AMPL

Features

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

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.

Availability

AMPL is available for many popular 32- and 64-bit operating systems including Linux, Mac OS X, some Unix, 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. A free student version with limited functionality and a free full-featured version for academic courses are also available.

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.

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.

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 a partial list of solvers supported by AMPL: