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Genetic Algorithms in Optimization Models 163

effect genetic diversity has on evolution. Some researchers refer to this modification as injection.
Salhi and Gamal (2003) propose to inject into the population once in a while a few chromosomes,
which are either randomly generated or obtained from another heuristic. The injection rate is not
necessarily constant but can slightly decrease with the number of generations.
Invasion is also common in nature in the distribution of plants and animals. In such cases,
competition for resources ensues. This competition with the invading species may signal the
extinction of the native species if they are less fit.

5.3.6 Gender

In nature, most advanced species require two genders in order to mate and reproduce. The gender
modification attempts to mimic this natural process. One can argue that the division into two
genders was selected over time as the preferred way for producing offspring and is therefore
superior to other possible mating schemes. In gender-specific genetic algorithms, the diversity of
the population is better maintained with no detrimental effects on run time.
It is easy to ‘‘convert’’ a given genetic algorithm to a gender-specific one. Three minor
modifications are suggested (Drezner and Drezner, 2005):

1. When the starting population is generated, half the population members are designated as males and
half are designated as females. The assignment of gender is done at random and no characteristic of
the population member is used for such determination.
2. When selecting two parents, the first parent is randomly selected while the second is randomly
selected from the pool of the opposite gender.
3. When an offspring is generated, it is randomly assigned a gender with a 50% probability of being
assigned a male gender and 50% probability a female. Again, no characteristic of the offspring
should be used to determine its gender.
No extra effort is required for the implementation of the gender-specific modification. A vector
of genders for population members needs to be maintained, along with the gender determined for
each offspring. In Drezner and Drezner (2005) it has been statistically shown that the gender-
specific algorithm significantly improves the solutions on four sets of problems.
Note that it is important that an offspring’s gender is randomly determined. An early attempt
(Allenson, 1992) for the gender line a modification failed because it was suggested that the
offspring is assigned the gender of the discarded population member. The rationale for his rule is
to keep the population half males and half females. But this rule is inconsistent with nature. The
concern is that if the population becomes all males or all females no further evolution is possible.
The evolutionary process must be terminated prematurely if such a population structure evolves. In
Drezner and Drezner (2005), it is shown that for a sufficiently large population (50 or more
members), the probability that all population members will have the same gender is extremely
low and can be ignored.

5.3.7 Distance-Based Parent Selection

All human cultures prohibit marriage between siblings or between parents and children (genetically
similar pairs). In societies where marriages are arranged, similarity in socio-economic standing, but
not genetic make-up, is prevalent. Some plants avoid pollination from genetically similar or
identical individuals because self-pollination or pollination by ‘‘siblings’’ is typically unsuccessful,
a phenomenon referred to in biology as ‘‘inbreeding depression.’’ Mating between close relatives
often results in less fit offspring. Another, less well known biological fact, is that mating between
genetically distant members of the same species can lead to a decline in offspring fitness, a
condition known as ‘‘outbreeding depression’’ or ‘‘hybrid breakdown.’’ Some species avoid pol-
lination from individuals that are geographically distant or genetically dissimilar, as offspring