Research On Optimization Algorithms Based On Smoothing Technique And Filled Function

The practical application scenarios of global optimization methods are numerous,including many fields in the real world such as engineering design,intelligent transportation,financial economy and image processing.In recent years,as the complexity and scale of the objective function increase,it is difficult for the traditional optimization methods to find a global optimal solution.The difficulties are mainly reflected in two aspects: firstly,the objective function has a large number of local minima,which is a challenge to the efficiency of the optimization algorithm;Secondly,the optimization algorithm is easy to fall into the current valley and difficult to jump to another valley,aggravating the difficulty in obtaining the global minimizer.Aiming at the above difficulties,this paper studies effective solutions and puts forward the corresponding optimization algorithms.Filled function method as an efficient and deterministic global optimization algorithm,whose main principle is: the objective function is minimized to obtain its minimizer,and how to jump out of the valley to find a better solution would rely on the filled function.A novel filled function is constructed and a local search is performed to obtain its minimizer,then according to the unique property of the filled function,the point must be located in a better valley of target function,and by searching the target function in the valley,we can obtain a better solution.Thus we can use above process to prevent algorithm from falling into local minimizers.Using the smoothing technique to process the objective function,which can eliminate all such points worse than the current local minimizer and keep the same or better points unchanged.The technique can significantly cut down the number of local minima and raise the efficiency of the algorithm.Combining the smoothing technique and the filled function method,this paper proposes two efficient optimization algorithms.The main work is as follows:(1)In order to solve the problems that the objective function has a large number of local minima and algorithms are easy to fall into the current valley,we put forward a new filled function method based on smoothing technique and adaptive strategy.Smoothing technique is used to smooth the objective function,and a new one parameter filled function is constructed on the processed objective function.In the filled function,a constant coefficient is added to adjust the range of the objective function value,which can greatly reduce the difficulty of parameter adjustment of the filled function.At the same time,for improving the searching efficiency of the filled function,we put forward a deterministic method to generate initial points based on the position relation between the current minimizer and the previous local minimizer and the domain.Combining the above methods,we put forward a new filled function algorithm.(2)To put forward a more effective global optimization algorithm,we construct another new filled function based on smoothing technique,which contains only one parameter and does not include any index entry,thus the adjustment of the parameter is more convenient.Traditional filled function methods usually move the fixed step size in fixed directions to generate initial points.Apparently,the above method fail to consider the difference of problems and the quality of the points,and the searching efficiency is low.To tackle this problem,we absorb the idea of simplex method and design a new method to determine the initial search points of the filled function by using reflection,expansion and contraction operations.Since the method adds random strategy and local search ability to the optimization process,the optimization efficiency is improved.Based on these methods,a new filled function algorithm is proposed.Finally,we use 12 widely used standard test functions to carry out numerical experiments on the new algorithms,and select four representative filled function algorithms for detail comparison and analysis.The experimental results show that the proposed algorithms are effective and efficient.