Example of GA

5.8 Search Termination (Convergence Criteria)
In short, the various stopping condition are listed as follows:
• Maximum generations–The genetic algorithm stops when the specified number of generation’s have evolved.
• Elapsed time–The genetic process will end when a specified time has elapsed.
Note: If the maximum number of generation has been reached before the specified time has elapsed, the process will end.
• No change in fitness–The genetic process will end if there is no change to the population’s best fitness for a specified number of generations.
Note: If the maximum number of generation has been reached before the specified number of generation with no changes has been reached, the process will end.
• Stall generations–The algorithm stops if there is no improvement in the objective function for a sequence of consecutive generations of length Stall generations.
• Stall time limit–The algorithm stops if there is no improvement in the objective function during an interval of time in seconds equal to Stall time limit.





Example:Maximizing a Function
Consider the problem of maximizing the function, f(x) = x2
where x is permitted to vary between 0 to 31. The steps involved in solving this problem are as follows:

Step 1: For using genetic algorithms approach, one must first code the decision variable ‘x’ into a finite length string. Using a five bit (binary integer) unsigned integer, numbers between 0(00000) and 31(11111) can be obtained. The objective function here is f(x) = x2 which is to be maximized. A single generation of a genetic algorithm is performed here with encoding, selection, crossover
and mutation. To start with, select initial population at random. Here initial population of size 4 is chosen, but any number of populations can be elected based on the requirement and application. Table 1. shows an initial population randomly selected.