A Two-Stage, Nested Co-Optimization Framework with Adaptive Evolutionary Operators for Component-Level Constellation Morphology and Mission Planning
Chao Zhang, Yunfeng Dong*
School of Astronautics, Beihang University, Beijing, China
* Corresponding Author: Yunfeng Dong. Email: 
Computers, Materials & Continua https://doi.org/10.32604/cmc.2026.083353
Received 02 April 2026; Accepted 17 June 2026; Published online 07 July 2026
Abstract
The missile warning constellation is fundamental to national territorial security and has significant strategic and military value. This study proposes a two-stage, nested co-optimization framework with adaptive evolutionary operators, termed TNC-A, to address challenges in genetic representation, evaluation distortion, the curse of dimensionality, and search inefficiency within the co-optimization of component-level constellation morphology and mission planning. A hybrid encoding scheme combining tree-structured and real-valued vector representations was adopted to encode all optimization variables, including constellation configuration, component-level unified platform information, and mission planning parameters. Second, a multi-stage optimization strategy integrated with a double-nested structure was implemented. This approach mitigates the dimensionality curse and addresses the evaluation distortion inherent in traditional engineering methods. Third, adaptive evolutionary operators based on online contribution learning were designed to dynamically adjust the search focus using historical experience, thereby significantly enhancing search efficiency. The simulation results demonstrate the effectiveness and practical applicability of TNC-A, demonstrating its superiority over comparative algorithms under a constrained function evaluation budget. TNC-A reduced the average and standard deviation of the optimization results by 13.7% and 65.3%, respectively, compared with the baseline of traditional engineering methods.
Keywords
Co-optimization; double-nested optimization structure; multi-stage optimization strategy; adaptive evolutionary operators; component-level; missile warning constellation
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