基于均值改进控制策略的昂贵约束并行代理优化算法

针对具有黑箱特性的昂贵约束优化问题及工程中计算资源利用率不高问题,提出了新的基于均值改进控制策略的并行代理优化算法.该算法为了减少仿真建模计算负担,选取Kriging近似模型对目标函数和约束函数进行近似估计.在Kriging模型基础上,利用均值改进与新增试验样本间的不等关系构建具有距离特性的控制函数.算法的均值改进控制策略通过控制函数调整最大改进值,实现样本设计空间的多点填充.算法适用范围:1)计算成本主要来自于仿真估计而非优化;2)复杂的工程或商业软件内部无法修改的昂贵仿真问题.数值算例和仿真案例表明:该算法可有效获取近似最优解,减少仿真试验次数的同时弱化均值改进准则的贪婪特性.相比于其他多点填充策略,均值改进控制策略可有效提升算法计算效率.此外,算法获取优化问题近似最优解的稳定性和精度均具有一定优势.

Expensive constraints parallel surrogate-based optimization algorithm based on mean improvement control strategy

Considering the expensive black box constrained optimization problem and the low utilization of computing resources in engineering, a new parallel surrogate-based optimization algorithm based on mean improvement control strategy is proposed. In order to reduce the computational burden of simulation modeling, Kriging model is employed to approximate the objective function and constraint function. On the basis of Kriging approximation model, the control function with distance characteristic is constructed by using the inequality relationship between mean improvement and new test sample. The mean improvement control strategy of the algorithm adjusts the maximum improved value through the control function to realize the multi-point filling in the sample design space. The algorithm is suitable for: 1) the computational cost mainly comes from simulation estimation rather than optimization; 2) complex engineering or commercial software can not be modified for expensive simulation problems. Numerical examples and simulation cases show that the algorithm can effectively obtain approximate optimal solution, Compared with other multi-point filling strategies, the mean improvement control strategy can effectively improve the computational efficiency of the algorithm. In addition, the stability and accuracy of the approximate optimization solution obtained by the algorithm have certain advantages.