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The coordinates of point N are found by

R(LARGEST 0)

f2 R'iNEXT LARGEST 0)

R(LARGEST 0)

f2 R'iNEXT LARGEST 0)

(1) Evaluate O at each of the vertices. Number of vertices > number of search variables.

(2) Compute centroid Ai based on points 1, 2, 4, and locate point N.

(4) If C^ > 0R , evaluate Q, ; if 0M <0R, accept point M and reject R.

(5) If 0N > 0R, 0Si > 0R, repeat procedure for the next poorest point R

Figure 9-6 Graphical representation of Box's method.

If the value of 0 at xN is less than its value at the rejected point R, then the new point N is accepted. If the new point N gives a poorer value for the objective function than that given by the rejected point R, then the value of the objective function at the centroid M is found. If the value of the objective function at the centroid M is less than its value at the rejected point R, then the centroid M is accepted as the new point. Otherwise, if neither N nor M give a smaller value for 0 than does the rejected point R, then the rejected point of the simplex is retained, and the next poorest point of the simplex is selected as the rejected point and the procedure described above is repeated.

Integral values for the number of plates were found by rounding the corresponding values of xitJ to the nearest integer. For example, if the value of xitj corresponding to the number of plates in a given section is found to be 5.6, then the integral number of plates used for this section of the column in the evaluation of the objective function was taken equal to 6. If, however, a value of x, j = 5.4 is found, then the corresponding integral number of plates was taken equal to 5 in the evaluation of the objective function. The original values of x, j (5.6 or 5.4) were used, however, in the subsequent generation of vertices.

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