Research On Cuckoo Algorithm And Improved Algorithm For Solving Nonlinear Algebraic Equations

It is difficult for solving the nonlinear algebraic equations in numerical calculation. If solved well, it will have a profound impact on engineering technology, economy, financial and scientific computing. However, the traditional method has limitations of low accuracy and computational complexity. In recent years, although intelligent optimization algorithms with high adaptness and robustness is widely applied to solving the problem of nonlinear algebraic equations, the convergence speed and accuracy of intelligent optimization algorithms is still not up to the requirements. The intelligent optimization algorithms for solving high dimensional nonlinear algebraic equations are not stable, and some of intelligent optimization algorithms even cannot solve these problems.The cuckoo search algorithm is a swarm intelligence optimization algorithm, which not only has an advantage of simple operation and programming, but also has few parameters and ability of global optimization. Therefore, in conclusion of the previous researches, the cuckoo search algorithm is applied to solve nonlinear algebraic equations. For the problem of multi-solution of nonlinear algebraic equation solution, this paper shows the fitness sharing niche cuckoo search algorithm.In this paper, the using of multi-modal function optimization problem is to verify the validity of the algorithm. Simulation results show that the improved algorithm and the cuckoo algorithm have high advantages of calculation speed and accuracy. On this basis, the cuckoo algorithm which solving typical nonlinear algebraic equations verifies the advantage of high speed and precision of cuckoo search algorithm. Subsequently, for the nonlinear algebraic equations to solve multi-solution problem of high dimension, the paper proposes an improved cuckoo search algorithm, which is based on fitness sharing niche cuckoo search algorithm. The results of numerical experiments show that the improved cuckoo search algorithm can search more solutions, and get higher success rate. In addition, the cuckoo and its improved algorithm are analyzed with the sensitivity of parameters in the future. The results show that the accuracy of solution is not affected by the length of the interval. With the decrease of the number of nests and the increase of discard probability, it may decrease accuracy, in turn increasing time. The number of niche is appropriate to choice between upper and lower double of the number of solutions. Not only can reasonable selection of these parameters improve the accuracy of the solution, but also reduce the computation time. Therefore, in one hand, this paper improves the accuracy of solution and convergence speed of the nonlinear algebraic equations, in the other hand it provides a new way for solving the problem of the nonlinear algebraic equations with the high dimensional and multi solution.