Cooperative evolutionary algorithm for space trajectory optimization

Original Article

Abstract

A hybrid evolutionary algorithm which synergistically exploits differential evolution, genetic algorithms and particle swarm optimization, has been developed and applied to spacecraft trajectory optimization. The cooperative procedure runs the three basic algorithms in parallel, while letting the best individuals migrate to the other populations at prescribed intervals. Rendezvous problems and round-trip Earth–Mars missions have been considered. The results show that the hybrid algorithm has better performance compared to the basic algorithms that are employed. In particular, for the rendezvous problem, a 100% efficiency can be obtained both by differential evolution and the genetic algorithm only when particular strategies and parameter settings are adopted. On the other hand, the hybrid algorithm always attains the global optimum, even though nonoptimal strategies and parameter settings are adopted. Also the number of function evaluations, which must be performed to attain the optimum, is reduced when the hybrid algorithm is used. In the case of Earth–Mars missions, the hybrid algorithm is successfully employed to determine mission opportunities in a large search space.

Keywords

Trajectory optimization Evolutionary algorithms Mission planning Hybrid algorithm Earth–Mars round-trip mission 

References

  1. Bessette C., Spencer D.: Optimal space trajectory design: a heuristic-based approach. Adv. Astronaut. Sci. 124, 1611–1628 (2006)Google Scholar
  2. Biesbroek, R.: Study of genetic algorithm settings for trajectory optimisation. In: Paper Presented at the 54th International Astronautical Congress, Bremen, Germany, IAF-03-A.P.30, Sept.–Oct. (2003)Google Scholar
  3. Biesbroek, R.: A comparison of differential evolution method with genetic algorithms for orbit optimisation. In: Paper Presented at the 57th International Astronautical Congress, Valencia, Spain, IAF-06-C1.4.02, Oct. (2006)Google Scholar
  4. Bramlette M.: Initialization, mutation, and selection methods in genetic algorithms for function optimization. In: Belew, R.K., Booker, L.B.(eds) Proceedings of the Fourth International Conference on Genetic Algorithms, pp. 100–107. Morgan Kaufmann, San Mateo, CA (1991)Google Scholar
  5. Casalino L., Colasurdo G., Pastrone D.: Mission opportunities for human exploration of Mars. Planet. Space. Sci. 46(11/12), 1613–1622 (1998)CrossRefADSGoogle Scholar
  6. Colasurdo, G., Pastrone, D.: Indirect optimization method for impulsive transfer. In: Paper Presented at the AIAA/AAS Astrodynamics Conference, Scottsdale, AZ, AIAA 94-3762 (1994)Google Scholar
  7. Conway B.A., Chilan C.M., Wall B.J.: Evolutionary principles applied to mission planning problems. celest. Mech. Dyn. Astron. 97(2), 73–86 (2007)MATHCrossRefMathSciNetADSGoogle Scholar
  8. Crain T., Bishop R., Fowler W., Rock K.: Interplanetary flyby mission optimization using a hybrid global-local search method. J. Spacecr. Rockets. 37(4), 468–474 (2000)CrossRefADSGoogle Scholar
  9. Dachwald B., Wie B.: Solar sail kinetic energy impactor trajectory optimization for an asteroid-deflection mission. J. Spacecr. Rockets. 44(4), 755–764 (2007)CrossRefADSGoogle Scholar
  10. Di Lizia, P., Radice, G.: Advanced global optimization tools for mission analysis and design. Final report of ESA Ariadna ITT AO4532/ 18139/04/NL/MV, Call 03/4101, ESA (2004)Google Scholar
  11. Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Sixth International Synposium on Micro Machine and Human Science, pp. 39–43. IEEE, Piscataway, NJ, (1995)Google Scholar
  12. Gage P., Braun R., Kroo I.: Interplanetary trajectory optimization using a genetic algorithm. J. Astron. Sci. 43(1), 59–76 (1995)Google Scholar
  13. Goldberg D., Deb K.: A comparison of selection schemes used in genetic algorithms. In: Rawlins, G.(eds) Foundations of Genetic Algorithms, vol. 1, pp. 450–457. Morgan Kaufmann, San Francisco, CA (1991)Google Scholar
  14. Goldberg D.: Genetic Algorithms in Engineering Design. Wiley, New York, NY (1997)Google Scholar
  15. Hartman J., Coverstone-Carroll V., Williams S.: Optimal interplanetary spacecraft trajectories via pareto genetic algorithm. J. Astron. Sci. 46(3), 267–282 (1998)Google Scholar
  16. Holland J.: Adaption in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, MI (1975)MATHGoogle Scholar
  17. Izzo D., Becerra V., Myatt D., Nasuto S., Bishop J.: Search space pruning and global optimization of multiple gravity assist spacecraft trajectories. J. Glob. Optim. 38(2), 283–296 (2007)MATHCrossRefMathSciNetGoogle Scholar
  18. Kennedy, J., Eberhart, R., Particle swarm optimisation. In: Proceedings of the IEEE International Conference on Neural Networks, pp. 1942–1948. IEEE, Piscataway, NJ, (1995)Google Scholar
  19. Mitchell M.: Introduction to Genetic Algorithms. MIT Press, Ann Arbor, MI (1996)Google Scholar
  20. Myatt, D., Becerra, V., Nasuto, S., Bishop, J.: Advanced global optimization tools for mission analysis and design. Final Report of ESA Ariadna ITT AO4532/18138/04/NL/MV, Call 03/4101, ESA (2004)Google Scholar
  21. Olds A., Kluever C., Cupples M.: Interplanetary mission design using differential evolution. J. Spacecr. Rockets. 44(5), 1060–1070 (2007)CrossRefADSGoogle Scholar
  22. Prussing J.E., Chiu J.-H.: Optimal multiple-impulse time-fixed rendezvous between circular orbits. J. Guid. Control Dyn. 9(1), 17–22 (1986)MATHCrossRefADSGoogle Scholar
  23. Rauwolf G., Coverstone-Carroll V.: Near-optimal low-thrust orbit transfers generated by a genetic algorithm. J. Spacecr. Rockets. 33(6), 859–862 (1996)CrossRefADSGoogle Scholar
  24. Rauwolf G., Coverstone-Carroll V.: Near-optimal low-thrust trajectories via micro-genetic algorithms. J. Guid. Control Dyn. 20(1), 196–198 (1997)CrossRefGoogle Scholar
  25. Rosa Sentinella, M.: Comparison and integrated use of differential evolution and genetic algorithms for space trajectory optimisation. In: Proceedings of the 2007 IEEE Congress on Evolutionary Computation, pp. 973–978. IEEE Press, Singapore, (2007)Google Scholar
  26. Rosa Sentinella, M.: Development of new procedures and hybrid algorithms for space trajectories optimisation. Ph.D. thesis, Politecnico di Torino, Turin, Italy (2008)Google Scholar
  27. Rosa Sentinella, M., Casalino, L.: Genetic algorithm and indirect method coupling for low-thrust trajectory optimization. In: Paper Presented at the 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Sacramento, CA, Paper AIAA 06-4468, June (2006)Google Scholar
  28. Rosa Sentinella M., Casalino L.: Hybrid evolutionary algorithm for the optimization of interplanetary trajectories. J. Spacecr. Rockets. 46(2), 365–372 (2009)CrossRefADSGoogle Scholar
  29. Storn, R.: On the Usage of differential evolution for function optimization. In: 1996 Biennial Conference of the North American Fuzzy Information Processing Society, pp. 519–523. NAFIPS, Berkeley, (1996)Google Scholar
  30. Storn, R., Price, K.: Differential evolution—a simple and efficient adaptive scheme for global optization over continuos spaces. ICSI TR-95-012, ICSI (1995)Google Scholar
  31. Tomassini M.: A survey of genetic algorithm. In: Stauffer, D.(eds) Annual Reviews of Computational Physics, vol. III, pp. 87–118. World Scientific, Singapore (1995)Google Scholar
  32. Trelea I.C.: The particle swarm optimization algorithm: convergence analysis and parameter selection. Inf. Process. Lett. 85(6), 317–325 (2003)MATHCrossRefMathSciNetGoogle Scholar
  33. Vasile M., De Pascale P.: Preliminary design of multiple gravity-assist trajectories. J. Spacecr. Rockets. 43(4), 794–805 (2006)CrossRefADSGoogle Scholar
  34. Vinko, T., Izzo, D., Bombardelli, C.: Benchmarking different global optimisation techniques for preliminary space trajectory design. In: Paper Presented at the 58th International Astronautical Congress, Hyderabad, India, IAC-07-A1.3.01, Oct. (2007)Google Scholar
  35. Walberg G.: How shall we go to Mars? A review of mission scenarios. J. Spacecr. Rockets. 30(2), 129–139 (1993)CrossRefADSGoogle Scholar
  36. Whitley D., Rana S., Heckendorn R.B.: Exploiting separability in search: the island model genetic algorithm. J. Comput. Inf. Technol. 7(1), 33–47 (1999) (special issue on evolutionary computing)Google Scholar
  37. Woo B., Coverstone-Carroll V., Cupples M.: Low-thrust trajectory optimization procedure for gravity-assist, outer-planet missions. J. Spacecr. Rockets. 43(1), 121–129 (2006)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Diparimento di EnergeticaPolitecnico di TorinoTorinoItaly

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