The GA Procedure

Initializing the Problem Data

The GA procedure offers great flexibility in how you initialize the problem data. Either you can read data from SAS data sets that are created from other SAS procedures and DATA steps, or you can initialize the data with programming statements.

In the PROC GA statement, you can specify up to five data sets to be read with the DATA$n$= option, where $n$ is a number from 1 to 5, that can be used to initialize parameters and data vectors applicable to the optimization problem. For example, weights and rewards for a knapsack problem could be stored in the variables WEIGHT and REWARD in a SAS data set. If you specify the data set with a DATA1= option, the arrays WEIGHT and REWARD are initialized at the start of the procedure and are available for computing the objective function and evaluating the constraints with program statements. You could store the number of items and weight limit constraint in another data set, as illustrated in the sample programming statements that follow:

   data input1;
      input weight reward;
   1    5
   2    3
   4    7
   1    2
   8    3
   6    9
   2    6
   4    3
   data input2;
      input nitems limit;
   10  20

   proc ga data1 = input1  /* creates arrays weight and reward */
           data2 = input2; /* creates variables nitems and limit */

   function objective( selected[*], reward[*], nitems);
      array x[1] /nosym;
      call dynamic_array(x, nitems);
      call ReadMember(selected,1,x);
      obj = 0;
      do i=1 to nitems;
        obj = obj + reward[x[i]];

   [Other statements follow]

With these statements, the DATA1= option first establishes the arrays weight and reward from the data set input1, and the DATA2= option causes the variables nitems and limit to be created and initialized from the data set input2. The reward array and the nitems variable are then used in the objective function.

For convenience in initializing two-dimensional data such as matrices, the GA procedure provides you with the MATRIX$n$= option, where $n$ is a number from 1 to 5. A two-dimensional array is created within the GA procedure with the same name as the option, containing the numeric data in the specified data set. For example, a table of distances between cities for a traveling salesman problem could be stored as a SAS data set, and a MATRIX1= option specifying that data set would cause a two-dimensional array named MATRIX1 to be created containing the data at the start of the GA procedure. This is illustrated in the following program:

   data distance;
      input d1-d10;
   0 5 3 1 2 ...
   5 0 4 2 6 ...
   3 4 0 1 3 ... 
   proc ga matrix1 = distance;
   ncities = 10;
   call SetEncoding('S10');
   call SetObj('TSP','distances',matrix1);

   [Other statements follow]

In this example, the data set distance is used to create a two-dimensional array matrix1, where matrix1$[i,j]$ is the distance from city $i$ to city $j$. The GA procedure provides a simple traveling salesman Problem (TSP) objective function, which is specified by the user with the SetObj call. The distances between locations are specified with the distances property of the TSP objective, which is set in the call to be matrix1. Note that when a MATRIX$n$= option is used, the names of variables in the data set are not transferred to the GA procedure as they are with a DATA$n$= option; only the numeric data are transferred.

You can also initialize problem data with programming statements. The programming statements in the GA procedure are executed before the optimization process begins. The variables created and initialized can be used and modified as the optimization progresses. The programming statement syntax is much like the SAS DATA step, with a few differences (see the section Syntax: GA Procedure). Special calls are described in the next sections that enable you to specify the objective function and genetic operators, and to monitor and control the optimization process. In the following program, a two-dimensional matrix is set up with programming statements to provide the distances for a 10-city symmetric traveling salesman problem, between locations specified in a SAS data set:

   data positions;
      input x y;
   100 230
   50  20
   150 100

   proc ga data1 = positions;

   call SetEncoding('S10');
   ncities = 10;

   array distance[10,10] /nosym;

   do i = 1 to ncities;
      do j = 1 to i;
         distance[i,j] = sqrt((x[i]-x[j])**2 + (y[i] - y[j])**2);
         distance[j,i] = distance[i,j];

   call SetObj('TSP','distances', distance);

In this example, the DATA1= option creates arrays x and y containing the coordinates of the cities in an $x$-$y$ grid, read in from the positions data set. An ARRAY programming statement creates a matrix of distances between cities, and the loops calculate Euclidean distances from the position data. The ARRAY statement is used to create internal data vectors and matrices. It is similar to the ARRAY statement used in the SAS DATA step, but the /NOSYM option is used in this example to set up the array without links to other variables. This option enables the array elements to be indexed more efficiently and the array to be passed efficiently to subroutines. You should use the /NOSYM option whenever you are creating an array that might be passed as an argument to a function or call routine.