Research On Biogeography-based Optimization Algorithm For Complex Optimization Problems

Biogeography-based optimization(BBO),as a new evolutionary algorithm to simulate species migration in nature,has the characteristics of simple principle,easy algorithm implementation and low parameter sensitivity.Compared with other evolutionary algorithms(EAs),BBO has unique advantages in solving high-dimensional and complex optimization problems.Based on this,this thesis mainly studies the BBO algorithm,analyzes and discusses the defects of BBO and its existing variants,and puts forward targeted improvement strategies on this basis to obtain new variants of it.The global convergence and computational complexity of the improved BBO algorithms are proved and discussed theoretically.At the performance level,the effectiveness and advancement of the algorithms are verified by systematic experiments.At the application level,They are applied to complex engineering optimization problems in the real-world.In this thesis,two variants of BBO are designed and 27 sets of comparison experiments are conducted,including 42 comparison algorithms,involving 5 test sets and covering166 questions.The main work is summarized as follows:1.For high-dimensional global optimization problems,this thesis proposes a dual BBO algorithm based on sine cosine algorithm(SCA)and dynamic hybrid mutation,named SCBBO.Firstly,the Latin hypercube sampling method is innovatively used to improve the initial population ergodicity.Secondly,a nonlinear transformation parameter and a inertia weight adjustment factor are designed into the position update formula of SCA to make SCBBO suitable for high dimensional environments.Then,a dynamic hybrid mutation operator is designed by combining Laplacian and Gaussian mutation,which helps the algorithm to escape from local optima and balance the exploration and exploitation.Finally,the dual learning strategy is integrated,so the convergence accuracy is further improved by generating dual individuals.Meanwhile,A sequence convergence model is established to prove the algorithm can converge to the global optimal solution with probability 1.Compared with other advanced EAs,SCBBO effectively improves the optimization accuracy and convergence speed for large scale optimization problems.To further show the superiority of SCBBO,its performance is compared on 1000,2000,5000 and 10000 dimensions,respectively.The comparsions show that SCBBO’s optimization results on these dimensions are basically the same,which can effectively solve the high-dimensional global optimization problems.2.For complex global optimization problems,this thesis proposes a BBO variant based on hybrid migration operator and feedback differential evolution mechanism,referred to as HFBBO.Firstly,the example learning method is used to ensure the inferior solutions can not destroy the superior solutions.Secondly,the hybrid migration operator is presented to balance the exploration and exploitation.It enables the algorithm to switch freely between local search and global search.Finally,the feedback differential evolution mechanism is designed to replace the random mutation operator.HFBBO can select the mutation mode intelligently by this mechanism to avoid getting stuck in local optima.Meanwhile,the Markov model is established to prove the convergence of HFBBO,and the complexity is also discussed.A series experiments are carried out on 24 benchmark functions,CEC2013 test suite,CEC2014 test suite and CEC2017 test suite.The results of the Wilcoxon’s rank-sum test and Friedman’s test show that HFBBO has better competitiveness and stability than all compared algorithms,which can effectively solve complex global optimization problems.3.For various complex constrained optimization problems in real life,an improved Oracle penalty function method is embedded into two improved BBO algorithms.In addition,to solve constrained optimization problem with mixed variables,a general discrete variable processing method is introduced to convert the discrete variables into continuous variables.Based on the above processing,SCBBO-CH and HFBBO-CH algorithms are obtained.SCBBO-CH and HFBBO-CH are applied to 57 engineering constrained optimization problems in the CEC2020 real optimization problem test suite,and five state-of-the-art algorithms are used for comparative analysis.The research results show that SCBBO-CH and HFBBO-CH have achieved ideal results on nearly half of the problems,have obvious advantages in solving complex constrained optimization problems,and the algorithm performance is superior to other advanced algorithms.There are 25 figures,45 tables and 173 references in this thesis.It is hoped that the simple work of this thesis can provide some thoughts for the further research of BBO algorithm.