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

More documents

Recommendations

Info

TABLE OF CONTENTS ACKNOWLEDGEMENTS............................................................................................... iv LIST OF TABLES............................................................................................................. ix LIST OF FIGURES .............................................................................................................x LIST OF SYMBOLS AND ABBREVIATIONS ..............................................................xv SUMMARY................................................................................................................... xviii I INTRODUCTION ...................................................................................................1 1.1 Low-Thrust Trajectory Optimization Methods and Tools...........................4 1.1.1 Improvements to Indirect Methods..................................................8 1.1.2 Improvements to Direct Methods ....................................................9 1.1.3 Shape-Based Analytic Methods.....................................................13 1.1.4 Low-Thrust Trajectory Optimization Tools...................................15 1.2 Global Optimization Methods and Applications .......................................18 1.2.1 Evolutionary Algorithms ...............................................................18 1.2.2 Evolutionary Neurocontrollers.......................................................24 1.2.3 Combinatorial Optimization ..........................................................27 1.3 Research Objectives and Contributions.....................................................33 II DEVELOPMENT OF METHODOLOGY............................................................38 2.1 Approach....................................................................................................38 2.2 Candidate Pruning Methods.......................................................................39 2.2.1 Ephemeris-Based Pruning Techniques ..........................................39 2.2.2 Phase-Free, Ballistic Approximations ...........................................42 2.2.3 Pruning Techniques Based on Phasing..........................................43 2.3 Candidate Global Optimization Methods ..................................................44 2.3.1 Genetic Algorithm .........................................................................46 2.3.2 Branch-and-Bound.........................................................................48 2.4 Low-Thrust Trajectory Optimization.........................................................50 vi
2.5 Small Sample Problem...............................................................................54 2.5.1 Evaluation of Pruning Techniques on the Sample Problem ..........58 2.5.2 Evaluation of Global Optimization Methods on the Sample Problem..........................................................................................72 III OVERVIEW OF METHODOLOGY....................................................................86 3.1 Overview of Methodology.........................................................................86 3.2 Assumptions and Scope .............................................................................91 IV VALIDATION OF METHODOLOGY ................................................................94 4.1 Intermediate Sample Problem....................................................................94 4.2 Application of Methodology to Intermediate Problem..............................96 4.2.1 Pruning Phase.................................................................................96 4.2.2 Global Optimization Phase ............................................................99 V APPLICATION OF METHODOLOGY TO LARGER PROBLEMS................105 5.1 Modified GTOC3 Problem ......................................................................106 5.2 GTOC2 Problem ......................................................................................117 5.2.1 Modified GTOC2 Problem ..........................................................119 5.2.2 Full GTOC2 Problem...................................................................127 5.3 Sensitivity of Methodology to User-Defined Parameters........................134 5.3.1 Pruning Phase Sensitivity to Selection of Leg Pruning Percentages ..................................................................................135 5.3.2 Global Optimization Phase Sensitivity to Selection of Initial Lower Bound.....................................................................138 VI CONCLUSIONS AND RECOMMENDATIONS ..............................................141 6.1 Performance of Methodology ..................................................................141 6.1.1 Pruning Phase...............................................................................141 6.1.2 Global Optimization Phase ..........................................................145 6.1.3 Overall Performance ....................................................................148 vii
Page 1 and 2: DESIGN SPACE PRUNING HEURISTICS AND
Page 3 and 4: “The mediocre teacher tells. The
Page 5: I am thankful for all of my friends
Page 9 and 10: LIST OF TABLES Table 1 Ten best ast
Page 11 and 12: LIST OF FIGURES Figure 1 Mars round
Page 13 and 14: Figure 35: Low-thrust optima as a f
Page 15 and 16: LIST OF SYMBOLS AND ABBREVIATIONS A
Page 17 and 18: σBXB υ φ ω Ω Sample standard d
Page 19 and 20: optimization scheme to locate a bro
Page 21 and 22: provide clues to the nature of the
Page 23 and 24: additional constraints and objectiv
Page 25 and 26: Pontryagin’s Minimum Principle, w
Page 27 and 28: improved accuracy (as compared to d
Page 29 and 30: Figure 2: Trajectory structure of t
Page 31 and 32: flyby problems with numerous interm
Page 33 and 34: Gravity assists are modeled as inst
Page 35 and 36: Prior to the LTTT effort, the prima
Page 37 and 38: the shape of the trajectory and ana
Page 39 and 40: draws upon the theory of niche and
Page 41 and 42: the sequence of encounter bodies, t
Page 43 and 44: 1.2.2 Evolutionary Neurocontrollers
Page 45 and 46: Figure 6: Converting an evolutionar
Page 47 and 48: which find good solutions but can n
Page 49 and 50: functions. In this problem, only im
Page 51 and 52: As aforementioned, branch-and-bound
Page 53 and 54: consuming, user-intensive, and ofte
Page 55 and 56: asteroid tour mission design proble
Page 57 and 58:
CHAPTER II DEVELOPMENT OF METHODOLO
Page 59 and 60:
Kˆ ĥ i ν ê v r ω Ĵ Ω nˆ Î
Page 61 and 62:
Finally, both the eccentricity of a
Page 63 and 64:
maximum possible number of revoluti
Page 65 and 66:
outer loop: a genetic algorithm and
Page 67 and 68:
2.3.2 Branch-and-Bound The branch-a
Page 69 and 70:
The order in which the branches are
Page 71 and 72:
approach performs best, followed by
Page 73 and 74:
Figure 16: Effect of number of segm
Page 75 and 76:
Within the sample problem, MALTO wa
Page 77 and 78:
Table 2: Orbital elements of astero
Page 79 and 80:
final mass. The correlation coeffic
Page 81 and 82:
Maximum Final Mass (kg) 1500 1250 L
Page 83 and 84:
The next approach is to compare the
Page 85 and 86:
Final Mass (kg) 950 900 850 800 750
Page 87 and 88:
pruning metric must be calculated f
Page 89 and 90:
educed-size problem. Furthermore, t
Page 91 and 92:
aBiB < 25%, and 15% for Leg 1, Leg
Page 93 and 94:
Earth departure date and three time
Page 95 and 96:
algorithm, which determines the opt
Page 97 and 98:
is calculated using the same specif
Page 99 and 100:
metrics which were calculated in th
Page 101 and 102:
sorted by final mass. All of the se
Page 103 and 104:
impulse optima. Figure 35 plots the
Page 105 and 106:
CHAPTER III OVERVIEW OF METHODOLOGY
Page 107 and 108:
(1) All asteroid sequences are rank
Page 109 and 110:
two-impulse optimum solutions. Ther
Page 111 and 112:
identifying another metric that cou
Page 113 and 114:
CHAPTER IV VALIDATION OF METHODOLOG
Page 115 and 116:
Table 8 lists the 10 best asteroid
Page 117 and 118:
In order to further validate the pr
Page 119 and 120:
impulse ∆V). The first iteration
Page 121 and 122:
Because the impulsive multiplier ha
Page 123 and 124:
Table 12: Effectiveness of the meth
Page 125 and 126:
function calls to MALTO were requir
Page 127 and 128:
order of 0.8 (assuming a final mass
Page 129 and 130:
Table 16: Design variables for gene
Page 131 and 132:
known solution to 1621 kg. Based on
Page 133 and 134:
MBfB (kg) #1, #63, and #16, respect
Page 135 and 136:
problem (Table 17). Additionally, t
Page 137 and 138:
≤ Inclination (deg) 60 50 40 30 2
Page 139 and 140:
order to have a benchmark with whic
Page 141 and 142:
Of the remaining sequences, the 1 s
Page 143 and 144:
Table 22: Settings for the genetic
Page 145 and 146:
120 Impulsive Solutions Low-Thrust
Page 147 and 148:
of exactly four weeks. As a benchma
Page 149 and 150:
Objective Function (kg/yr) 120 100
Page 151 and 152:
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 and 204:
[38] Petropoulos, A., Kowalkowski,
Page 205 and 206:
[57] Wuerl, A., Crain, T., Braden,
Page 207 and 208:
[78] Cosmic Vision: Space Science f
Page 209:
time, she enjoys traveling as well
show all

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

Create successful ePaper yourself

Delete template?

Save as template?