Research On Global Optimization Algorithm Based On Deflation Techniques And Genetic Evolution

With the progress of science and technology,the focus of the world has gradually changed from physical industry to digital industry.In the process of this transformation,the importance of optimization algorithm is becoming more and more obvious.As a branch of optimization algorithm,global optimization algorithm has been paid more and more attention because of its important role in artificial intelligence,image processing and information communication.In the era of big data,the amount of data expands exponentially,and the optimization problems often have the characteristics of high dimension and extreme ill-condition,which makes it difficult for the existing optimization algorithms to effectively solve its global optimal solution.From the perspective of ODE,this paper first improves the traditional continuous Newton method and designs a continuation Newton flow method(CNMTr)which can effectively solve nonlinear equations.Then,by introducing the generalized inverse,the continuation Newton flow method can effectively deal with the problem of underdetermined nonlinear equations.In this paper,an adaptive Jacobian matrix updating strategy similar to the quasi Newton method is proposed,which effectively improves the computational efficiency of the continuation Newton flow method.Numerical results show that the continuation Newton method proposed in this paper can greatly improve the efficiency and robustness of the algorithm for nonlinear equations,and its calculation time is 1/8 to 1/50 of that of the traditional Levenberg-Marquardt method.Then,this paper improves the deflation techniques and combines it with the continuation Newton flow method to effectively improve the problems of numerical overflow and underflow,so that the algorithm can obtain as many stable points of the objective function as possible.In this paper,the genetic algorithm is used to find the global optimal solution of the unconstrained optimization problems.Finally,this paper tests the proposed algorithm with the general test set,and compares it with international advanced global optimization algorithms,such as Couenne,a global optimization algorithm based on branch and bound technology,representative global optimization methods based on derivative-free method(CMA-ES,MCS)and GlobalSearch,a global optimization method based on multi-start method,Numerical results show that the proposed algorithm(CNMGE)is more robust and efficient than the existing representative methods,and can effectively solve the global optimal solution of large-scale unconstrained optimization problems.