Research On Multimodal Function Extremum Recognition Algorithm Based On Selection Features

In applications,it is a common solution to convert the actual engineering problem into a multimodal function problem.The problem of multimodal function optimization is generally to find the global optimal solution in the feasible region.However,the global optimal solution is not applicable under any conditions,which requires the local optimal solution of the multimodal function that is the extremum of the multimodal function.Therefore,researching the method that is to solve the extreme value of multimodal function is not only beneficial to the practical engineering application,but also has important scientific research value.This paper studies the multimodal function to solve the local optimal solution,and proposes an algorithm named Multivariate Subset Mean Features(MSMF for short).The research contents are as follows:1.The concept of the mean value of selected subset smY and the method of calculating smY using MSMF method are given.It is proved that smY has the property of continuity and additivity.The shortcoming of smY is found in the feature recognition.The concept of the width-not-changed mean value of feature smYw is introduced.According to the extremum feature of smYw,the theorem of the recognition of the extremum feature based on the MSMF is proposed.2.According to the extremum theorem of MSMF,the extremum feature of the recognition function depends on smYw,but if the multi-extreme feature of the function is to be identified,it must be based on smY.Therefore,the method of alternate use of smY and smYw is adopted.For some functions,the initial smYw may not have the characteristics of extreme value.This paper studies a method that the algorithm automatically import the extreme effective search trajectory,and concludes 8 kinds of treatment that smYw is monotone convex or concave.Aiming at the recognition of the extremum function,this paper proposes a method based on MSMF for segmentation,which successfully solves the problem of identification of multimodal function.3.Through testing the MSMF algorithm of multimodal with different features,it is found that although the extreme value recognition rate of MSMF algorithm achieve 100%success rate,the time complexity rule does not have a positive correlation with the number of extreme values.Therefore,the time complexity of the MSMF algorithm is analyzed,and it is found that the number of calculations of the smY or smYw and the size of the subregion are the key factors affecting the time-consuming of the algorithm,indicating the direction for further improving and improving the efficiency of the MSMF algorithm.