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84 Tibor Csendes, Balázs Bánhelyi, and Barnabás Garay1. In case a global optimization algorithm finds a point for which the objective function g has a valuebelow C, i.e. when each penalty term max z∈T (I) inf y∈Si d(z, y) is zero, then all the conditions of chaosare fulfilled by the found region represented by the corresponding optimal parameters found. At thesame time, the checking routine provided a guaranteed reliability computational proof of the respectivesubset relations.2. In case the given problem does not have a parameter set within the bounds of the parameters to beoptimized such that the corresponding region would fulfill the criteria of chaos, then the optimizationcannot result in an approximate optimizer point with an objective function value below C.Talk will provide an insight into the theoretical statements and their proofs. On this basiswe have checked chaos for an earlier investigated 7th iterate Hénon mapping and also otherproblem instances, some of them have involved tolerance optimization too [3]. The numericalresults (see also in [1], [4]) will be covered by an other talk.AcknowledgmentsThis work has been partially supported by the Bilateral Austrian-Hungarian project öu56011as well as by the Hungarian National Science Foundation Grants OTKA No. T 037491, T032118, T 034350, T 048377, and T 046822.References[1] Bánhelyi, B., T. Csendes, and B.M. Garay: Optimization and the Miranda approach in detecting horseshoetypechaos by computer. Manuscript, submitted for publication. Available atwww.inf.u-szeged.hu/∼csendes/henon2.pdf[2] Csendes, T.: “Nonlinear parameter estimation by global optimization – efficiency and reliability”, Acta Cybernetica8, 361–370, 1988.[3] Csendes, T., Zabinsky, Z. B. & Kristinsdottir, B. P.: “Constructing large feasible suboptimal intervals for constrainednonlinear optimization”, Annals of Operations Research 58, 279–293, 1995.[4] Csendes, T., Garay, B. M. & Bánhelyi, B.: “A verified optimization technique to locate chaotic regions of aHénon system”, Manuscript, submitted for publication. Available atwww.inf.u-szeged.hu/∼csendes/henon.pdf[5] C-XSC Languages home page: http://www.math.uni-wuppertal.de/org/WRST/index en.html[6] Zgliczynski, P.: Computer assisted proof of the horseshoe dynamics in the Hénon map. Random & ComputationalDynamics 5:1-17, 1997.
Proceedings of GO 2005, pp. 85 – 90.Global Optimization of Low-Thrust Space Missions UsingEvolutionary NeurocontrolBernd DachwaldGerman Aerospace Center (DLR), Institute of Space Simulation, Cologne, Germany,bernd.dachwald@dlr.deAbstractKeywords:Low-thrust space propulsion systems enable flexible high-energy deep space missions, but the designand optimization of the interplanetary transfer trajectory is usually difficult. It involves muchexperience and expert knowledge because the convergence behavior of traditional local trajectoryoptimization methods depends strongly on an adequate initial guess. Within this extended abstract,evolutionary neurocontrol, a method that fuses artificial neural networks and evolutionary algorithms,is proposed as a smart global method for low-thrust trajectory optimization. It does notrequire an initial guess. The implementation of evolutionary neurocontrol is detailed and its performanceis shown for an exemplary mission.Evolutionary Neurocontrol, Spacecraft Trajectory Optimization, Low-Thrust Propulsion.1. Introduction to Low-Thrust MissionsInnovative interplanetary deep space missions require ever larger velocity increments (∆V s)and thus ever more demanding propulsion capabilities. Chemical high-thrust propulsion systems(rocket engines) have a limited ∆V -capability because the chemical energy of the propellantlimits its exhaust velocity. Electric low-thrust propulsion systems can significantlyenhance or even enable high-energy missions by providing much larger exhaust velocitiesthan chemical high-thrust systems. Consequently, they permit significantly larger ∆V s, whileat the same time allowing direct trajectories with simpler mission profiles, flexible launch windows,and mostly even reduced flight times because no gravity assist maneuvers are required.Another innovative low-thrust propulsion system is the solar sail, a large ultra-lightweightreflecting surface made of thin aluminized plastic film. Solar sails utilize solely the freelyavailable solar radiation pressure for propulsion and require therefore no propellant at all.Therefore, their ∆V -capability depends only on their lifetime in the space environment (andtheir distance from the sun). Electric propulsion systems have already been successfully flownin space while solar sails are under development [10].A spacecraft trajectory is, in simple terms, the spacecraft’s path from A (the initial body ororbit) to B (the target body or orbit). In general, the optimality of a trajectory can be definedaccording to several objectives, like transfer time or propellant consumption. Because solarsailcraft does not consume any propellant, trajectories are typically optimized with respectto transfer time alone. Trajectory optimization for electric spacecraft is less straightforwardbecause transfer time minimization and propellant minimization are mostly competing objectives.Spacecraft trajectories can also be classified with respect to the final constraints. If, atarrival, the position r SC and the velocity ṙ SC of the spacecraft must match that of the target, r Tand ṙ T respectively, one has a rendezvous problem. If only the position must match, one hasa flyby problem.
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PROCEEDINGS OF THEINTERNATIONAL WOR
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ContentsPrefaceiiiPlenary TalksYaro
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ContentsviiFuh-Hwa Franklin Liu, Ch
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PLENARY TALKS
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4 Yaroslav D. Sergeyevto work with
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EXTENDED ABSTRACTS
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10 Bernardetta Addis and Sven Leyff
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16 Bernardetta Addis, Marco Locatel
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18 April K. Andreas and J. Cole Smi
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24 Charles Audet, Pierre Hansen, an
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30 János Balogh, József Békési,
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32 János Balogh, József Békési,
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Page 44 and 45: 36 Balázs Bánhelyi, Tibor Csendes
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Page 62 and 63: 54 R. Blanquero, E. Carrizosa, E. C
Page 64 and 65: 56 R. Blanquero, E. Carrizosa, E. C
Page 66 and 67: 58 Sándor Bozókiwhere for any i,
Page 68 and 69: 60 Sándor Bozóki[6] Budescu, D.V.
Page 70 and 71: 62 Emilio Carrizosa, José Gordillo
Page 72 and 73: 64 Emilio Carrizosa, José Gordillo
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Page 80 and 81: 72 Leocadio G. Casado, Eligius M.T.
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Page 84 and 85: 76 Leocadio G. Casado, Eligius M.T.
Page 86 and 87: 78 András Erik Csallner, Tibor Cse
Page 88 and 89: 80 András Erik Csallner, Tibor Cse
Page 90 and 91: 82 Tibor Csendes, Balázs Bánhelyi
Page 94 and 95: 86 Bernd DachwaldFor spacecraft wit
Page 96 and 97: 88 Bernd Dachwaldcurrent target sta
Page 98 and 99: 90 Bernd Dachwaldreference launch d
Page 100 and 101: 92 Mirjam Dür and Chris TofallisMo
Page 102 and 103: 94 Mirjam Dür and Chris Tofallis2.
Page 104 and 105: 96 Mirjam Dür and Chris Tofallis[3
Page 106 and 107: 98 José Fernández and Boglárka T
Page 108 and 109: 100 José Fernández and Boglárka
Page 110 and 111: 102 José Fernández and Boglárka
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Page 118 and 119: 110 Juergen Garloff and Andrew P. S
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Page 125 and 126: Global multiobjective optimization
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Page 138 and 139: 130 Eligius M.T. Hendrix4h(x)3.532.
Page 140 and 141: 132 Eligius M.T. Hendrixneighbourho
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134 Kenneth Holmströmcomputed by R
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136 Kenneth Holmströmα(x) =∑i=1
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138 Kenneth HolmströmGL-step Phase
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140 Kenneth Holmströmsurrogate mod
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142 Dario Izzo and Mihály Csaba Ma
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148 Leo Liberti and Milan DražićV
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150 Leo Liberti and Milan Dražićs
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Set-covering based p-center problem
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Set-covering based p-center problem
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On the Solution of Interplanetary T
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On the Solution of Interplanetary T
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Parametrical approach for studying
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Parametrical approach for studying
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An Interval Branch-and-Bound Algori
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An Interval Branch-and-Bound Algori
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A New approach to the Studyof the S
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A New approach to the Studyof the S
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184 Katharine M. Mullen, Mikas Veng
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190 Niels J. Olieman and Eligius M.
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196 Andrey V. Orlovwhere A is (m 1
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198 Andrey V. OrlovStep 4. Beginnin
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200 Blas Pelegrín, Pascual Fernán
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208 Deolinda M. L. D. Rasteiro and
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214 José-Oscar H. Sendín, Antonio
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220 Ya. D. Sergeyev and D. E. Kvaso
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226 J. Cole Smith, Fransisca Sudarg
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232 Fazil O. Sonmezcost of a config
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234 Fazil O. Sonmezhere f h is the
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236 Fazil O. SonmezThe optimal shap
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238 Alexander S. StrekalovskyDevelo
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PSfrag replacementsPruning a box fr
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Pruning a box from Baumann point in
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A Hybrid Multi-Agent Collaborative
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A Hybrid Multi-Agent Collaborative
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Improved lower bounds for optimizat
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258 Graham R. Wood, Duangdaw Sirisa
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264 Yinfeng Xu and Wenqiang Daiopti
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266 Yinfeng Xu and Wenqiang DaiThe
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Author IndexAddis, BernardettaDipar
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Author Index 271Nasuto, S.J.Departm
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