×

zbMATH — the first resource for mathematics

Cooperative evolutionary algorithm for space trajectory optimization. (English) Zbl 1223.70098
Summary: 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.

MSC:
70M20 Orbital mechanics
70-08 Computational methods for problems pertaining to mechanics of particles and systems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bessette C., Spencer D.: Optimal space trajectory design: a heuristic-based approach. Adv. Astronaut. Sci. 124, 1611–1628 (2006)
[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)
[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)
[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)
[5] Casalino L., Colasurdo G., Pastrone D.: Mission opportunities for human exploration of Mars. Planet. Space. Sci. 46(11/12), 1613–1622 (1998) · Zbl 0908.93047 · doi:10.1016/S0032-0633(97)00220-1
[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)
[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) · Zbl 1162.70021 · doi:10.1007/s10569-006-9052-7
[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) · doi:10.2514/2.3607
[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) · doi:10.2514/1.22586
[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)
[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)
[12] Gage P., Braun R., Kroo I.: Interplanetary trajectory optimization using a genetic algorithm. J. Astron. Sci. 43(1), 59–76 (1995)
[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)
[14] Goldberg D.: Genetic Algorithms in Engineering Design. Wiley, New York, NY (1997)
[15] Hartman J., Coverstone-Carroll V., Williams S.: Optimal interplanetary spacecraft trajectories via pareto genetic algorithm. J. Astron. Sci. 46(3), 267–282 (1998)
[16] Holland J.: Adaption in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, MI (1975) · Zbl 0317.68006
[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) · Zbl 1179.90342 · doi:10.1007/s10898-006-9106-0
[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)
[19] Mitchell M.: Introduction to Genetic Algorithms. MIT Press, Ann Arbor, MI (1996)
[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) · Zbl 1179.90342
[21] Olds A., Kluever C., Cupples M.: Interplanetary mission design using differential evolution. J. Spacecr. Rockets. 44(5), 1060–1070 (2007) · doi:10.2514/1.27242
[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) · Zbl 0606.93046 · doi:10.2514/3.20060
[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) · doi:10.2514/3.26850
[24] Rauwolf G., Coverstone-Carroll V.: Near-optimal low-thrust trajectories via micro-genetic algorithms. J. Guid. Control Dyn. 20(1), 196–198 (1997) · doi:10.2514/2.4020
[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)
[26] Rosa Sentinella, M.: Development of new procedures and hybrid algorithms for space trajectories optimisation. Ph.D. thesis, Politecnico di Torino, Turin, Italy (2008)
[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)
[28] Rosa Sentinella M., Casalino L.: Hybrid evolutionary algorithm for the optimization of interplanetary trajectories. J. Spacecr. Rockets. 46(2), 365–372 (2009) · Zbl 1223.70098 · doi:10.2514/1.38440
[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)
[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)
[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)
[32] Trelea I.C.: The particle swarm optimization algorithm: convergence analysis and parameter selection. Inf. Process. Lett. 85(6), 317–325 (2003) · Zbl 1156.90463 · doi:10.1016/S0020-0190(02)00447-7
[33] Vasile M., De Pascale P.: Preliminary design of multiple gravity-assist trajectories. J. Spacecr. Rockets. 43(4), 794–805 (2006) · doi:10.2514/1.17413
[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)
[35] Walberg G.: How shall we go to Mars? A review of mission scenarios. J. Spacecr. Rockets. 30(2), 129–139 (1993) · doi:10.2514/3.11521
[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)
[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) · doi:10.2514/1.14665
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.