多级递阶工程系统是复杂工程项目的主要工程结构依照功能逻辑关系所构成的多层次分支结构体系,表征了常见复杂项目的一般性分布。以结构设防烈度为优化指标,以抗地震设计为工程背景,本文针对该系统结构特点,提出全局优化方法两个层次划分的概念;然后从Lagrange对偶理论出发,提出第一层次的对偶分解法和分解-协调法,结合第二层次的离散型最优化方法,分别实现大系统约束、无约束全局优化的有效计算。算例讨论了复杂项目在最优设防标准、最优造价和总投资最优分配三个方面的工程决策,并与其他方法的结果作了比较。上述概念与方法使大系统整体优化空间达到高度的降维,为复杂工程项目的系统化设计、工程问题的科学决策奠定了理论分析的基础。 Multi-level hierarchical engineering system is the main engineering structure of complex engineering projects in accordance with the logical relationship between functions formed by the multi-level hierarchical structure of the system, characterized by the general distribution of common complex projects. Taking fortification intensity of structure as optimization index and anti-seismic design as engineering background, this paper proposes the concept of two levels of global optimization method according to the structural features of the system. Then, based on Lagrange duality theory, the first level dual decomposition method and Decomposition - coordination method, combined with the second level of discrete optimization methods, respectively, to achieve large system constraints, global optimization of unconstrained effective calculation. The example discusses the engineering decision-making of the complex project in terms of the optimal fortification standard, the optimal cost and the optimal allocation of total investment, and compares the results with other methods. The above concept and method make the overall system optimization space to achieve a high degree of dimensionality reduction, which lays a theoretical foundation for the systematic design of complex engineering projects and scientific decision-making of engineering problems.