Optimization

In this example, a simple maximization problem that is composed of a two - parameter objective function with non- linear constraints, is discussed.

This maximization problem can be formulated as follows:

maximize 2·x + y

subject to x² + y² <= 25

x² - y² <= 7

In the following figure, this objective function and constraints are plotted. As the objective function is linear, its representation give rise to a plane. The maximum of this function is situated in the upper - right corner, where both constraints are active. This point's coordinates are:

x = 4

y = 3

In the following text box, GOAL source code for this problem is shown. You can copy this code to the clipboard and paste it in a text file:

PARAMETERS {{ REAL: x[-6;6] REAL: y[-6;6] }} MODEL {{ '*************************************************************** '***** DECLARATIONS ******************************************** '*************************************************************** 'TODO: Declare your global variables here using a Dim sentence '*************************************************************** '***** PREPROCESSING ******************************************* '*************************************************************** Sub PreProcessing() 'TODO: Add the code of the preprocessing function here 'This code will be executed only once at the beginning of the execution End Sub '*************************************************************** '***** OBJECTIVE FUNCTION ************************************** '*************************************************************** Function ObjectiveFunction() ObjectiveFunction = 2*x+y End Function '*************************************************************** '***** POSTPROCESSING ****************************************** '*************************************************************** Sub PostProcessing() 'TODO: Add the code of the postprocessing function here 'This code will be executed only once at the end of the execution End Sub }} CONSTRAINTS {{ #r1: Function Constr_1() Constr_1 = x^2 + y^2 <= 25 End Function #r2: Function Constr_2() Constr_2 = x^2 - y^2 <= 7 End Function }} ALGORITHM {{ POPULATION: 70 GENERATIONS: 100 REPRODUCTION_TYPE: 1 REPRODUCTION_PROBABILITY: 0,85 SELECTION_TYPE: 2 SELECTION_PROBABILITY: 0,85 MUTATION: 0,005 ELITISM: 1 REFRESH_PERIOD: 10 REFRESH_PERCENT: 10 }}

Send an e-mail to geneticoptimization@yahoo.es with questions or comments about this web page Last modification: 01/27/03

Send an e-mail to geneticoptimization@yahoo.es with questions or comments about this web page
Last modification: 01/27/03