AMPL

AMPL features a mix of declarative and imperative programming styles. Formulating optimization models occurs via declarative language elements such as sets, scalar and multidimensional parameters, decision variables, objectives and constraints, which allow for 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 theory problems (MPECs) in discrete or continuous variables
• Constraint programming

{{Cite journal

|author-link = Robert Fourer

| title = Extending an Algebraic Modeling Language to Support Constraint Programming

| journal = INFORMS Journal on Computing

| volume = 14

| issue = 4

| pages = 322–344

| year = 2002

| url = http://joc.journal.informs.org/content/14/4/322

| doi=10.1287/ijoc.14.4.322.2825| last1 = Fourer

| first1 = Robert

| last2 = Gay

| first2 = David M.

| citeseerx = 10.1.1.8.9699

}}

AMPL invokes a solver in a separate process which has these 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.

AMPL is available for many popular 32 & 64-bit operating systems including Linux, macOS, Solaris, AIX, and Windows.{{cite web|url=https://ampl.com/products/platforms/|title=Platforms|website=AMPL Optimizations Inc.|access-date=1 November 2019|archive-date=14 May 2022|archive-url=https://web.archive.org/web/20220514181833/https://ampl.com/products/platforms/|url-status=dead}}

The translator is proprietary software maintained by AMPL Optimization LLC. However, several online services exist, providing free modeling and solving facilities using AMPL.{{cite web|url=http://www.neos-server.org/neos/|title=NEOS Server for Optimization|access-date=11 August 2015}}{{cite web|url=http://www.ampl.com/TRYAMPL/|title=Try AMPL!|access-date=11 August 2015}} A free student version with limited functionality and a free full-featured version for academic courses are also available.{{cite web|url=http://www.ampl.com/DOWNLOADS/index.html|title=AMPL Downloads|access-date=11 August 2015|archive-url=https://web.archive.org/web/20150526013237/http://www.ampl.com/DOWNLOADS/index.html|archive-date=26 May 2015|url-status=dead}}

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

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

This table present significant steps in AMPL history.

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.

{{cite book |first=George |last=Dantzig |author-link=George Dantzig |chapter=3. Formulating a Linear Programming Model |title=Linear Programming and Extensions |chapter-url=https://books.google.com/books?id=hUWPDAAAQBAJ&pg=PA32 |date=2016 |orig-year=1963 |publisher=Princeton University Press |isbn=978-1-4008-8417-9 |pages=32–62}}

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;

Here is a partial list of solvers supported by AMPL:{{cite web|url=http://www.ampl.com/solvers.html|title=Solvers - AMPL|access-date=21 January 2018|archive-date=27 February 2014|archive-url=https://web.archive.org/web/20140227083015/http://www.ampl.com/solvers.html|url-status=dead}}

• sol (format)
• GNU MathProg (previously known as GMPL) is a subset of AMPL supported by the GNU Linear Programming Kit{{cite web|url=https://www.gnu.org/software/glpk/|title=GLPK official site|access-date=17 September 2020}}

{{Reflist|30em}}

• {{Official website|www.ampl.com}}
• [https://web.archive.org/web/20061127232734/http://iems.northwestern.edu/~4er/ Prof. Fourer's home page] at Northwestern University

{{Mathematical optimization software}}

{{DEFAULTSORT:Ampl}}

Category:1990 software

Category:Computer algebra systems

Category:Mathematical modeling

Category:Mathematical optimization software

Category:Numerical programming languages

Category:Scripting languages

Category:Text-oriented programming languages

Category:Programming languages created in 1985

Category:Proprietary cross-platform software