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[47] Man, K.F., Tang, K.S., Kwong, S., Genetic Algorithms, Springer, London, England, 1999. [48] Schaefer, Robert, Foundation of Global Genetic Optimization, Springer, Berlin, Germany, 2007. [49] Goldberg, D.E., Richardson, J., “Genetic Algorithms with Sharing for Multimodal Function Optimization,” Proceedings of the 2nd International Conference on Genetic Algorithms, Lawrence Erlbaum Associates: Hillsdale, NJ, 1987. [50] Deb, K., Multi-Objective Optimization using Evolutionary Algorithms, John Wiley & Sons: Chichester, Great Britain, 2001. [51] Deb., K., Pratap, A., Agarwal, S., Meyarivan, T., “A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,” Transactions on Evolutionary Computation, Vol. 6, No. 2, April 2002, pp. 182-197. [52] Bessette, C.R., Spencer, D.B., “Identifying Optimal Interplanetary Trajectories through a Genetic Approach”, AIAA 2006-6306, AIAA/AAS Astrodynamics Specialist Conference, 21-24 August 2006, Keystone, CO. [53] Crain, T. P., Bishop, R.H., Fowler, W., “Interplanetary Flyby Mission Optimization Using a Hybrid Global-Local Search Method,” Journal of Spacecraft and Rockets, Vol. 37, No. 4, July-Aug. 2000, pp. 468-474. [54] Gage, P.J., Braun, R.D., Kroo, I.M., “Interplanetary Trajectory Optimization Using a Genetic Algorithm”, The Journal of the Astronautical Sciences, Vol. 43, No. 1, January-March 1995, pp. 59-75. [55] Vasile, M., Pascale, P. De, “Preliminary Design of Multiple Gravity-Assist Trajectories”, Journal of Spacecraft and Rockets, Vol. 43, No. 4, July-August 2006, pp. 794-805. [56] Dewell, L., Menon, P., “Low-Thrust Orbit Transfer Optimization Using Genetic Search,” AIAA Guidance, Navigation, and Control Conference and Exhibit, AIAA, Reston, VA, 1999, pp. 1109-1111. 185
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Page 1 and 2:
DESIGN SPACE PRUNING HEURISTICS AND
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“The mediocre teacher tells. The
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I am thankful for all of my friends
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2.5 Small Sample Problem...........
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LIST OF TABLES Table 1 Ten best ast
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LIST OF FIGURES Figure 1 Mars round
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Figure 35: Low-thrust optima as a f
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LIST OF SYMBOLS AND ABBREVIATIONS A
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σBXB υ φ ω Ω Sample standard d
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optimization scheme to locate a bro
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provide clues to the nature of the
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additional constraints and objectiv
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Pontryagin’s Minimum Principle, w
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improved accuracy (as compared to d
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Figure 2: Trajectory structure of t
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flyby problems with numerous interm
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Gravity assists are modeled as inst
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Prior to the LTTT effort, the prima
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the shape of the trajectory and ana
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draws upon the theory of niche and
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the sequence of encounter bodies, t
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1.2.2 Evolutionary Neurocontrollers
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Figure 6: Converting an evolutionar
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which find good solutions but can n
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functions. In this problem, only im
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As aforementioned, branch-and-bound
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consuming, user-intensive, and ofte
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asteroid tour mission design proble
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CHAPTER II DEVELOPMENT OF METHODOLO
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Kˆ ĥ i ν ê v r ω Ĵ Ω nˆ Î
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Finally, both the eccentricity of a
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maximum possible number of revoluti
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outer loop: a genetic algorithm and
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2.3.2 Branch-and-Bound The branch-a
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The order in which the branches are
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approach performs best, followed by
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Figure 16: Effect of number of segm
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Within the sample problem, MALTO wa
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Table 2: Orbital elements of astero
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final mass. The correlation coeffic
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Maximum Final Mass (kg) 1500 1250 L
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The next approach is to compare the
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Final Mass (kg) 950 900 850 800 750
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pruning metric must be calculated f
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educed-size problem. Furthermore, t
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aBiB < 25%, and 15% for Leg 1, Leg
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Earth departure date and three time
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algorithm, which determines the opt
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is calculated using the same specif
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metrics which were calculated in th
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sorted by final mass. All of the se
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impulse optima. Figure 35 plots the
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CHAPTER III OVERVIEW OF METHODOLOGY
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(1) All asteroid sequences are rank
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two-impulse optimum solutions. Ther
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identifying another metric that cou
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CHAPTER IV VALIDATION OF METHODOLOG
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Table 8 lists the 10 best asteroid
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In order to further validate the pr
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impulse ∆V). The first iteration
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Because the impulsive multiplier ha
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Table 12: Effectiveness of the meth
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function calls to MALTO were requir
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order of 0.8 (assuming a final mass
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Table 16: Design variables for gene
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known solution to 1621 kg. Based on
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MBfB (kg) #1, #63, and #16, respect
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problem (Table 17). Additionally, t
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≤ Inclination (deg) 60 50 40 30 2
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order to have a benchmark with whic
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Of the remaining sequences, the 1 s
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Table 22: Settings for the genetic
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120 Impulsive Solutions Low-Thrust
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of exactly four weeks. As a benchma
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Objective Function (kg/yr) 120 100
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these two problems, the best known
Page 153 and 154: asteroid sequences would be require
Page 155 and 156: Table 27: Best known solutions rema
Page 157 and 158: Table 29: Best known solutions rema
Page 159 and 160: good solutions exist in the design
Page 161 and 162: heuristics chosen were based on the
Page 163 and 164: problem, the best set of solutions
Page 165 and 166: Finally, for each set of inner loop
Page 167 and 168: solutions from the GTOC2 competitio
Page 169 and 170: sequences were optimized in low-thr
Page 171 and 172: application is for the conceptual d
Page 173 and 174: types of the TSP, they have not bee
Page 175 and 176: methodology would be applied in the
Page 177 and 178: APPENDIX A SET OF GTOC2 ASTEROIDS T
Page 179 and 180: 3054373 "2000 UK11" 0.88325596 0.24
Page 181 and 182: 3152317 "2003 GQ22" 0.87232869 0.18
Page 183 and 184: 3283227 "2005 MR5" 0.85281863 0.295
Page 185 and 186: 2000089 Julia 2.5500653 0.18377079
Page 187 and 188: 2000496 Gryphia 2.1987751 0.079568
Page 189 and 190: 2001216 Askania 2.2322234 0.1793551
Page 191 and 192: 2000134 Sophrosyne 2.5632069 0.1166
Page 193 and 194: 2000712 Boliviana 2.5738464 0.18812
Page 195 and 196: 2005209 "1989 CW1" 5.1533221 0.0495
Page 197 and 198: 36 2006 RJ1 0.9508113 0.30070707 1.
Page 199 and 200: REFERENCES [1] Rayman, M.D., Willia
Page 201 and 202: [20] Hargraves, C. R., and Paris, S
Page 203: [38] Petropoulos, A., Kowalkowski,
Page 207 and 208: [78] Cosmic Vision: Space Science f
Page 209: time, she enjoys traveling as well
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