
AMPL (textbook cover).jpg
Paradigm(s) multi-paradigm: declarative, imperative
Appeared in 1985
Designed by Robert Fourer
David Gay
Brian Kernighan
Bell Labs
Stable release 20120126 (January 26, 2012)
Influenced by AWK, C
OS Cross-platform (multi-platform)
License Proprietary (translator), free and open-source (AMPL Solver Library)
Usual filename extensions .mod .dat .run

AMPL, an acronym for "A Mathematical Programming Language", is an algebraic modeling language for describing and solving high-complexity problems for large-scale mathematical computation (i.e. large-scale optimization and scheduling-type problems). [1] It was developed by Robert Fourer, David Gay and Brian Kernighan at Bell Laboratories. AMPL supports dozens of solvers, both open source and commercial, including CBC, CPLEX, FortMP, Gurobi, MINOS, IPOPT, SNOPT and KNITRO. Problems are passed to solvers as nl files. AMPL is used by more than a hundred corporate clients. It is also used by government agencies and academic institutions.[2]

One particular advantage of AMPL is the similarity of its syntax to the mathematical notation of optimization problems. This allows for a very concise and readable definition of problems in the domain of optimization. Many modern solvers available on the NEOS [3] server (formerly hosted at the Argonne National Laboratory, currently hosted at the University of Wisconsin, Madison [4]) accept AMPL input. According to the NEOS statistics AMPL is the most popular format for representing mathematical programming problems.

Contents

Features [edit]

AMPL features a mixture of declarative and imperative programming styles. Formulation of optimization models takes place through declarative language elements such as sets, scalar and multidimensional parameters, decision variables, objectives and constraints, which allow for a concise description of most problems in the domain of mathematical optimization.

Procedures and control flow statements are available in AMPL for

  • the exchange of data with external data sources such as spreadsheets, databases, XML and text files
  • data pre- and post-processing tasks around optimization models
  • the construction of hybrid algorithms for problem types for which no direct efficient solvers are available.

To support re-use and simplify construction of large-scale optimization problems, AMPL allows separation of model and data.

AMPL supports a wide range of problem types, among them:

AMPL invokes a solver in a separate process which has the following advantages:

  • Solver crashes do not affect the interpreter
  • 32-bit version of AMPL can be used with a 64-bit solver and vice versa

Interaction with the solver is done through a well-defined nl interface.

Availability [edit]

NEOS input statistics for January 2011.

AMPL is available for many popular 32- and 64-bit platforms including Linux, Mac OS X and Windows. The translator itself is a proprietary software currently maintained by AMPL Optimization LLC. However there exist several online services [3][6] providing free modeling and solving facilities using AMPL. Also a free student version with limited functionality is available.[7]

The AMPL Solver Library (ASL) which allows to read the nl files and provides the automatic differentiation functionality is open-source. It is used in many solvers to implement AMPL connection.

Status history [edit]

This table present significant steps in AMPL history.

Year Highlights
1985 AMPL was designed and implemented [1]
1990 Paper describing the AMPL modeling language was published in Management Science[8]
1991 AMPL supports nonlinear programming and automatic differentiation
1993 Robert Fourer, David Gay and Brian Kernighan were awarded ORSA/CSTS Prize [9] by the Operations Research Society of America, for writings on the design of mathematical programming systems and the AMPL modeling language
1995 Extensions for representing piecewise-linear and network structures
1995 Scripting constructs
1997 Enhanced support for nonlinear solvers
1998 AMPL supports complementarity problems
2000 Relational database and spreadsheet access
2002 Support for constraint programming [5]
2005 AMPL Modeling Language Google group opened [10]
2008 Kestrel: An AMPL Interface to the NEOS Server introduced
2012 Robert Fourer, David Gay and Brian Kernighan were awarded the 2012 INFORMS Impact Prize as the originators of one of the most important algebraic modeling languages.[11]

A sample model [edit]

A transportation problem from George Dantzig is used to provide a sample AMPL model. This problem finds the least cost shipping schedule that meets requirements at markets and supplies at factories.

Dantzig, G B, chapter 3.3 in Linear Programming and Extensions, Princeton University Press, Princeton, New Jersey, 1963.

set Plants;
set Markets;

# Capacity of plant p in cases
param Capacity{p in Plants};

# Demand at market m in cases
param Demand{m in Markets};

# Distance in thousands of miles
param Distance{Plants, Markets};

# Freight in dollars per case per thousand miles
param Freight;

# Transport cost in thousands of dollars per case
param TransportCost{p in Plants, m in Markets} :=
    Freight * Distance[p, m] / 1000; 

# Shipment quantities in cases
var shipment{Plants, Markets} >= 0;

# Total transportation costs in thousands of dollars
minimize cost:
    sum{p in Plants, m in Markets} TransportCost[p, m] * shipment[p, m];

# Observe supply limit at plant p
s.t. supply{p in Plants}: sum{m in Markets} shipment[p, m] <= Capacity[p];

# Satisfy demand at market m
s.t. demand{m in Markets}: sum{p in Plants} shipment[p, m] >= Demand[m];

data;

set Plants := seattle san-diego;
set Markets := new-york chicago topeka;

param Capacity :=
    seattle   350
    san-diego 600;

param Demand :=
    new-york 325
    chicago  300
    topeka   275;

param Distance : new-york chicago topeka :=
    seattle        2.5      1.7     1.8
    san-diego      2.5      1.8     1.4;

param Freight := 90;

Solvers [edit]

Here is an incomplete list of solvers supported by AMPL:[12]

Solver Supported problem types
APOPT mixed integer nonlinear programming
Bonmin mixed integer nonlinear programming
BPMPD linear and quadratic programming
CBC mixed integer programming
CLP linear programming
CONOPT nonlinear programming
CPLEX linear, quadratic, second-order cone and mixed integer programming
CPLEX CP Optimizer [13] constraint programming
FILTER nonlinear programming
FortMP linear, quadratic and mixed integer programming
Gecode [14] constraint programming
Gurobi linear, quadratic, second-order cone and mixed integer programming
IPOPT nonlinear programming
KNITRO linear, quadratic and nonlinear programming
MINOS linear and nonlinear programming
MINTO mixed integer programming
MOSEK linear, mixed integer linear, quadratic, mixed integer quadratic, quadratically constrained, conic and convex nonlinear programming
SCIP mixed integer programming
SNOPT nonlinear programming
WORHP nonlinear programming
Xpress linear, quadratic and mixed integer linear programming

See also [edit]

References [edit]

  1. ^ a b Fourer, Robert; David M. Gay, Brian W. Kernighan (2002). AMPL: A Modeling Language for Mathematical Programming. Duxbury Press. ISBN 978-0-534-38809-6. 
  2. ^ "Position Available". Retrieved 2011-07-29. 
  3. ^ a b http://www.neos-server.org/neos/
  4. ^ http://neos-guide.org/About/
  5. ^ a b "Extending an Algebraic Modeling Language to Support Constraint Programming". INFORMS Journal on Computing 14: 322–344. 2002. 
  6. ^ http://www.ampl.com/TRYAMPL/
  7. ^ http://www.ampl.com/DOWNLOADS/index.html
  8. ^ "A Modeling Language for Mathematical Programming". Management Science 36: 519–554–83. 1990. 
  9. ^ http://computing.society.informs.org/pdf/GreenbergHistory.pdf
  10. ^ http://groups.google.com/group/ampl
  11. ^ http://www.informs.org/Blogs/E-News-Blog/INFORMS-Impact-Prize
  12. ^ http://www.ampl.com/solvers.html
  13. ^ https://github.com/vitaut/ampl/tree/master/solvers/ilogcp
  14. ^ https://github.com/vitaut/ampl/tree/master/solvers/gecode

External links [edit]

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