Integrated cooperative co-evolutionary optimization method for multi-constraint satellite pursuit-evasion game

The significance of satellite pursuit-evasion games in space security is increasingly recognized, driven by growing demands for space safety. Traditional methods often exhibit low efficiency in addressing multi-objective and multi-constraint optimization problems, failing to meet the requirements of dynamic and complex environments. This study aims to address these challenges by proposing a hybrid cooperative co-evolution algorithm. The primary goal is to optimize the trajectories and strategies of satellites in pursuit-evasion scenarios, ensuring efficient task completion under multiple constraints such as fuel consumption, time limits, and observational conditions. The significance of this work lies in its potential to enhance the reliability and adaptability of space-based reconnaissance and surveillance missions.

The proposed method integrated three key components: the ZOA (zebra optimization algorithm), cooperative co-evolution mechanisms, and differential game theory. The mission was divided into two phases—the approach phase and the sustained phase—each with its own specialized optimization model tailored to the specific requirements and challenges of that mission segment. A multi-population co-evolution mechanism was employed to dynamically adjust the strategies of both the mission satellite and the target satellite. The ZOA was specifically selected for its demonstrated superior performance in global exploration and local convergence, as confirmed through rigorous comparative testing against established optimization methods using benchmark functions including Rastrigin, Ackley, Sphere, and Griewank functions. Constraints such as relative distance, sunlight angle, pulse control, and energy consumption were rigorously incorporated into the optimization framework. Differential game theory was integrated to improve the stability and reliability of game strategies.

Simulation experiments demonstrated the effectiveness of the proposed algorithm. Key findings include:

1. Task completion: The mission satellite successfully completed the reconnaissance task within 47720 seconds, achieving the desired relative distance (1~20 km) and sunlight angle (0~40°) for 1,000 seconds.

2. Maneuver efficiency: The mission satellite executed 12 pulse maneuvers with a total velocity increment of 11.58 m/s, while the target satellite performed 14 maneuvers with a total velocity increment of 3.23 m/s.

3. Computational performance: The algorithm exhibited fast convergence, with average computation times of 60 s for the approach phase and 8 s for the sustained phase.

4. Dynamic adaptation: The co-evolutionary mechanism enabled real-time strategy adjustments, ensuring robust performance against the target satellite's maneuvers.

This study presented a groundbreaking solution for satellite pursuit-evasion games by combining ZOA, cooperative co-evolution, and differential game theory. The proposed algorithm not only addressed multi-constraint optimization challenges but also adapted to dynamic environments, significantly improving mission success rates and computational efficiency.

For complex and variable space environments, this research could not only be effectively applied to space reconnaissance scenarios but also provide valuable references for other space missions. For instance, in space blockade missions, the proposed method could dynamically adjust strategies based on the target satellite's maneuverability, achieving effective area blockade and control through game-theoretic optimization. In space defense missions, mission satellites could modify defense strategies according to the behavior of satellites with varying threat levels while considering inter-satellite coordination and confrontation during the gaming process. Although these application scenarios have different specific mission objectives, the dynamic adjustment mechanism based on the integrated cooperative co-evolution algorithm could provide flexible and effective optimization solutions. Future research may further expand into broader space mission domains, including but not limited to space blockade and space defense, exploring how to optimize mission execution effectiveness in these complex space environments using the integrated cooperative co-evolution algorithm while further enhancing its universality and practicality.