Classical Genetic Algorithms

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numerical optimization algorithms which are inspired by the species evolution in the natural world. More specifically, the GA approach imitates the adaptation phenomenon of species by both natural selection and natural genetics. After it was first introduced by Holland in 1960s, this approach has been gaining a growing following in the physical, computer systems, social science and in engineering (Coley 1999).

A classical GA initialized with a population of random guesses within the search space instead of starting from a single guess. These guesses are called as the individuals of the population and each individual represents a potential solution of the optimization problem. Typically, an individual in a population is modeled as a binary encoding string that divided into several sub-strings, which has a similar structure with a chromosome. Each sub-string simulates a single gene of the chromosome that corresponds to a true variable for an optimization problem. A typical binary encoding string or chromosome with 𝑁_𝑣𝑎𝑟 genes is shown in Figure 4.1. A simple GA utilizes selection, crossover and mutation as the three main operators to direct the evolution of the population. These numerical operators are developed by analogy with the mechanisms of the natural selection, genetic crossover and the genetic mutation during the species evolution. With a series of generations processed by the operators and the appropriate maintenance of population diversity, the population are normally directed towards convergence at the global optimum of the search space (Mitchell 1998).

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4.1.1 Selection

Selection is defined as a fundamental operator to apply the evolutionary pressure upon the population similar to natural selection existing in biological systems. Individuals with poorer performance (e.g. lower fitness) in a population are weeded out during process of selection (Mitchell 1998). In contrast, individuals with better performance (e.g. higher fitness) are provided a greater probability of transferring the characteristic they contain to the next generation. In terms of engineering optimization problems, the fitness function (or cost function) for evaluating the fitness of each individual, should be established properly regarding the balance of the considered optimization objectives. Rather than using the simple method that selecting the best 50% of the individuals to reproduce and weed out the rest individuals, a more applicable and useful selection operator called fitness-proportional or roulette wheel selection is commonly recommended. With the application of this approach as illustrated in Figure 4.2, the probability for determining a selected individual is directly proportional to the fitness of this individual and hence the distinctions can be made between different fitness levels (Coley 1999).

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4.1.2 Crossover

Crossover makes use of the exchange of the binary sub-strings to swap the information or characteristics within pairs of individuals, which is similar to the natural organism undergoing sexual reproduction. This operator provides a method to maintain the exploration of the search space for differing the potential solutions of the optimization problem, that could be analogy with the enhancement of diversity for species population in ecological systems (Coley 1999). While there are other sophisticated recombination operators for crossover, single point crossover is still considered as a common operator of crossover. In accordance to the implementations of this operator, pairs individuals processed by the selection operator are selected and stochastically cut at a single point within the binary strings to divide them into sub-strings. Then the sub strings are forced to swap between the two individuals to create pairs of child strings. Figure 4.3 provides an intuitional explanation for the process of crossover. The probability 𝑃_𝐶, which dominates the selections for the pairs of individuals undergoing crossover, should be normally defined around 0.4 to 0.9 (Mitchell 1998).

Figure 4.3 The process of crossover

4.1.3 Mutation

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the gene replication. In terms of the representation of a binary encoding in genetic algorithms, mutation is manually implemented by flipping the values of random single bits within the individual encoding strings. In addition, the probability of mutation 𝑃𝐶 is commonly assigned a sparing value (e.g. from

0.001 to 0.01), in order to slow down the rate of population convergence to guarantee enough exploration for the search space (Coley 1999).

4.1.4 Additional Optional Settings

As it is known, roulette wheel selection (or some other selection operators) could not always guarantee the selection for a fittest individual, unless the fitness of this individual is extremely higher than others. Therefore, the best solution in a generation and some superior solutions to the global optimization problem, that normally contain desired ‘genes’ can be occasionally weed out during the process of selection. This potentially slows down the convergence process of the population evolution, which results in a waste of computational time. To prevent the population from undergoing the unnecessary search space and to maintain the superior features for the population, the ‘elite’ individuals in a generation can be directly transferred to the next generation. This can be simply achieved by defining the number of the elite individuals to be propagated to the next generation. Ensuring the inheritance of the superior individuals for every generations is called as ‘elitism’ in genetic algorithms.

Another optional setting is for the initialization of the population. As is mention above, the initial population of GA is normally assigned with a series of random individuals. In attempt to improve the computational time, GA can be adjusted to initial with individuals that are estimated to have high performing values of the problem.

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