Crossover and mutation in genetic algorithms employing canonical signed-digit number system

In this paper, a novel approach is presented for the restoration of canonical signed-digit (CSD) numbers to their correct format after the application of crossover and mutation operations in genetic algorithms. The proposed approach has two main distinct features: First, it employs the same restoration process for both crossover and mutation operations, yielding the process as uniform. Second, it is based on a local, as opposed to global, restoration of the produced offspring numbers, making the corresponding computational implementation efficient. A new technique is also proposed to predict the illegal break-points for the crossover and the illegal bit-locations for the mutation operation, preventing the possibility of generating any out-of-range CSD numbers. An application example is given to illustrate the results.