基于FCM改进遗传算法的工字梁多目标优化设计

摘要

为了对工字梁结构进行优化设计,建立了以工字梁横截面积最小和给定负载条件下的最小化静挠度最小为目标函数,以满足梁的弯曲强度条件及截面尺寸限制条件为约束条件的多目标优化模型,并提出了一种基于模糊C均值聚类改进的多目标优化算法来对其进行求解.该算法利用FCM的模糊划分和最大隶属度来对交配选择过程进行交配约束限制.将该算法与其他典型的多目标优化算法在GLT系列测试函数上进行对比测试,结果表明所提出的算法性能更好,能得到具有更好收敛性且分布更均匀的Pareto前端.工字梁实例的求解也证明了该算法的优良性及实用性.%To optimize the design of an I-beam, the paper took the minimization of the cross-sectional area of the I-beam and the minimum static deflection that under given load condition as the objective functions, established the model for the multi-objective optimization and under that the I-beam structure meet the needs for bending strength and sectional size limitation and others.An improved multi-objective optimization algorithm based on fuzzy C-means clustering was proposed.The algorithm uses the fuzzy partition of FCM and the maximum membership degree to constrain the mating selection process.The comparative performance test results on a set of test instances(GLT) reveal that the proposed algorithm outperforms some state-of-the-art algorithms in terms of convergence and diversity.The I-beam example also proved the superiority and practicality of the algorithm.