Improved Genetic Annealing Algorithm For Complex Nonlinear Equations

As a new type of Hybrid Genetic Algorithm, Genetic Annealing Algorithm is robust, versatile and so on. It been applied successfully in many areas.Solving nonlinear equation is a hot topic in the fields of industrial application and scientific research. From traditional methods such as Newton method and quasi-Newton method to evolution algorithm such as Genetic Algorithm, Coupled Neural Network Algorithm and Fish Algorithm, these methods had been used to solve nonlinear equations and made some results. However, there are some flaws in these methods which solving nonlinear equations because of the complexity of nonlinear equations. Genetic Annealing Algorithm is a good method to avoid these flaws. Based on popular of multi-core processors and multi-thread programming, taking multi-thread into Genetic Annealing Algorithm will improve its performance. Applying improved Genetic Annealing Algorithm to nonlinear equation also is an important research topic.Based on previous research and characteristics of nonlinear equations, this paper improved Genetic Annealing Algorithm and applied it to nonlinear equations. The main job of this paper is as follows:For the need of solving complex nonlinear equations with the improved Genetic Anneal Algorithm, introducing relevant knowledge and information. briefly introduce Genetic Algorithm and Simulated Annealing Algorithm in the general situation of the development, basic concept, basic principle and its application, and also introduce basic information of Genetic Annealing Algorithm. introduce the heap in basic concept, implementation method and so on, give a more deep introduce in the time complexity of heap's basic operations. Briefly introduce the basic situation of multi-thread, and make a deep analysis in its safety, liveness and performance.Based on standard Genetic Algorithm and Simulated Annealing Algorithm, a improved Genetic Annealing Algorithm whit heap been proposed for the properties of nonlinear equations and the purpose of reducing the time complexity of some key steps; In multi-core processors environment, the purpose of introducing multi-thread to Genetic Annealing Algorithm is to increase utilization of CPU; Give a discuss for the binary-division of search range to avoid repeat search in a range. Finally, algorithm is implemented in Java and simulation results indicate: compared to traditional method, the improved Genetic Annealing Algorithm for solving nonlinear equations has the advantages of good convergence and high precision; At the same time, introducing multi-threads to Genetic Annealing Algorithm and dividing the subinterval, the algorithm is more efficient and have a great improvement in performance.