AMPL

AMPL ( A M athematical P rogramming L anguage ) is a mathematical modeling language used by Robert Fourer , David Gay and Brian Kernighan at Bell Laboratories developed. It allows the formulation of mathematical models in an abstract form that is close to algebraic notation. Many optimization problems can be formulated with AMPL.

Since AMPL does not solve these problems directly, but translates them into a form that an optimization algorithm understands, AMPL needs suitable solvers in order to function.

Sufficiently difficult problems such as global optima, nonlinear mixed integer problems etc. therefore require special solvers .

example

The following mathematical model is given:

Variables:

• ${\displaystyle x_{1}}$: Number of product 1
• ${\displaystyle x_{2}}$: Number of product 2

Objective function:

• Maximize ${\displaystyle z=400x_{1}+50x_{2}}$

Constraints:

• ${\displaystyle 0\leq x_{1}\leq 70}$(Range from ) ${\displaystyle x_{1}}$
• ${\displaystyle 0\leq x_{2}\leq 500}$(Range from ) ${\displaystyle x_{2}}$
• ${\displaystyle 25x_{1}+10x_{2}\leq 5000}$ (Limitation for resource 1)
• ${\displaystyle 100x_{1}+20x_{2}\leq 8000}$ (Limitation for resource 2)

An equivalent formulation in AMPL could look like this:

 # Variablen:
 var x1 integer;
 var x2 integer;

 # Zielfunktion:
 maximize z: 400*x1 + 50*x2;

 # Nebenbedingungen:
 subject to Bereich_x1: 0 <= x1 <= 70;
 subject to Bereich_x2: 0 <= x2 <= 500;
 subject to Ressource1: 25*x1 + 10*x2 <= 5000;
 subject to Ressource2: 100*x1 + 20*x2 <= 8000;

 # wenn man dieses Problem loesen will
 # braucht man nur noch
 solve;
 # der Maximierer wird mit
 display x1, x2;
 # angezeigt

See also

• AIMMS
• GAMS
• GLPK - open source alternative to the proprietary AMPL
• MPL
• OPL Studio

literature

• Robert Fourer, David Gay, Brian Kernighan : AMPL: a modeling language for mathematical programming . Duxbury Resource Center, ISBN 0-534-38809-4

Web links

• AMPL homepage