GAs: Selected Topics

Abstract

GA theory provides some explanation why, for a given problem formulation, we may obtain convergence to the sought optimal point. Unfortunately, practical applications do not always follow the theory, with the main reasons being:

• the coding of the problem often moves the GA to operate in a different space than that of the problem itself,

• there is a limit on the hypothetically unlimited number of iterations, and

• there is a limit on the hypothetically unlimited population size.

One of the implications of these observations is the inability of GAs, under certain conditions, to find the optimal solutions; such failures are caused by a premature convergence to a local optimum. The premature convergence is a common problem of genetic algorithms and other optimization algorithms. If convergence occurs too rapidly, then the valuable information developed in part of the population is often lost. Implementations of genetic algorithms are prone to converge prematurely before the optimal solution has been found, as stated in [46]:

“...While the performance of most implementations is comparable to or better than the performance of many other search techniques, it [GA] still fails to live up to the high expectations engendered by the theory. The problem is that, while the theory points to sampling rates and search behavior in the limit, any implementation uses a finite population or set of sample points. Estimates based on finite samples inevitably have a sampling error and lead to search trajectories much different from those theoretically predicted. This problem is manifested in practice as a premature loss of diversity in the population with the search converging to a sub-optimal solution.”

Eshelman and Schaffer [105] discuss a few strategies for combating premature convergence; these include (1) a mating strategy, called incest prevention,¹ (2) a use of uniform crossover (see section 4.6), and (3) detecting duplicate strings in the population (similar to the crowding model; see section 4.1).

A man once saw a butterfly struggling to emerge from its cocoon, too slowly for his taste, so he began to blow on it gently. The warmth of his breath speeded up the process all right. But what emerged was not a butterfly but a creature with mangled wings.

Anthony de Mello, One Minute Wisdom