基于并行EGO和代理模型辅助的多参数优化方法研究

Research on multi-parameter optimization method based on parallel EGO and surrogate-assisted model

化工流程模拟优化问题常常具有高维、非线性的特点,使得仿真计算难以收敛。过长的求解时间是调度优化和运行优化的主要瓶颈之一。采用代理模型对机理模型进行替代是降低计算复杂度、保证结果准确性的有效途径。Kriging代理模型具有较强的非线性近似性,但处理高维问题依然较为困难。因此,本文研究并行EGO(efficient global optimization)算法与代理模型集成,并将模型应用于化工过程。并行EGO算法以Kriging代理模型的预测函数和误差函数为基础,先推导出样本分布概率密度函数与累积分布函数相结合的解析表达式;然后通过PEI(pseudo expected improvement)准则得到新的样本点以更新代理模型;最后结合改进的差分进化算法对优化参数进行全局搜索。在保证结果准确性的前提下,将本文算法与其他优化算法进行比较。8个多峰测试函数的测试结果表明,该算法的收敛速度提高了85%。然后将其应用于双级氨吸收制冷过程的模拟,结果表明该方法的模拟误差小于0.01%,优化时间从9846 s缩短至3705 s。

Process simulation and optimization have the characteristics of high-dimensional and non-linear,which makes the simulation calculation difficult to converge.Excessive solution time is one of the bottlenecks during scheduling and operation optimization.Using surrogate models to replace mechanistic models is an effective way to reduce computational complexity and ensure the accuracy of results.Though the Kriging surrogate model has a stronger nonlinear approximation,it is still difficult to deal with high-dimensional problems.Therefore,this paper investigates the parallel EGO(efficient global optimization)algorithm integrated with the surrogate model and applies the model to typical chemical process.The parallel EGO algorithm is based on the prediction function and error function of the Kriging surrogate model.First,an analytical expression is derived from data sample combined by the probability density function and cumulative distribution function.Then the surrogate model is updated by new sample points obtained by PEI(pseudo expected improvement)criterion.Finally,combined with the improved differential evolution algorithm,the optimization parameters are searched globally.Under the premise of ensuring the accuracy of the results,the algorithm in this paper is compared with other optimization algorithms.Taking eight multi-peaked test functions as a test case,it is found that the convergence speed of the algorithm is improved by 85%.Then,it is applied to the study case of the two-stage ammonia absorption refrigeration process.The results show that the simulation error is less than 0.01%,and the optimization time is reduced from 9846 s to 3705 s.