Abstract: To improve convergence rate,optimization efficiency and global search capability of Kriging-based global optimization method,an unconstrained global optimization method based on Kriging and duality theory was proposed.The non-convex Kriging optimization problem was transformed into a convex optimization problem by introducing the canonical duality transformation.The improved trust region strategy based on Kriging was used to sequentially optimize the convex optimization problem.The proposed method could effectively balance the global and local search behavior and greatly improve the algorithm performance.Seven numerical test cases and an engineering example were given to demonstrate the effectiveness and practicability of the proposed method.

Key words: unconstrained global optimization, surrogate model, Kriging model, duality theory, trust region method

摘要： 针对基于Kriging模型的全局优化方法收敛速度慢、优化效率低且无法跳出局部最优区域等缺点,提出一种基于Kriging模型和对偶理论的无约束全局优化方法,引入正则对偶变化将普通Kriging模型本身的非凸优化问题转换为凸优化问题,利用基于Kriging模型的改进信任域策略对该凸优化问题进行迭代寻优。该方法能有效平衡全局和局部搜索行为,并大幅提高算法性能。通过7个数值测试例子和一个工程仿真实例,验证了所提方法的有效性和实用性。

关键词: 无约束全局优化, 代理模型, Kriging模型, 对偶理论, 信任域策略