用进化-模拟退火算法求解Lambert方程

Lambert方程在轨道拦截和初始轨道确定起着重要作用。求解Lambert方程的传统算法主要有Newton迭代方法和超几何级数展开方法等,但这些算法都有一定的局限性(如有可能出现迭代收敛过慢,级数展开收敛性问题)。采用进化-模拟退火算法(EA-SA)算法求解Lambert方程,其中进化算法具有全局搜索能力,而模拟退火具有局部锁搜索能力。该方法克服了某些情况下梯度下降法有时收敛过慢和超几何级数不收敛的缺点,并具有通用性,便于操作和理解。通过仿真计算对比表明,EA-SA具有普适性,而且精度优于其它两种算法。

Solution of Lambert Theorem By Evolutionary Algorithm and Simulated Annealing

Lambert theorem plays an important role in orbital interception and initial orbit determination. The classical methods, such as Newton iteration, hyper-geometry expansion and et al, are always valid in limited conditions. Evolutionary Algorithm and Simulated Annealing (EA-SA) was proposesed to solving Lambert theorem, which EA has global search performance and SA has local search performance. The algorithm overcomes the defects of low convergent speed of Newton iteration method in some cases and it is easy to be operated and understood. Finally, the computation verifies that EA-SA is universal adaptive and it is more precise than the classical methods.