Genetic algorithm with double roulette wheels

Double roulette wheels genetic algorithm was proposed to deal with the inequality constraints directly. Deferent fitness function was built for the feasible and infeasible individual in the population, respectively. The fitness function of the feasible individual reflected the objective function value; the fitness function of the infeasible individual reflected the degree of which the constraints were satisfied. Double roulette wheels was employed to select them respectively. A formula to decide the rotation times of each roulette wheel was given to make the feasible individual has greater probability to be selected than the infeasible ones. During the evolution, the individuals could move to the feasible region automatically. Then the inequality constraints were dealt with in a directive way and all infeasible initial population could be allowed. In addition, an improved real-coding copulation operator was also raised. This operator has more detecting ability than the classical two points inner interpolative operator. Examples show that the algorithm is not only an easy way to give global solution but also a simple and high effective method to deal with the inequality constraints.