By Zenon Waszczyszyn
ISBN-10: 3211997679
ISBN-13: 9783211997673
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Having constructed the convex hull for Si , the algorithm then adds one point at a time from S to Si updating Genetic Algorithms for Design 49 the convex hull as it progresses. For example, consider a finite set of points S p 1 p 2 p 3p n (18) The convex hull is initialised using a tetrahedron which is defined by four points taken from S. The base of the tetrahedron is formed by 3 non-collinear points and a fourth point at its apex, non-coplanar with the first three (if S does not contain these points, then it is a 2D set and invalid for this problem).
This makes the choice of operator a matter of vital importance. As discussed in the preceding chapter, the usual crossover mechanism uses a mask and the components are swapped directly. For the problem shown in Figure 29 above, the problem is essentially two dimensional and so mask based crossover in two dimensional form works as shown below in Figure 30. However, experience has shown that using this form of Genetic Algorithms for Design 45 Figure 30. Two dimensional crossover using a conventional mask (Zhang and Miles, 2004) .
Unlike BGRID, that restricts the new spacing to a value between the two adjacent genes, the new system simply generates a random spacing and, if required, sorts the genome so that the column spacings increase from left to right. Having altered its genome, the section is placed back into the building and all adjacent sections are updated (Figure 19). This final step means the mutation operator is able to modify the building in only one location but the change ripples throughout the building preventing column alignments degenerating.
Advances of Soft Computing in Engineering by Zenon Waszczyszyn
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