Genetic Operators Designing Research Based On Binary-encoded Theory

In virtue of the theories of binary encoding, this paper studies on the change rules of solutions in the feasible solution set, after implementing the standard genetic operations in the coding space. Based on the theories and rules of converting a binary number to a decimal one, we puts forward some concepts of genetic operators, such as crossover and mutation. These operators are only depended on the length of binary string and the position of crossover or mutation.Using the theoretic methods of division algorithm, we carry out the crossover and mutation operators on the solution individuals directly, give and prove some theories and lemmas, design new genetic operators in the integer space sequentially. Furthermore, this paper generalizes the conclusions of division algorithm in the integer space into the problems with real-valued unknown and more than one unknown, and offers the proof of theories about corresponding new genetic operators concretely.The new operators overcome the computational time-consuming burden decoding brought by the decoding process of the standard GA, which improves the computational efficiency of the standard GA to a certainty. The results of numerical simulation indicate that our new operators GA can effectively solve any optimization problems that can be solved by the standard GA, which achieves the target of enhancing GA's computational efficiency basically.