Convergence Criteria

The ideal convergence criterion for a genetic algorithm would be one that guaranteed that each and all of the parameters converge independently Beasley et al. (1993a); Goldberg (1989). However, this may be too demanding or may result in too many iterations, so more relaxed convergence criteria are usually employed. Here I used four convergence criteria:

1.

The fitness function value must be below a given threshold value.

2.

The difference between the best and the average fitness is less than a given fraction of the fitness of the average individual.

3.

The difference between the best individual of the current population and the best individual so far must be very small (even zero). This means that the most fit individual has converged even if the population itself has not.

4.

the number of iterations (generations of the sample population) exceeds a given limit. This prevents the algorithm from spending too much time refining an existing solution.

The combination of these criteria is intended to guarantee that the solution is not due to a lucky guess of the random generator but to a comprehensive search of the model space.