Research On Probabilistic Multimodal Optimization Algorithm In Noisy Environment

Solving multimodal optimization problems in noisy environment has practical significance for modern optimization problems in economics,medicine and engineering,and it can provide multiple optimized schemes for engineering optimization problems with noise interference,such as robotics,intelligent control and decision,signal identification and measurement,intelligent manufacturing,etc.In recent years,more and more attention has been paid to multimodal optimization in noisy environment.However,the uncertainty of the stochastic optimization algorithm and the uncertainty of the noise make it difficult for the researchers to predict the probability of the optimization results.Therefore,it is of great theoretical significance and practical value to study the probabilistic characteristics of the algorithm.The probabilistic characteristics of the optimization algorithm reflect the probabilistic reliability of the optimization results and provide useful prediction information for the selection of the optimization algorithm and that of the optimization results when solving practical optimization problems.How to realize multiple extremum points optimization with probabilistic estimation is the main research content of this thesis.The main achievements of the thesis include:1.The technical route to solve probabilistic multimodal optimization problem in noisy environment and the overall framework of optimization algorithm are put forward.The influence of six kinds of common noise models on the objective function and optimization algorithm is analyzed.The solution and algorithm design framework for solving the probabilistic multimodal optimization problem under noise environment.The algorithm framework consists of global strategy,local strategy and discrimination strategy,aiming at solving the four problems of reserving multiple extremum points,jumping out of the local optimal caused by noise,exploring the probability rule of optimization results,and the same peak detection of extremum points.2.A Fibonacci multimodal optimization(FMO)algorithm is proposed.Regional scaling criterion based on Fibonacci principle and the search mechanism of global/local alternate optimization are proposed.Three problems of multiple extremum optimization in noisy environment are solved,including reserving multiple extremum points,jumping out of local optima caused by noise and determineing the position coordinates of the extremum points.The optimization experiments are carried out based on 35 benchmark functions in different noise environments and compared with genetic algorithm and four different particle swarm optimization algorithms.The experimental results show that the improved Fibonacci search strategy proposed in this thesis has better global convergence and anti-noise performance.The FMO algorithm can identify the corresponding solution vector of each extremum point,and has better stability and multiple extremum optimization performance.3.A probabilistic multimodal optimization algorithm based on Buffon distance(PMB)is proposed.For the first time,the fixed probability principle of Buffon needles is introduced into the optimization problem in noisy environment,and the concepts of Buffon distance and extreme value resolution in the noise environment are put forward.The theoretical derivation proves that the relationship between peak detection rate of PMB algorithm and Buffon distance conforms to a probabilistic relation.In the global scope,the search space is divided according to the Buffon distance,so that the peak detection rate of the algorithm conforms to the probabilistic relation,and the local areas where multiple extremum are located are preserved.Based on 34 test functions,experiments are carried out from four perspectives of probabilistic feature verification,analysis of influencing factors of optimization results,multiple extremum points optimization and multidimensional optimization,and are compared with the improved bat algorithm.Experimental results show that the peak detection rate of PMB algorithm and the Buffon distance are in accordance with the deduced probabilistic relationship,and the PMB algorithm can more accurately locate multiple extremum points in noisy environment according to the determined probability.Thus the PMB algorithm has good characteristics of probabilistic optimization and multiple extremum optimization.4.A probabilistic multimodal optimization algorithm(PMO)based on improved same-peak detection method is proposed.The same-peak detection method based on Nyquist sampling theorem is proposed to solve the problem of the discrimination of whether the extreme points are located at the same peak under noise interference.The relation between the highest frequency component of the function and the extreme value resolution is analysed.According to the Nyquist sampling theorem,an appropriate sampling point interval is set,so as to capture the changing state of the function and judge the position state of the candidate solution,and the identification problem of real extrema and noisy optima is solved.Based on12 test functions,the experiments are conducted from three aspects,including probabilistic convergence,multiple extremum optimization and the effectiveness of the same peak detection method,and the results are compared with the improved bat algorithm.The experimental results show that the PMO algorithm has the characteristics of probabilistic optimization and multiple extremum optimization,and the proposed same-peak detection method based on the sampling theorem is effective for the determination of the same peak extreme points under noisy environment.5.Experimental platform of probabilistic multimodal optimization algorithm in noise environment is designed and realized,and the applications of the algorithm in practical engineering problems are studied.The design and implementation of the experimental platform of probabilistic multimodal optimization algorithm in noise environment is completed,in order to provide a convenient and unified platform for the characteristics research of the algorithm.The algorithm is applied to three production practice optimization problems including peak detection of magnetic sensor signal for rail spike location in tamping wagon,radio spectrum monitoring signal processing and cutting parameters multi-scheme optimization in computer numerical control(CNC)manufacturing.The expected effect is achieved.For the uncertainty problem of multimodal function optimization in noisy environment,this thesis proposes a fixed probability partition strategy of search space based on Buffon needles principle,a regional scaling criterion based on Fibonacci principle and a detection method for the same peak points based on sampling theorem.In order to realize the probabilistic characteristic,multiple extremum points optimization and anti-noise performance of the algorithm,so the probabilistic prediction information and multiple solutions could be provided for the actual optimization problems.In this thesis,the solution of optimization problem in noisy environment is studied,and the theoretical research and application of optimization algorithm in noisy environment are enriched.