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Genetic Algorithms in Optimization Models 173

Table 5.6 Results for Hybrid Genetic Algorithms
Distance Gender * Average Maximum Time per run (sec)
Steepest descent
K ¼ 1 No 86 1452 1264 0.57
K ¼ 2 No 125 1471 1254 0.62
K ¼ 3 No 114 1469 1214 0.64
K ¼ 4 No 79 1458 1170 0.65
K ¼ 5 No 50 1449 1180 0.66
K ¼ 1 Yes 78 1452 1236 0.57
K ¼ 2 Yes 115 1469 1334 0.62
K ¼ 3 Yes 74 1460 1262 0.65
K ¼ 4 Yes 61 1448 1164 0.66
K ¼ 5 Yes 56 1440 1120 0.67
10 Levels
K ¼ 1 No 430 1510 1420 25.54
K ¼ 2 No 584 1524 1432 27.15
K ¼ 3 No 631 1528 1428 28.29
K ¼ 4 No 607 1527 1400 28.82
K ¼ 5 No 626 1528 1428 29.32
K ¼ 1 Yes 448 1511 1412 25.51
K ¼ 2 Yes 612 1525 1422 27.14
K ¼ 3 Yes 591 1525 1398 28.17
K ¼ 4 Yes 594 1526 1420 28.91
K ¼ 5 Yes 568 1524 1402 29.36
25 Levels
K ¼ 1 No 538 1518 1426 58.46
K ¼ 2 No 616 1526 1438 62.01
K ¼ 3 No 691 1532 1448 64.06
K ¼ 4 No 688 1532 1450 65.49
K ¼ 5 No 664 1531 1420 66.56
K ¼ 1 Yes 516 1517 1402 58.58
K ¼ 2 Yes 632 1527 1448 61.86
K ¼ 3 Yes 660 1530 1420 64.27
K ¼ 4 Yes 673 1531 1428 65.60
K ¼ 5 Yes 639 1529 1384 66.46
*Number of times out of 1000 that the best known solution of 1550 was obtained.

definition keeps evolving with changing environmental conditions and across species. For example,
the male bird of paradise in New Guinea is the fittest when his feathers and tail are very colorful and
attractive to the female bird of paradise. The same colorful and beautiful male would not be the
fittest in a different environment (off the island), one that is predator rich. Similarly, the peppered
moth, in England, during the Industrial Revolution would not have survived without a color
adaptation. In urban areas, the fittest was the darker peppered moth that adapted to the new gray,
ash-covered trees on which it rests. By blending into the tree, it protected itself from predators,
while at the same time, in rural areas, the peppered moth continued to thrive and survive on lichen-
covered tree branches. Unlike nature, in genetic algorithms the definition of the ‘‘fittest’’ is stable.
The more stable definition of ‘‘fittest’’ in genetic algorithms, in turn, allows for the ultimate
achievement of an ‘‘ideal’’ population, a situation not paralleled in nature.
In nature, species have to cope with invasion of other species and competition for resources.
Species diversity is rampant as genetic diversity is instrumental to adaptation. The survival of the
fittest individual leads to survival of the species. In genetic algorithms, by comparison, there is one
species only. Occasionally generating offspring who are ‘‘fitter’’ than existing members in order to
‘‘enrich’’ the population ‘‘gene pool’’ incorporates invasion in genetic algorithms. PGA allow
population movements, but those are of the same species. In compounded genetic algorithms,
there is no population movement between the isolated populations.
Offspring mutation is another natural selection tenet incorporated in genetic algorithms. Muta-
tions occur quite frequently in nature. Most mutations are not beneficial to the species, while some,