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by seeding. Randomly generated solutions are the preferred method for problems about which no
a priori knowledge exists or for assessing the performance of an algorithm. However, there is the
danger that the initial population does not adequately cover all of the search space; in these cases,
researchers tend to use systematic initialisation procedures. Random initialisation of the population
can be complemented by inclusion of heuristic solutions in the initial population. This allows the
EA to use solutions provided by other algorithms. This is termed seeding and has been found to
benefit the algorithm in terms of both speed and the quality of the final solution found (Ponterosso
and Fox 1999; Alba and Cotta 2006).
The second method uses a priori knowledge about the problem. In these cases, the EA starts the
optimisation with a set of approximately known solutions and will therefore converge to an optimal
solution faster than starting with the randomly chosen initial population of solutions.
7.4.2 f itneSS f function
One of the most important components of building a successful EA is the fitness function. As
Alba and Cotta (2006) state, it is 'the unique point of interaction with the problem that is intended
to be solved'. The fitness function quantifies how well the proposed solution performs for a prob-
lem. This function could be a set of criteria that needs to be fulfilled; for example, Xiao (2008)
used population equality as the fitness function in the application of political redistricting prob-
lems or simply a goodness of fit statistic such as standardised root mean square error (SRMSE)
(Heppenstall et al. 2007a).
7.4.3 S election
In order to evolve better performing solutions, a sample of the fittest individuals of the popula-
tion are selected and randomly exposed to mutation and recombination. Individuals are nor-
mally selected through fitness-proportionate methods (see Table 7.1). This produces offspring
or what are the solutions for the next generation. The least fit solutions die out through natural
selection as they are replaced by new recombined, fitter, individuals. Evaluation of the fitness
values of the individuals involves some form of comparison between observed and model data or
a test to see if a particular solution meets a predefined criterion or constraint. For further details
on these selection types, see Whitley (2001), Bickle and Thiele (1995), CantĂș-Paz (2002) and
Goldberg and Deb (1991).
TABLE 7.1
Description of Several of the Most Common Forms of Parental Selection
Selection Type
Description
Ranking
The population of individual solutions is sorted from best to worst (based on the fitness metric).
The number of copies that an individual solution receives is given by an assignment function and is
proportional to the rank assignment of an individual. This method avoids the appearance of
superindividuals (an individual whose fitness is much better than that of the remaining individuals).
Tournament
A random number of individuals are selected from the population. The best individual from this group
is chosen as a parent for the next generation. This process is repeated until the mating pool is filled.
Roulette wheel
Individuals are mapped to contiguous segments of a line, such that each individual's segment is equal in
size to its fitness. A random number is generated and the individual whose segment spans the random
number is selected. This process is repeated until the desired number of individuals is obtained.
Truncation
Truncation sorts individuals according to their fitness (from best to worst). Only the best individuals are
selected to be parents.
 
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