**2.1 Initialization**

At the first iteration many individual solutions are randomly generated to form the population. The population size depends on the nature of the problem, but typically contains several hundreds or thousands of possible solutions. Traditionally, the population is generated randomly, covering the entire range of possible solutions (the search space).

### **2.2 Selection**

During each successive generation, a proportion of the existing population is selected to breed a new generation. Individual solutions are selected through a fitness-based process, where fitter solutions (as measured by a fitness function) are typically more likely to be selected. Certain selection methods rate the fitness of each solution and preferentially select the best solutions. Other methods rate only a random sample of the population, as this process may be very time-consuming.

Fringe Pattern Demodulation Using Evolutionary Algorithms 85

Stochastic universal sampling (SUS) is a technique used in genetic algorithms for selecting

SUS is a development of fitness proportionate selection which exhibits no bias and minimal spread. Where fitness proportionate selection chooses several solutions from the population by repeated random sampling, SUS uses a single random value to sample all of the solutions

While candidate solutions with a higher fitness will be less likely to be eliminated, there is still a chance that they may be. Contrast this with a less sophisticated selection algorithm, such as truncation selection, which will eliminate a fixed percentage of the weakest candidates. With fitness proportionate selection there is a chance some weaker solutions may survive the selection process; this is an advantage, as though a solution may be weak, it may include some component which could prove useful following the recombination

The analogy to a roulette wheel can be envisaged by imagining a roulette wheel in which each candidate solution represents a pocket on the wheel; the size of the pockets are proportionate to the probability of selection of the solution. Selecting *N* chromosomes from the population is equivalent to playing *N* games on the roulette wheel, as each candidate is

It involves running several "tournaments" among a few individuals chosen at random from the population. The winner of each tournament (the one with the best fitness) is selected for crossover. Selection pressure is easily adjusted by changing the tournament size; if it is

Deterministic tournament selection selects the best individual (when *p* 1 *)* in any tournament. A *1-way* tournament ( *k* 1 ) selection is equivalent to random selection. The chosen individual can be removed from the population that the selection is made from if it is desired, otherwise individuals can be selected more than once for the next generation.

Tournament selection has several benefits: it is efficient to code, works on parallel

Crossover is a genetic operator used to vary the programming of a chromosome or chromosomes from one generation to the next. It is analogous to reproduction and biological crossover, upon which genetic algorithms are based. Cross over is a process of taking more

larger, weak individuals have a smaller chance to be selected.

architectures and allows the selection pressure to be easily adjusted.

than one parent solutions and producing a child solution from them.

potentially useful solutions for recombination. It was introduced by James Baker.

**2.2.2 Stochastic universal sampling** 

by choosing them at evenly spaced intervals.

process.

drawn independently.

**2.3 Crossover** 

Crossover techniques :

 One-point crossover (fig. 8a). Two-point crossover (fig. 8b).

**2.2.3 Tournament selection** 

A generic selection procedure may be implemented as follows:


Retaining the best individuals in a generation unchanged in the next generation, is called elitism or elitist selection. It is a successful (slight) variant of the general process of constructing a new population.
