演化算法求解桁架多目标拓扑优化的收敛速度研究

A convergence speed study on evolutionary algorithms for solving truss multi-objective topology optimization

演化算法能够同时满足结构拓扑优化的前沿领域对全局优化、黑箱函数优化、组合优化和多目标优化的需求,但采用此类算法的可行性与必要性由其收敛性与计算效率决定。本文以应力约束桁架多目标拓扑优化问题为求解对象,致力于揭示在收敛性与计算效率两方面具有竞争力的算法。首先提出评估演化算法求解拓扑优化问题收敛性与计算效率的通用方法,采用穷举法严格推导了典型桁架多目标拓扑优化问题的全局最优解,并采用超体积指标定义了多层次收敛性能准则。最后通过比较研究得到不同收敛性需求下具有最快收敛速度的演化算法,并揭示了具有竞争力的算法机制。本研究为演化算法求解多目标拓扑优化问题的收敛速度奠定了理论基础,同时为高效求解实际工程拓扑优化问题提供算法支持。

Though evolutionary algorithms（EAs）are capable of satisfying the demands arising from the new advancements in structural topology optimization on global optimization,black-box function optimization,combinatorial optimization and multi-objective optimization,the necessity of applying them to this field still depends on their convergence and computational efficiency simultaneously.This paper aims to reveal competent algorithms on these two aspects for stress constrained truss multi-objective topology optimization（MOTO）problems.We first propose a general method tailor-made for examining the convergence and efficiency of EAs on solving MOTO.The global optima of typical MOTO problems are rigorously derived using enumeration.Then multi-level convergence criteria are defined using hypervolume metric.The comparative study reveals outstanding EAs with greatest convergence speeds under different convergence requirement and the corresponding algorithmic mechanism.This way,this paper not only contributes to the theoretical foundation of solving MOTO problems using EAs,but also provides support for high efficiently solving practical engineering topology optimization problems.