## Abstract

Many space mission planning problems may be formulated as hybrid optimal control problems, i.e. problems that include both continuous-valued variables and categorical (binary) variables. There may be thousands to millions of possible solutions; a current practice is to pre-prune the categorical state space to limit the number of possible missions to a number that may be evaluated via total enumeration. Of course this risks pruning away the optimal solution. The method developed here avoids the need for pre-pruning by incorporating a new solution approach using nested genetic algorithms; an outer-loop genetic algorithm that optimizes the categorical variable sequence and an inner-loop genetic algorithm that can use either a shape-based approximation or a Lambert problem solver to quickly locate near-optimal solutions and return the cost to the outer-loop genetic algorithm. This solution technique is tested on three asteroid tour missions of increasing complexity and is shown to yield near-optimal, and possibly optimal, missions in many fewer evaluations than total enumeration would require.

Original language | English (US) |
---|---|

Pages (from-to) | 493-508 |

Number of pages | 16 |

Journal | Journal of Global Optimization |

Volume | 44 |

Issue number | 4 |

DOIs | |

State | Published - Aug 2009 |

## Keywords

- Bilevel programming problem (BLPP)
- Genetic algorithm
- Global trajectory optimization competition (GTOC)
- Hybrid optimal control
- Spacecraft trajectory optimization

## ASJC Scopus subject areas

- Computer Science Applications
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics