Lethalization, penalty and repair functions for constraint handling in the genetic algorithm methodology

A genetic algorithm was designed to find low energy distributions of ions above a crystal surface. To solve this constrained optimization problem, several constrained handling techniques were applied, i.e., lethalization, penalty and repair functions. It was shown that the simple lethalization scheme performs very well, and was at least comparable to some of the penalty functions. This was unexpected because, in general, it is believed that a severe penalization (i.e., lethalization) leads to poor results. An analysis of the fitnesses of trial distributions that violated a constraint as a function of the time, suggested that the properties of genetic based search were responsible for this result. From this it was concluded that a genetic algorithm in combination with lethalization may be an good choice to solve constrained optimization problems if the design of optimal penalty functions is difficult or impossible.