Research On Improved Firefly Algorithm And Arithmetic Optimization Algorithm For Structural Optimization Problems

Meta-heuristic optimization algorithm has the idea of natural evolution,which comes from human’s long-term careful observation and practice of physical,biological,social and other phenomena.It is the knowledge crystallization of humans gradually learning from nature and imitating the operation mechanism of its natural phenomena.The optimization problem of engineering structure includes mixed design variables and multiple constraints,which has large design space,many variables and complex constraints.The classical gradient algorithm is difficult to effectively deal with such optimization design problems.Meta-heuristic algorithms are widely concerned and applied because of their simple theory,clear process,fewer control parameters,strong adaptability and good global search ability.However,meta-heuristic optimization algorithms are prone to premature convergence,low solution accuracy and poor stability,which is worthy of further study and application.This paper proposes several improved algorithms and an adaptive penalty function method with targeted improvement strategies based on the performance analysis of firefly algorithms(FA)and arithmetic optimization algorithms(AOA).These algorithms are applied to the optimization problems of engineering structure.The main research contents and results are summarized as follows:1)FA has a slow convergence speed and is easy to fall into the local optimum when dealing with complex engineering optimization problems.The theoretical research on FA’s performance is insufficient.The mechanism and deficiency of the attraction model are revealed by theoretical analysis,and the variation rules of related parameters during the iteration process are found by benchmark function test.The influence of the stochastic model on algorithm convergence is analyzed,and the relationship between stochastic parameter and convergence is researched.The computational time complexity of FA is obtained based on the analysis of FA.2)Self-adaptive strategy FA(SAFA)is proposed for the shortcomings of the attraction model and stochastic model.In the adaptive strategy of the attraction model,the fitness value is considered and the search direction of firefly is modified to improve the solution accuracy of the algorithm.In the adaptive strategy of the stochastic model,the stochastic parameter decreasing with iteration is used for the adjustment of the stochastic model to ensure reasonable population diversity and speed up the convergence of the algorithm.The effect of initial parameters on the performance is researched and the optimal combination of initial parameters is obtained.Unimodal,multimodal and CEC2015 benchmark functions are used to compare SAFA and other FA variants.Friedman and Wilcoxon tests are employed for the study of the calculation results.The results show that SAFA has higher accuracy,stability and convergence speed than other algorithms.Finally,SAFA is applied to four classical engineering optimization design problems,and the results show that SAFA can obtain better designs with a smaller number of analyses.3)Integrated FA(IFA)is proposed based on the FA,opposition-based learning and adaptive penalty function method for the high computational complexity,lack of specific updating methods for optimal solutions and the low constraint efficiency of standard penalty functions.IFA adopts the virtual attraction model and global optimal attraction model to reduce the computational complexity of FA and balance the exploitation and exploration.The random opposition-based learning strategy is applied to update the optimal solution,and help the algorithm jump out of the local optimum.An adaptive penalty function method is developed to improve the solution accuracy of the algorithm in dealing with constraint optimization problems.The benchmark functions are used to determine the optimal initial parameters combination.Finally,IFA is applied to four practical engineering optimization design problems.The results show that IFA improves the solution accuracy,convergence rate and constraint handling efficiency compared with FA.The computational cost is also significantly reduced.4)Hybrid sine cosine FA(HSCFA)is proposed to handle size,shape and topology structure optimization with different constraints such as frequency,stress and displacement.HSCFA combines and takes advantages of the sine cosine algorithm(SCA),Levy flight and FA.The population is classified and synchronized updated by SCA and FA,respectively.Levy flight is employed to update the solutions with stagnation or serious constraint violation in the iterative process,so as to enrich the population diversity of the algorithm.The elitist selection strategy is utilized to improve the solution selection and accelerate the convergence speed of the algorithm.Finally,the effectiveness and robustness of the algorithm are verified by optimizing the size,shape and topology of truss structures.The results indicate that the algorithm can provide more promising designs.5)Fractional-order arithmetic optimization algorithm(FO-AOA)is proposed to solve large-scale structure optimization problems with massive structural analysis times and huge computational costs.FO-AOA uses uniform opposition-based learning to initialize the population and obtain more reasonable initial solutions.Fractional-order calculus is employed to extract the information of global optimal solution in iterative history to improve the exploitation ability of the algorithm.The math optimizer probability of AO A is modified to better balance the exploitation and exploration.FO-AOA is tested by lowdimensional,high-dimensional and ultra-high-dimensional benchmark functions,and the results are compared with the classical algorithms.Finally,the response surface method is adopted to build the surrogate model for the holding pole and stiffened cylindrical shell,and FO-AOA is used for the optimization design.The results indicate that the response surface method can precisely simulate the mechanical response of the structures,and FOAOA can significantly reduce the structural mass and improve the optimization efficiency.