Genetic algorithm/neural network synergy for nonlinearly constrained optimization problems

Michalewicz and Janikow (1991) proposed a methodology for applying genetic algorithms to constrained optimization problems in which the constraint equations are linear. They show that the set of feasible solutions can be more thoroughly searched by requiring the genetic population to remain in the set of feasible solutions and propose adopting a weighted average rule for combining parent gene strings in genetic crossover. Because the set of feasible solutions is convex, the population remains feasible. Unfortunately, this technique does not extend to the general case of nonlinear constraints. The purpose of this paper is to present a general technique by which a population can be restricted to a set of feasible solutions, even when the constraints are nonlinear. The technique combines the strengths of neural networks with the strengths of genetic algorithms by substituting a neural network operator for the usual method of genetic crossover