AMPL

AMPL

Paradigm	multi-paradigm: declarative, imperative
Designed by	Robert Fourer David Gay Brian Kernighan Bell Labs
First appeared	1985
Stable release	20131012 / October 12, 2013
OS	Cross-platform (multi-platform)
License	Proprietary (translator), free and open-source (AMPL Solver Library)
Filename extensions	.mod .dat .run
Website	www.ampl.com
Influenced by AWK, C Influenced Coopr

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, KNITRO, and LGO. 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.

Features

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:

• Linear programming
• Quadratic programming
• Nonlinear programming
• Mixed-integer programming
• Mixed-integer quadratic programming with or without convex quadratic constraints
• Mixed-integer nonlinear programming
• Second-order cone programming
• Global optimization
• Semidefinite programming problems with bilinear matrix inequalities
• Complementarity problems (MPECs) in discrete or continuous variables
• Constraint programming^[5]

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

• User can interrupt the solution process at any time
• Solver errors 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

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 is proprietary software maintained by AMPL Optimization LLC. However, several online services exist, providing free modeling and solving facilities using AMPL.^[3][6] A free student version with limited functionality and a free full-featured version for academic courses are also available.^[7]

AMPL can be used from within Microsoft Excel via the SolverStudio Excel add-in.

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

This table present significant steps in AMPL history.

A sample model

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

Here is an incomplete list of solvers supported by AMPL:^[13]

See also

• Algebraic modeling language
• nl (format)
• sol (format)

References

1. ↑ 1.0 1.1 Fourer, Robert; 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. ↑ 3.0 3.1 http://www.neos-server.org/neos/
4. ↑ http://neos-guide.org/About/
5. ↑ 5.0 5.1 Fourer, Robert; Gay, David M. (2002). "Extending an Algebraic Modeling Language to Support Constraint Programming". INFORMS Journal on Computing 14 (4): 322–344. doi:10.1287/ijoc.14.4.322.2825. 
6. ↑ http://www.ampl.com/TRYAMPL/
7. ↑ http://www.ampl.com/DOWNLOADS/index.html
8. ↑ Fourer, Robert; Gay, David M.; Kernighan, Brian W. (1990). "A Modeling Language for Mathematical Programming". Management Science 36 (5): 519–554–83. doi:10.1287/mnsc.36.5.519. 
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. ↑ https://groups.google.com/forum/#!topic/ampl/y1FJcYZz-_Q
13. ↑ http://www.ampl.com/solvers.html
14. ↑ https://projects.coin-or.org/Couenne
15. ↑ https://github.com/ampl/mp/tree/master/solvers/ilogcp
16. ↑ https://github.com/ampl/mp/tree/master/solvers/gecode
17. ↑ https://github.com/ampl/mp/tree/master/solvers/jacop
18. ↑ http://ampl.com/products/solvers/solvers-we-sell/lgo/
19. ↑ https://github.com/ampl/mp/tree/master/solvers/localsolver
20. ↑ http://www.ampl.com/SOLVERS/GUIDE.lpsolve.html
21. ↑ https://github.com/ampl/mp/tree/master/solvers/sulum

External links

• AMPL home page
• Prof. Fourer's home page at Northwestern University