基于混合算法的半刚性连接钢框架结构优化

Optimization for Steel Frames with Semirigid Connections Based on Hybrid Algorithms

海豚回声算法(DEA)是一种模拟海豚利用回声定位进行捕食的元启发式优化算法,具有高效的搜索能力。本研究通过对海豚回声算法的基本原理进行分析,发现该算法的选择机制容易导致优化结果陷入局部最优解,而算法本身不具备跳出局部最优解的机制。因此,为了改进海豚回声算法的全局搜索能力,引入了遗传算法(GA),提出了一种海豚回声-遗传混合算法(DEA-GA):在每一个迭代步中,首先基于海豚回声算法生成子代,再引入遗传算法中搜索能力很强的交叉、变异操作生成新的子代。该混合算法结合了海豚回声算法和遗传算法的优势,既拥有海豚回声算法收敛速度快、效率高等优点,也具备遗传算法全局寻优能力强的特点,同时克服了海豚回声算法容易产生局部最优解和遗传算法容易出现“早熟”等缺陷。本研究以一榀单跨5层和一榀两跨10层的平面框架为例,建立以结构总重最小为目标的半刚性钢框架结构优化的数学模型,分别使用遗传算法、海豚回声算法和本研究提出的混合算法进行求解,优化过程通过Matlab编程实现。算例结果显示:海豚回声-遗传混合算法所得结构的总重比遗传算法小50%以上、比海豚回声算法小7%以上,且该趋势随着设计变量的增加而增加;同时,混合智能优化算法在复杂结构的优化上效率更高、效果更好。

The dolphin echo algorithm(DEA)is a meta-heuristic optimization algorithm that simulates dolphins using echolocation to prey and has efficient search capabilities.By analyzing the basic principle of the dolphin echo algorithm,it is found that the selection mechanism of the algorithm can easily lead to the optimization result falling into the local optimal solution,and the algorithm itself does not have the mechanism to jump out of the local optimal solution.Therefore,to improve the global search ability of the dolphin echo algorithm,the genetic algorithm(GA)was introduced,and a hybrid dolphin echo-genetic algorithm(DEA-GA)was proposed:in each iterative step,the offspring was first generated based on the dolphin echo algorithm,and then the crossover and mutation operations with strong search ability in the genetic algorithm were introduced to generate new offspring.The hybrid algorithm combines the advantages of the dolphin echo algorithm and the genetic algorithm,so it not only has the advantages of fast convergence speed and high efficiency of the dolphin echo algorithm,but also takes the advantage of the strong global optimization ability of the genetic algorithm.Moreover,it overcomes the defects of the dolphin echo algorithm that is easy to generate local optimal solutions and the genetic algorithm that is prone to‘prematurity’.In this paper,a single-span 5-storey and a two-span 10-storey plane frame were used as examples to establish a mathematical model for the optimization of semi-rigid steel frame structures with the objective function of minimizing the total weight of the structure.Genetic algorithm,dolphin echo algorithm and hybrid algorithm were used respectively,and the optimization process was realized by Matlab programming.The results indicate that the total weight of the structure obtained by the dolphin echo-genetic hybrid algorithm is more than 50%smaller than that of the genetic algorithm,and more than 7%smaller than that of the dolphin echo algorithm,and the trend increases with the increase of design variables.At the same time,the hybrid intelligent optimization algorithm is more efficient and effective in the optimization of complex structures.