design space pruning heuristics and global optimization method for ...

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[67] Kreher, D.L., Stinson, D.R., Combinatorial Algorithms: Generation, Enumerations, and Search, CRC Press: Boca Raton, FL, 1999. [68] Helvig, C.S., Robins, G., Zelikovsky, A., “The Moving-Target Traveling Salesman Problem,” Journal of Algorithms, Volume 49, 2003, pp. 153-174. [69] Laporte, G., Asef-Vaziri, A., Sriskandarajah, C., “Some Applications of the Generalized Travelling Salesman Problem,” The Journal of the Operational Research Society, Vol. 47, No. 12, December 1996, pp. 1461-1467. [70] Gutin, G., Punnen, A.P., The Traveling Salesman Problem and Its Variations, Springer, 2002. [71] Stodgell, T. R., Spencer, D.B., “Satellite Rendezvous Tours Using Multiobjective Evolutionary Optimization,” AAS 07-382, AAS/AIAA Astrodynamics Specialist Conference, Mackinac Island, MI, 19-23 August 2006. [72] Wall, B.J., Conway, B.A., “Developing a Systematic Approach to the Use of Genetic Algorithms for the Solution of Optimal Spacecraft Trajectory Problems,” AAS 07-161, AAS/AIAA Space Flight Mechanics Meeting, Sedona, AZ, 28 January – 1 February 2007. [73] Vanderplaats, G.N., Numerical Optimization Techniques for Engineering Design, Vanderplaats Research & Development, Inc: Colorado Springs, CO, 2001. [74] Shen, Tsiotras, “Optimal Two-Impulse Rendezvous Using Multiple Revolution Lambert Solutions,” Journal of Guidance, Control, and Dynamics, Vol. 26, No. 1, January-February 2003, pp. 50-61. [75] “Final Rankings and Brief Descriptions of the Returned Solutions and Methods Used for the 2nd Global Trajectory Optimisation Competition,” [http://www2.polito.it/gtoc3/gtoc2_rankings.pdf. Accessed 25 September 2009]. [76] New Frontiers in the Solar System: An Integrated Exploration Strategy, National Research Council, Then National Academies Press, Washington D.C., 2003. [77] Opening New Frontiers in Space: Choices for the Next New Frontiers Announcement of Opportunity, National Research Council, Then National Academies Press, Washington D.C., 2008. 187
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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
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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 and 204: [38] Petropoulos, A., Kowalkowski,
Page 205: [57] Wuerl, A., Crain, T., Braden,
Page 209: time, she enjoys traveling as well
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