For the $N$ -impulse transfer between two earth orbits, this paper introduces $N - 1$ intermediate orbits to describe the orbit transfer scheme. The eccentricity vector of the intermediate orbits and the true anomalies corresponding to the impulsive points are chosen as the optimization variables. Based on the patched conic theory, candidate solution can be analytically derived, constraints are removed from the optimization model, and the original problem is converted to a parameter optimization problem. The only difficulty lies in the initialization because the number of optimization variables increases linearly with $N$ , which can be very large. This is settled by a hybrid optimization algorithm that comprises two searching methods. The problem is solved first by an improved particle swarm optimization method and, then, by an adaptive conjugate gradient method. The proposed method is adaptive to problems with any finite $N$ and can calculate the optimal $N$ in any transfer scenarios. The simulation validates the proposed method with some well-known cases and demonstrates its adaptation to $N$ .

中文翻译：

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使用混合优化方法的燃料优化多脉冲轨道转移

为了 $N$ -两个地球轨道之间的脉冲传递，本文介绍 $N - 1$ 中间轨道来描述轨道转移方案。选择中间轨道的偏心向量和脉冲点对应的真实异常作为优化变量。基于补丁圆锥理论，可以解析导出候选解，从优化模型中去除约束，并将原始问题转换为参数优化问题。唯一的困难在于初始化，因为优化变量的数量随着 $N$ ，这可能非常大。这是由包含两种搜索方法的混合优化算法解决的。该问题首先通过改进的粒子群优化方法解决，然后通过自适应共轭梯度方法解决。所提出的方法适用于任何有限 $N$ 并且可以计算出最优 $N$ 在任何传输场景中。仿真通过一些众所周知的案例验证了所提出的方法，并证明了它对 $N$ .