The Improvement And Application Of Multi-scale Quantum Harmonic Oscillator Algorithm

For global optimization problems,the multi-scale quantum harmonic oscillator algorithm(MQHOA)is a novel optimization algorithm based on the wave function of quantum harmonic oscillator.In addition to its concision on parameters' settings and superior optimization speed,it can obtain high accurate solutions for the low dimensional functions.But for high dimensional problems,MQHOA's scales can't be regulated dynamically,which leads to convergence difficulties,and it lacks appropriate memory mechanisms.This paper is proposed to improve MQHOA.It's inspired by estimation of multivariate normal algorithm(EMNA)to improve the method of generating covariance matrix.In order to solve the problems of the original MQHOA's convergence process in both the quantum harmonic oscillator(QHO)and multi scales(M).The dynamic scales are applied to speed up the update rate of the new covariance matrix and to solve realistic problems.The main contents of this paper can be summarized as follows:(1)Improvement of QHO convergence process.QHO convergence is QHO's a horizontal search in solution space.It realizes the positioning and focusing of the solution space.But the core part of original algorithm in convergence process is the gathering of multi single-scale gauss distributions which lack sufficient interactive information of sampling points.The dimensions of single center sampling point are independent of each other.For this reason,the covariance matrix composed of the sampling points is introduced.It is improved to make the convergence direction of the algorithm consistent with the gradient direction of the optimization problem.Considering that the original algorithm is lack of memory,the learning rate is added to make the new covariance matrix gain most information from previous generations' covariance matrices,and the updated covariance matrix information is gained from current covariance matrix.This method greatly utilizes sampling points,and the experimental results show that the improved algorithm has higher precision.(2)Improvement of M convergence process.The mechanism of fixed-scales attenuation is used in M convergence process of the original MQHOA,which ignores the search of important dimensions.This paper introduces the mechanism of dynamicscales attenuation in each dimension.The scale is determined by the attenuation situation of current search.The experimental results show that the convergence speed of the new algorithm with improved M convergence process is much faster than that of the original algorithm.(3)This paper divides 18 evaluation functions into 3 groups to compare with 4 classic optimization algorithms in 30 and 500 dimensions.The experimental results are analyzed in terms of convergence accuracy,convergence speed,robustness and time cost,and it shows that the MQHOA based on covariance matrix is better.In addition,several excellent algorithms are selected to compare with the improved algorithm,and the experimental results also show its ability to deal with high dimensional complex problems.(4)The improved MQHOA algorithm is applied to cluster analysis.Each partition scheme of clusters corresponds to a solution which can be encoded.This paper selects both internal and external reasonable evaluation criteria to construct the fitness function.what's more,the clustering process of K-means algorithm is optimized.In experiment,we select the UCI standard high dimensional data set and the low dimensional and multi-cluster data set.Compared with other optimization algorithms,it has better optimization effect.