GPU Parallel Computation Algorithm And Application For Rapid Response Surface Optimization

With the improvement of design requirements for electromechanical products,the modeling and simulation process has become increasingly complex.In order to shorten the product's iteration cycle and improve the competitiveness of the product in the market,the response surface model is widely used to approximately replace the simulation model of complex products.This method will help to improve the simulation efficiency.However,the traditional global optimization algorithm is not fully applicable to find the optimization of response surface models.For example,a response surface with continuous multiple peaks and troughs,the algorithm will often fall into the local optimal solution due to premature convergence.Therefore,this paper uses the sequential quadratic programming algorithm to optimize each domain by equidistantly dividing the defined domain interval.Then comparing the optimal solution which is searched by each cell,and the global optimization problem can be obtained.Since the optimization of each cell requires a certain amount of time,and the total optimization time is proportional to the number of cells between the cells,when the high-order high-dimensional response surface model is processed,the number of divided intervals will increase exponentially which leads to a sharp increase in search time.The GPU has powerful parallel computing capabilities and the optimization of each cell is independent of each other,by turning on multiple threads to simultaneously perform multiple cell optimization tasks.In order to further verify the feasibility of partitioning optimization,this paper uses several standard test function models constructed by the response surface as the experimental object,and uses the sequential quadratic programming algorithm to optimize the inter-cell optimization.Comparing the record running time in CPU and GPU,there are four advantages of using inter-cell optimization algorithm based on GPU parallel computing:(1)Compared with the traditional simulated annealing method,for the continuous multiple peaks and valleys of the objective function,it will not fall into the local optimal solution.(2)For a flat objective function,the traditional method may lack the condition to jump out of the local optimal solution to cause the convergence to be slower,and it can also quickly find the global optimality;(3)Optimize the interval by dividing the domain.The method can solve the optimization problem of the response surface very well,but with the number of cells increasing,CPU spends a lot of time on optimization which is failed to meet the actual requirements.By utilizing the parallel computing capabilities of the GPU,simultaneous optimization of multiple cells can significantly reduce the total search time.For example,the Rastrigin function response surface model is shown in Table 2-3 and Table 2-4.When using the quadratic programming algorithm,the definition domain is divided into 100 intervals,the time spending on the CPU optimization is about 35 times as much as that of GPU optimization.;While in 10000 intervals,the time spent on CPU optimization is 3531 times that of GPU.(4)Under the condition of finding the global optimal solution,the simulated annealing algorithm spends at least the time for the low-order low-dimensional response surface model.for the seven-dimensional response surface model,it approaches the global optimal solution steadily with high precision,and the time cost is at most one-third that of the simulated annealing algorithm.