Abstract:Multi-target exploration presents an economically efficient scheme, which is gradually becoming the preferred choice for deep space missions such as asteroid exploration, and moons traverse flyby within the Jupiter and Saturn systems. However, the trajectory optimization problem under this scheme is extremely complex. It involves not only continuous variables such as exploration epochs and maneuvering impulses but also integer variables like target selection and visiting sequence. This falls under the domain of mixed-integer programming, constituting a challenging issue in the field of aerospace dynamics and control. First, this paper introduces the mixed-integer trajectory optimization problem in multi-target exploration. Then, the research progress in this problem is explored from three perspectives: transfer trajectory optimization, sequence optimization, and multi-spacecraft collaborative exploration optimization. The characteristics and applicability of various methodologies are discussed. Finally, the future developmental trajectory of this research field is anticipated, offering new perspectives for the optimization and innovation of deep space exploration missions.