基于双重权约束期望改进策略的多目标并行代理优化方法

Multi-objective parallel surrogate-based optimization based on dual weighted constraint expectation improvement strategy

针对多目标仿真优化的高昂成本及黑箱函数难以获取问题,提出基于双重权约束期望改进策略的多目标并行代理优化方法.首先,建立Kriging模型获取未试验点的预测不确定性;其次,构建双重权约束期望改进策略,并利用填充策略矩阵及距离聚合方法实现新改进策略的聚合;然后,最大化聚合双重权约束期望改进策略实现多目标并行优化;最后,达到终止条件,获得Pareto最优解集.选取测试函数及铰接夹芯梁设计案例进行优化验证.验证对比结果表明:所提方法可有效提升多目标问题优化效率,减少昂贵仿真成本;与同类方法相比,低维问题中获取Pareto最优解集的收敛性、多样性及分布性更优.

Considering the high computational cost in multi-objective simulation optimization and the difficulty of obtaining black box function, a multi-objective parallel surrogate-based optimization method based on the dual weighted constraint expectation improvement strategy is proposed. Firstly, the Kriging model is established to estimate the prediction uncertainty of untested points. Secondly, the dual weighted constraint expectation improvement strategy is constructed,and the new strategy is integrated by the infill strategy matrix and distance aggregation method. Then, the integration strategy is maximized to realize multi-objective parallel optimization;Finally, the Pareto optimal solution set is obtained when the termination condition reached. Test functions and pinned-pinned sandwich beam design cases are employed for optimization verification. Comparison and optimization results show that the proposed method can effectively improve the efficiency of multi-objective optimization. Compared with similar methods, the optimization results in low dimensional problems have better convergence, diversity and distribution.