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Unformatted text preview: MthSc 810: Mathematical Programming Lecture 6 Pietro Belotti Dept. of Mathematical Sciences Clemson University September 13, 2011 Sep. 13: AMPL . Reading: Bob Fourer’s notes, Chapters 12 Reading for Sep. 15: textbook, Sections 3.1 and 3.2 AMPL ◮ a modeling language for optimization problems ⇒ an interface between problems and solvers ◮ easy, intuitive syntax ◮ it’s interpreted 1 ⇒ that means errors are spotted as soon as they are executed. ◮ can be used from a command line interface or ◮ by editing command files and submitting them 1 As opposed to compiled . Example r h If we knew radius r and height h , ◮ the volume would be π r 2 h ◮ qty of tin would be 2 π r 2 + 2 π rh π r 2 h must be V = 20in 3 ⇒ h = V π r 2 Variables r : radius of the can’s base h : height of the can Objective 2 π rh + 2 π r 2 ( minimize ) Constraints π r 2 h = V h > r > The tin can problem var r >= 0; var h >= 0; minimize tin_foil: 2 * 3.14 * rˆ2 + 2 * 3.14 * r * h; vol_fixed: 3.14 * rˆ2 * h = 20; AMPL: Variables The command var specifies a variable of the problem, its bounds, its type, and (possibly) an initial value. var x1 >= 0 <= 4; var numtrucks >= 3 integer default 5; var buyObj1 binary; AMPL: Constraints Constraints are preceded by a name and a “:” myconstr1: x1 + 3 * x2 + x3 <= 4; c2: numtrucks >= ntr_AZ + ntr_NY + ntr_PA; at_most_1: buyObj1 + buyObj2 + buyObj3 <= 1; AMPL: Objective function Preceded by either minimize or maximize , name of the objective, and “:” minimize xpense: 10 * numtrucks + 3 * numcars; minimize myfun: x1 * x2  2 * x3; maximize distance: x1 + 2 * cos(x3); Caveats ◮ the semicolon : all commands must end with one 2 ; ◮ comments: # this won’t be interpreted...
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