Convergence

In general, establishing the convergence of a genetic-algorithm optimization may not be an easy matter because we do not know for sure if the algorithm has converged to a local or global minimum. In the first case we would like the algorithm to continue exploring the search space and in the second case we would like the algorithm to stop. There are several different ways in which we can proceed, for example:

• Set a threshold for the minimum cost function that constitutes an acceptable solution and stop the algorithm when this value is reached. The problem with this approach is that in some cases it may be too difficult to establish a priori what a good threshold should be.
• Set a threshold for the difference between the best and the average fit individual in the population. This has the advantage of not requiring a priori knowledge of the actual cost function values.
• Set a threshold for the difference between the best individuals of the present and the previous generation or generations. This has the advantage of preventing the algorithm from attempting to refine the search too much by slowly crawling to the bottom of the valley.
• Set a maximum number of generations to be evolved. This is a fail safe criterion which can be useful when comparing the performance of genetic algorithms with different combination of evolution parameters.

In most cases a combination of two or more of these and similar criteria are employed.