Degree preserving based crossover for constrained optimization problems

Real-coded genetic algorithms (RCGAs) have been effectively used to solve constrained optimization problems (COPs). However, the crossover operators do not have mechanisms to handle constraints and there is no guarantee that if the parents satisfy some constraints the offspring will satisfy them as well. Degree preserving based crossover operators are proposed to increase the probability of constructing feasible offspring and preserve the generated partial solutions which satisfy some constraints. A new concept of the feasibility degree (FD) of the building blocks of feasible solutions (BBFSs) based on the schema theorem and building block hypothesis is also proposed to measure the probability of an individual which contains the BBFS being a feasible solution. Therefore, feasible offspring can be constructed by mixing the building blocks of feasible solutions and the generated partial solutions which satisfy some constraints can be preserved. The theoretical validity of the new crossover operators is proved by the schema theorem and the mixing ladder climbing model. Finally, the proposed crossover operators were tested with benchmark problems and the results proved the efficiency of the operators.