The Global Optimization Algorithm Of Filled Function And Its Application

Optimization is widely used in real life,so the theories and methods of global optimization problems have received high attention.However,non-convex programming global optimization problems generally have many local minimizers,that is,seeking the global minimizer is a very difficult problem.The filled function method is a class of deterministic algorithms that effectively solve global optimization problems,and it is a transformation of a local minimization algorithm combined with a filled function.Therefore,the filled function method has been welcomed by scholars in recent years.This paper is divided into six parts,focusing on the global optimality conditions of a class of special non-convex programming problems and the filled function method for unconstrained global optimization problems and it's applications.The first chapter,we introduce the research background and significance of global optimization problems,and the research status of global optimization filled function method and the optimality conditions of non-convex programming global optimization problems.Finally,we propose the main purpose and work of this paper.The second chapter,for the special form of programming problem with the difference between a convex function and a polynomial function with box constraints,its optimality conditions are studied.The main idea is to describe the L-subdifferential form of the programming problem firstly,and then combine the methods of L-subdifferential and L-regular cone to give two different forms of global optimal sufficiency conditions,and derive the necessary conditions for global optimality.Applying these conditions proposed above to solve the corresponding numerical examples,and finally the calculation proves that the optimality condition is feasible.The third chapter,for the unconstrained global minimization problems,we propose a one-parameter filled function,and the form does not contain exponential and logarithmic,which avoids the situation of false stationary points,and we prove its related properties.Then the new one-parameter filled function is combined with a local optimization algorithm to design a new global optimization algorithm named AFF,and the algorithm is verified through test functions.Finally,the running results are compared with previous references to verify that the algorithm AFF is effective and feasible.The fourth chapter,in order to overcome the difficulties of filled functions with parameters in the process of parameter adjustment,for the unconstrained global optimization problem,We modify the definition of the filled function and propose a new filled function without parameter,then use the same method as in the third chapter,and we design the corresponding algorithm ANFF.Finally,some test functions were given to verify its effectiveness,and it was compared with other references.The fifth chapter,the two algorithms above-mentioned are applied to the prediction of renal cell carcinoma metastasis pathological analysis and the analysis of advertising costs and utility.In the first application,we introduced the Sigmoid function and crossentropy loss function for classification processing with reference to the neural network model to establish the optimization model,and then used the global optimization algorithm AFF to solve the model.The verification accuracy of the algorithm was 83.33%.In the second application,the first step is to obtain two important factors,the relationship between the company's actual sales volume and price,and the relationship between the sales growth factor and advertising costs.Then,a model is established based on the principle of profit maximization,which is Transformed into a minimization model,and finally solved it with the global optimization algorithm ANFF to get the company's maximum profit.The last chapter,summarizes the research work of this paper,puts forward the deficiencies,and makes further prospects for future research.