Selecting potential solutions

The selection process begins when the fitness has been calculated for all individual solutions in the population. Generally, the selection process is partially stochastic and biased towards better chromosomes in order that the GA can move forward. This is because if the selection was completely deterministic, the population would soon be dominated by the fittest chromosome and would quickly become homogenous before the desired solution is reached (Cartwright, 2008b). This phenomenon is known as premature convergence. However, if the solution did not have some guidance for selecting a fitter chromosome, the search would be largely random and the selected chromosome might not be the fittest chromosome, instead, it could be the poorest chromosome in the population. The process will then further deteriorate in subsequent evolutionary operations. Two widely adopted selection mechanism in a GA are the roulette wheel and the tournament selection.

Roulette wheel selection, also known as proportionate selection, ranked the GA chromosomes based on their fitness proportions in the current population. For roulette wheel selection, every individual chromosome is

assigned a slot, sized on the proportion of its fitness, on a virtual board. The better chromosome, normally, has a larger slot than the poorer chromosome. The wheel is then spun and the chromosome, into whose slot the virtual ball falls, is copied into the parent pool, i.e. the repository in which the chromosomes have a chance to mate. The selection process is repeated to pick the complement chromosomes until the parent pool is full. Roulette wheel selection leads to the fast convergence of chromosomes with larger fitness proportions being more likely to be picked than those chromosomes with smaller proportions, however, it cannot guarantee that the selected chromosomes are optimal. In addition, roulette wheel selection lacks stochastic power as the population is easily dominated by fitter chromosomes which, consequently, leaves an insufficient resource for the genetic mechanism to further exploit the population, resulting in the loss of better chromosomes being found.

Tournament selection, on the other hand, ranked the GA chromosomes based on the competition basis of at least two or more chromosomes. For a typical tournament selection, two chromosomes are randomly chosen from the population and compared. The chromosome with the greater fitness is selected and copied into the parent pool. The selection process is repeated, to yield a group of competent chromosomes in the parent pool. Since the tournament selection randomly picks chromosomes, the consequent results may vary each time the process is performed and fitter chromosomes may participate more than once in the competition. Even so, tournament selection often yields a more diverse population than roulette wheel selection (Mitchell, 1997b) and it leads to deeper exploitation of the chromosome search. A known benefit of tournament selection is that it provides a certain level of confidence of the selected chromosome being fitter than those not being picked. In addition, it also guarantee that the poorest chromosome will never be selected. The downside of this method is that it takes a longer time to identify fitter chromosomes than roulette wheel selection. Cartwright (2008b) noticed that both roulette wheel and tournament selections have a lack of stochastic features, as a result, neither can guarantee that the best chromosome, in the current generation, will be chosen again in the next generation. Therefore, a new hybrid-based selection was introduced to overcome the pitfall of roulette wheel and tournament selections, i.e. stochastic remainder selection.

Stochastic remainder selection is a hybrid method that combines a stochastic element with a deterministic step to ensure that the best chromosome in the current generation is never overlooked in the next generation. In stochastic remainder selection, the fitnesses of chromosomes are scaled in accordance with the average chromosome fitness of 1.0 (Cartwright, 2008b). Each chromosome is copied into the parent pool and the number of copies is based on the integer part of the average fitness. The fitness of the chromosome is then subtracted from the average fitness and yields a residual fitness value which must be below 1.0. A modified roulette wheel or tournament selection is then performed using these residual values to fill the remaining space in the parent pool. The deterministic step in the stochastic remainder selection ensures that every

chromosome with a fitness above 1.0 will appear at least once in the parent pool.

Goldberg and Deb (1990) criticised that by using suitable adjustment of selection parameters, except the roulette wheel selection, a similar performance can be achieved with most selection methods, thus, there is no absolute better selection method in the GA. They made such observations based on four different selection schemes: roulette wheel, tournament selection, fitness ranking and steady state selection.

In our design, to avoid the poorest chromosome being selected into the next generation and to prevent the premature convergence in our model, we chose the tournament selection. Additionally, we also applied the elitism strategy to retain fitter chromosomes in the parent pool.