面向结构拓扑优化收敛性与计算效率的多目标演化算法研究

Though multi-objective evolutionary algorithms (MOEAs) 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. In the purpose of revealing competent algorithms on these two aspects, the Pareto optimum solutions for widely collected and modified multi-objective topology optimization (MOTO) benchmarks are rigorously derived and the correspondence between problem characteristics and solving hardness are established. Then we seek for a general performance assessment methodology tailor-made for examining the convergence and efficiency of MOEAs on MOTO. In the subsequent comparative study, the state of the art of MOEAs' performance on MOTO is revealed by finding out promising real/binary metaheuristics, population updating mechanism and constraint handling technique. All these techniques are tested on large scale problems in conjunction with various co-evolution mechanisms. Finally, a new multi-objective co-evolution algorithm would be proposed. The significance of this study lies in the simultaneous examination of MOEAs' convergence and efficiency on MOTO. Hence, it does not only contribute to the theoretical foundation of solving topology optimization problems using MOEAs, but also provide the possibility of high efficiently solving large scale and complex practical topology optimization problems.

多目标演化算法能够同时满足结构拓扑优化对全局优化、黑箱函数优化、组合优化和多目标优化的需求，而采用这类算法的可行性与必要性由其收敛性与计算效率决定。本项目致力于探索在收敛性与计算效率两方面具有竞争力的算法，首先建立典型多目标拓扑优化问题集并推导其全局最优解集，归纳出问题特性与求解难度的关系；随后提出评估多目标演化算法求解拓扑优化问题的收敛性与计算效率的通用方法，并评估多目标演化算法在拓扑优化问题上的性能极限；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实数/布尔变量替代启发算子、种群更新及约束处理算子；最后考察这些算子与不同的协同演化机制在高维问题上的兼容性，提出面向结构拓扑优化需求的多目标协同演化算法。本项目的最大特色是同时考察收敛性和计算效率，不但为采用全局优化算法求解多目标拓扑优化问题的收敛性奠定理论基础，而且为高效求解大规模、复杂的工程拓扑优化问题提供技术支撑。

多目标演化算法能够同时满足结构拓扑优化对全局优化、黑箱函数优化、组合优化和多目标优化的需求，而采用这类算法的可行性与必要性由其收敛性与计算效率决定。本项目探索在收敛性与计算效率两方面具有竞争力的算法，首先建立了典型多目标拓扑优化Benchmark问题集并推导其全局最优解集，归纳出问题特性与求解难度的关系；随后提出了评估多目标演化算法求解拓扑优化问题的收敛性与计算效率的通用方法，并评估多目标演化算法在拓扑优化问题上的性能极限；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实数/布尔变量替代启发算子、种群更新及约束处理算子；考察这些算子与不同的协同演化机制在高维问题上的兼容性，提出面向结构拓扑优化需求的多目标协同演化算法。上述研究成果不但为采用全局优化算法求解多目标拓扑优化问题的收敛性奠定理论基础，而且为高效求解大规模、复杂的工程拓扑优化问题提供技术支撑。. 在此基础上，我们提出了基于粒度概率和后验偏好的风险优化理论与方法,将以往基于粗糙粒度的随机性和区间建模扩展到基于精细粒度的随机性和模糊性建模，提出两种基于广义不确定性原理的风险优化格式，指出基于粒度概率和后验偏好的风险优化本质上是高维多目标优化问题，并应用于高层建筑抗风设计多目标优化设计。基于混合混沌控制的自适应可靠度优化算法；多目标演化算法与梯度类逆可靠度分析算法的协同混合算法，整个计算过程均采用梯度类的逆可靠度分析方法，可以求解梯度类算法不能解决的高非线性问题，是一种计算效率高、鲁棒性好的可靠度分析方法。