基于自适应差分进化算法的变循环发动机模型求解方法研究

为了降低传统迭代算法在求解变循环发动机非线性模型时对初值的依赖性,将模型的求解问题转换为求最小值的优化问题,引入差分进化算法进行模型的求解,并提出一种自适应差分进化算法(ADE)。ADE借助轮盘赌选择法,利用种群的进化经验可以自适应的选择最适合当前种群的差分策略与算法控制参数。针对变循环发动机四个典型工作点的模型求解问题,研究了标准差分进化算法(SDE)的控制参数对其性能的影响,获取了SDE在求解四个典型工作点时的最优控制参数组合,对比分析了ADE与SDE的性能差异,最后研究了种群规模对ADE性能的影响。结果表明：SDE在求解发动机模型时具有较好的鲁棒性,在求解不同工作点时算法的最优控制参数并不完全相同；相比于使用最优控制参数的SDE,ADE可以在不影响算法鲁棒性的情况下提升效率50%以上；减少ADE的种群规模会在提升算法效率的同时破坏鲁棒性。

Solving Variable Cycle Engine Model Based on Adaptive Differential Evolution Algorithm

In order to reduce the dependence of the traditional iterative algorithm on the initial value in solving the nonlinear model of variable cycle engine, the model solving problem was converted to the optimization problem of finding the minimum value. Differential evolution algorithm was introduced to solve the model,and an adaptive differential evolution (ADE) algorithm was proposed. Using the evolution experience and roulette selection method, ADE can adaptively select the differential strategy and algorithm control parameters that are most suitable for the current population. For the model solving problem of the four typical operating points of the variable cycle engine, the influence of the control parameters of standard differential evolution (SDE) algorithm on its performance was studied. And the optimal combinations of control parameters of SDE in solving the four typical operating points were obtained. The performance difference between ADE and SDE was compared. Finally, the influence of population size on the performance of ADE was studied. The results show that SDE has pretty robustness in solving engine model, and its optimal control parameters are not completely the same when solving different operating points. Compared with SDE using the best control parameters, ADE can increase the efficiency by more than 50% without affecting the robustness of the algorithm. Reducing the population size of ADE will improve the efficiency while destroying the robustness of the algorithm.