Genetic algorithms applied to the solution of hybrid optimal control problems in astrodynamics

Bradley J. Wall, Bruce A. Conway

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)493-508
Number of pages16
JournalJournal of Global Optimization
Issue number4
StatePublished - Aug 2009


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

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics
  • Business, Management and Accounting (miscellaneous)
  • Computer Science Applications
  • Management Science and Operations Research


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