The biologically inspired concept of hidden genes has been recently introduced in genetic algorithms to solve optimization problems where the number of design variables is variable. In multigravity-assist trajectories, the hidden genes genetic algorithms demonstrated success in searching for the optimal number of swing-bys and the optimal number of deep space maneuvers. Previous investigations in the literature for multigravity-assist trajectory planning problems show that the standard differential evolution is more effective than the standard genetic algorithms. This paper extends the concept of hidden genes to differential evolution. The hidden genes differential evolution is implemented in optimizing multigravity-assist space trajectories. Case studies are conducted, and comparisons to the hidden genes genetic algorithms are presented in this paper. 1. Introduction A fundamental step in the planning of interplanetary space missions is the design of the spacecraft trajectory. The multigravity-assist trajectory with deep space maneuvers (MGADSMs) is a trajectory that benefits from the gravitational fields of other planets to attain a free momentum change, by performing swing-bys around the planets. MGADSM trajectories can also use impulsive thrust to apply deep space maneuvers (DSMs) as needed. A criterion that is usually used in designing the MGADSM trajectory is to find the MGADSM trajectory that has minimum fuel expenditure. Designing the MGADSM trajectory is then formulated as an optimization problem. The design parameters that need to be optimized are the number of swing-bys, the planets to swing by, the times of swing-bys, the number of DSMs, the components and directions of these DSMs, the times at which these DSMs are applied, and the exact launch and arrival dates. This optimization problem, in its general form, is a variable-length optimization problem where the number of design variables is a variable. For instance, one solution may have 2 DSMs, and another solution for the same problem may have 3 DSMs. The number of design variables is different in both cases. The different number of swing-bys also causes the number of design variables to vary among different solutions. Several optimization approaches have been proposed to solve the MGADSM trajectory design problem. Reference [1] developed a deterministic search space pruning algorithm to search for the optimal solution for a simplified version of the problem. When the gravity-assist sequence (i.e., the number of swing-bys and the planets to swing by) is known a priori, and assuming no
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