Genetic algorithms in constrained optimization

The behavior of the two-point crossover operator, on candidate solutions to an optimization problem that is restricted to integer values and by some set of constraints, is investigated theoretically. This leads to the development of new genetic operators for the case in which the constraint system is linear. The computational difficulty asserted by many optimization problems has lead to exploration of a class of randomized algorithms based on biological adaption. The considerable interest that surrounds these evolutionary algorithms is largely centered on problems that have defied satisfactory illation by traditional means because of badly behaved or noisy objective functions, high dimensionality, or intractable algorithmic complexity. Under such conditions, these alternative methods have often proved invaluable. Despite their attraction, the applicability of evolutionary algorithms has been limited by a deficiency of general techniques to manage constraints, and the difficulty is compounded when the decision variables are discrete. Several new genetic operators are presented here that are guaranteed to preserve the feasibility of discrete aspirant solutions with respect to a system of linear constraints. To avoid performance degradation as the probability of finding a feasible and meaningful information exchange between two candidate solutions decreases, relaxations of the modified genetic crossover operator are also proposed. The effective utilization of these also suggests a manipulation of the genetic algorithm itself, in which the population is evanescently permitted to grow beyond its normal size