Research On Improvement On Biogeography-based Optimization Algorithm And Its K-means Clustering Optimization

The optimization problem is ubiquitous in the real world,and the method of solving the optimization problem occupies an important position in many application fields and scientific research,and it has always been a research hotspot.But with the advancement of science,the optimization problems that need to be solved are becoming more and more complicated.Traditional mathematical methods based on precision cannot solve these problems well.In order to better solve such problems,intelligent optimization algorithms should be born from time to time.Biogeography-Based Optimization Algorithm(BBO)is an intelligent optimization algorithm that simulates the survival of species.It has the advantages of simple,flexible and easy to achieve results,and has been widely used.Although many scholars have improved it,when solving more complicated optimization problems,BBO and its variants still have shortcomings such as insufficient search capabilities.Aiming at the shortcomings of BBO and its variants in solving complex optimization problems,this paper proposes three improvement methods and applies them to K-cluster optimization problems.The main research contents are as follows:(1)In order to improve the optimization performance of BBO,Worst opposition learning and Random-scaled differential mutation BBO(WRBBO)is proposed.There are three main improvements to BBO.One is to propose a random scaling difference mutation operator to improve the global search ability.The other is to propose a dynamic heuristic crossover operator to improve the local search ability.The third is to propose the worst opposition learning to avoid the algorithm falling into local optimum.The complexity analysis of WRBBO is analyzied.Experimental results on classical functions,CEC-2013 test set and K-means clustering show that WRBBO has better optimization performance.(2)Laplacian Biogeography-Based Optimization(Lx BBO)is a variant of BBO.However,when dealing with some complex problems,there are shortcomings such as insufficient efficiency,so an improved Lx BBO(ILx BBO)is proposed.First,in each iteration,the first two best habitats are updated with dynamic differential mutation operators.Then,two global optimization guide operators are used to update the worst habitat in each iteration.Finally,an improved Laplace migration operator is used to update the rest habitats.The experimental results on the CEC-2013 test set show that ILx BBO obtains better optimization efficiency.ILx BBO is applied to the K-means clustering optimization problem.Experimental results show that ILx BBO can better solve the clustering optimization problem.(3)Two-stage Differential Biogeography-Based Optimization(TDBBO)is a recently proposed variant of BBO.In order to further improve the optimization efficiency and universality of TDBBO,a Hybrid migration and global optimal Gaussian mutation BBO(HGBBO)is proposed.First,the migration operator and the two-stage mechanism in TDBBO are replaced by hybrid migration operators.The hybrid migration operator includes two strategies,one is a linear dynamic random heuristic crossover strategy;the other is an exponential dynamic random differential mutation strategy.Then,the Gaussian mutation operator is executed early in the algorithm search;the global optimal mutation operator is executed later;and the global optimal Gaussian mutation operator is formed together.Finally,a random opposition learning strategy is embedded.The experimental results on 15 classical functions and CEC-2013 test set show that,compared with other algorithms,HGBBO obtains better optimization efficiency and its universality is also the best.And get better optimization performance on the K-means clustering optimization problem.The three improved algorithms follow the improvement from shallow to deep.First of all,in terms of algorithms,WRBBO is a basic improvement to BBO.ILx BBO and HGBBO are the second improvement.The three improvements all refer to the mutation operator in the DE algorithm.The three improvements are from shallow to deep,and new methods are added on the basis of the former.The first study improved the optimization performance of BBO,and the second study added new improvements on the basis of the first study,such as the optimization guide operator.Reduce the computational complexity of the algorithm and improve the operability of the algorithm.The third study adds Gaussian mutation operators on the basis of the second study.While improving the optimization efficiency of the algorithm,it further improves the universality of the algorithm and adapts to a variety of optimization problems.In the experimental part,from shallow to deep,the common feature is that the three are applied to the cluster optimization problem.The difference is that the second study adds a comparison of incomplete variants of the algorithm on the basis of the first study,and experiments on convergence analysis on the function and K-means clustering.The third study adds the algorithm's parameter sensitivity analysis,diversity analysis and Bonferroni-Holm correction experiment on the basis of the second study.Experimental results show that,compared with the comparison algorithms,the three studies proposed have achieved better optimization performance both in functions and K-means clustering.