摘要：

分布式卫星编队任务规划能同时处理多个具有时间和资源冲突的对地观测任务, 但随着卫星和任务数量的增多导致的冲突严重降低了观测收益和任务完成的质量。针对这一问题, 提出一种分割空间投影粒子群优化(SPPSO)算法, 对构建的任务规划混合整数模型进行求解。首先将种群根据适应度大小分割为不同的搜索空间, 采用快速傅里叶变换的投影策略在搜索空间中对种群进行重构, 然后利用感知算子促进适应度较低的粒子向最优空间靠拢, 提高收敛速度和有效减少陷入局部最优的问题。为验证SPPSO算法的有效性, 将在国际标准测试函数上与尖端PSO变体和解决类似规划问题的其他著名调度算法进行比较。根据Wilcoxon秩和Friedman检验结果, SPPSO算法在单峰和多峰函数上平均排名最高。此外, SPPSO算法在4种规模(25~100)的仿真测试案例中始终实现了最高的观测收益值和任务完成率。实验结果表明, 与次优算法相比, 在最大规模任务下观测收益值和任务完成率分别提升了6.8%和7.5%, 验证了其增加收敛速度和缓解陷入局部最优风险的有效性。

关键词: 分布式卫星编队, 粒子群优化算法, 空间投影策略, 傅里叶变换, 任务规划

Abstract:

Distributed satellite formation mission planning can simultaneously manage multiple Earth observation missions experiencing time and resource conflicts. However, as the number of satellites and missions increases, these conflicts severely reduce observation benefits and the quality of mission completion. To address this issue, this study proposes a partitioned Space Projection Particle Swarm Optimization (SPPSO) algorithm to adapt the constructed hybrid integer programming model for mission planning. First, the algorithm partitions the population into different search spaces based on fitness levels. Subsequently, it uses a projection strategy based on Fast Fourier Transform (FFT) to reconstruct the population within the search space and employs a perception operator to guide particles with lower fitness toward the optimal space. This approach enhances the convergence speed and effectively reduces the risk of becoming trapped in the local optima. To validate the effectiveness of the SPPSO algorithm, it was compared with state-of-the-art PSO variants and other well-known scheduling algorithms for similar planning problems using international standard test functions. According to the Wilcoxon rank-sum and Friedman test results, the SPPSO algorithm achieved the highest average ranking for both the unimodal and multimodal functions. Furthermore, in the simulation test cases of four different scales (25-100), the SPPSO algorithm consistently achieves the highest observation benefit values and mission completion rates. Compared with the suboptimal algorithm, the SPPSO algorithm improved the observation benefit value and mission completion rate by 6.8% and 7.5%, respectively, for the largest-scale tasks, thus validating its effectiveness in increasing the convergence speed and mitigating the risk of local optima.

Key words: distributed satellite formations, Particle Swarm Optimization (PSO) algorithm, space projection strategy, Fourier transform, mission planning