【作者】 王晓军； 倪博文； 王磊； 任强；

【Author】 Xiaojun Wang;Bowen Ni;Lei Wang;Qiang Ren;Institute of Solid Mechanics,Beihang University;

【机构】 北京航空航天大学固体力学研究所；

【摘要】 全局寻优旨在寻找可行域内设计变量的最佳组合使得目标函数取极值,广泛应用于航空、航天、化学、生物、经济、管理以及人工智能等领域。本文提出了一种新的基于"超体积迭代策略"的全局寻优算法(HVI),HVI算法以设计可行域内目标函数与多维坐标面所围成的"超体积"的变化为迭代计算准则和迭代收敛准则,可以实现快速、稳定的全局寻优。HVI算法适用于满足可积条件的单变量/多变量、连续/不连续、可微/不可微,显式/隐式以及无约束/有约束等问题,同时可实现并行化计算。此外,此算法是一种确定性的全局优化算法,经典的全局优化算法,如遗传算法设定了最大进化代数的停止准则,当进化过程停止后,无法判断其所得的全局最优值的"优"的程度,因而一般仅能获得设计可行域中比较令人满意的可行解,相比之下,HVI算法具有明确定义的基于超体积变化的收敛准则,可以获得真正的设计可行域内的目标函数的最值。本文通过若干算例,将HVI算法与遗传算法(GA)和模拟退火法(SA)等经典算法从计算效率上进行了比较,验证了该算法的上述特点,结果表明,当目标函数存在多个全局最优解时,相比于其余法,HVI算法可以找到所有的全局最优值。并基于此特点将其应用于高维数值积分、区间响应分析和代理模型构建等方面,体现了该算法的高效性。更多还原

【Abstract】 Global optimization is aimed at finding the extrema within the design domain. Global optimization is widely used in the fields of Aeronautics,astronautics,chemistry,biology,economy,management,and artificial intelligence. In this study,a global optimization algorithm based on the iterative calculation of the hyper-volume is proposed and called hyper-volume iteration(HVI). HVI is a general,stable,and parallelizable algorithm,which can be used for univariable/multivariable,continuous/discontinuous,differentiable/non-differentiable,explicit/implicit,and functions and constrained/unconstrained problems as long as the integrability conditions are satisfied. In addition,this algorithm is a deterministic global optimization algorithm,traditional global optimization algorithms,such as genetic algorithm,set a stop criterion of maximum evolution,when evolutionary process stopped,it may not obtain the global optima,by contrast,HVI algorithm has a well-defined stopping criterion based on the definition of super volume change,and it can get feasible solution of objective function in the design domain. Through some examples,the HVI algorithm,genetic algorithm(GA) simulated annealing(SA) and other classical algorithms are compared in the computational efficiency,verified the characteristics of this algorithm,the results show that,compared to the other method,when the objective function has multiple optima,HVI algorithm can find all the global optimal value. Based on this characteristic,the algorithm is applied to high dimensional numerical integration,interval response analysis and surrogate model construction,the efficiency of the algorithm is demonstrated as well.更多还原