Case I

Figure 8.16  Total Produced by the GA vs. number of generations.

When the GA is run on this case, the results shown in Table 8.6 were obtained. These results are also shown in Figure 8.17.

Table 8.6 GA results for transfer orbit parameters for non-planar elliptical initial and final orbits. (GA population size=150, number of generations=15, probability of crossover=0.9, probability of mutation=0.001)

	GA Results
Eccentricity	0.1652
α1	0.6222°
Semi-major axis	7007.6 km
	2.6019 km/sec

Figure 8.17  Initial and final orbits along with GA-produced transfer orbit.

Case II

Figure 8.18  Total ΔV produced by the GA vs. number of generations.

When the GA is run on this case, the following results (Table 8.8) (Figure 8.19), were obtained:

Table 8.8 GA results for transfer orbit parameters for non-planar elliptical initial and final orbits, (GA population size=150, number of generations=15, probability of crossover=0.9, probability of mutation=0.001.)

	GA Results
Eccentricity	0.2717
α1	4.2387°
Semi-major axis	8835.6 km
	5.736 km/sec

Figure 8.19  Initial and final orbits along with GA-produced transfer orbit.

Case III

When the GA is run on this case, it produced the following results (Table 8.10) (Figure 8.20):

Table 8.10 GA results for transfer orbit parameters for non-planar elliptical initial and final orbits. (GA population size=150, number of generations=10, probability of crossover=0.9, probability of mutation=0.01.)

	Analytical Results	GA Results
Eccentricity	0.2289	0.241
α1	0°	0°
Semi-major axis	8300 km	8432 km
	0.5963 km/sec	0.6643 km/sec

Figure 8.20  (a) Initial and final orbits along with analytical transfer orbit (b) Initial and final orbits along with GA produced transfer orbit.

CONCLUSIONS

A genetic algorithm was used to search for transfer orbits which minimize the velocity change needed to transverse from one orbit to another. The effectiveness of using this approach was tested through comparison to two problems with known solutions. The GA produced near optimum results for the coplanar and non-coplanar Hohmann transfer problems. The GA was then used to search for transfer orbits between non-circular orbits which are inclined. While no analytical solutions exist for such problems, the resulting GA solution appeared quite reasonable. Therefore, it can be concluded that a genetic algorithm can be used successfully to find near optimum transfer orbits for ΔV_TOT requirements.

REFERENCES

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3  Lawden, D. S. (1962). Impulsive transfer between elliptical orbits. Optimization Techniques (Chapter 11), edited by G. Leitmann, New York: Academic Press.

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