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34 János Balogh, József Békési, Gábor Galambos, and Mihály Csaba Markót4. SummaryThe paper dealt with a nice connection between a discrete (combinatorial) optimization problemand global optimization. The lower bound constructions given for special bin packingproblems led to a nonlinear optimization problem, and after some transformations the solutionswere delivered. Our construction is more general than the ones of [11] and [9], and itsspecial cases improved the results of [9] by answering the questions raised in the paper.AcknowledgmentsThe research was supported by the Hungarian National Research Fund (projects T 048377 andT 046822) an by the MÖB-DAAD Hungarian-German Researcher Exchange Program (projectNo. 21). The authors wish to thank to Tamás Vinkó for his ideas and for the first, previousnumerical tests.References[1] J. Balogh, J. Békési, and G. Galambos. Lower Bound for Bin Packing Problem with Restricted Repacking.Manuscript, 2005. Available at http://www.jgytf.u-szeged.hu/∼bekesi/crestbinp.ps.[2] E.G. Coffman, G. Galambos, S. Martello, and D. Vigo. Bin Packing Approximation Algorithms: CombinatorialAnalysis. In Handbook of Combinatorial Optimization (Eds. D.-Z. Du and P.M. Pardalos), pages 151-208.Kluwer Academic Publishers, 1999.[3] J. Csirik and G.J. Woeginger. Online packing and covering problems. In: Online Algorithms: The State of theArt, Eds. A. Fiat and G.J. Woeginger, pages 147-177, Berlin, 1998. Springer-Verlag, LNCS 1442.[4] G. Galambos. A new heuristic for the classical bin packing problem. Technical Report 82, Institute fuer Mathematik,Augsburg, 1985.[5] G. Galambos and G.J. Woeginger. Repacking helps in bounded space on-line bin packing. Computing, 49:329-338, 1993.[6] G. Gambosi, A. Postiglione, and M. Talamo. Algorithms for the Relaxed Online Bin-Packing Model. SIAM J.Computing, 30(5): 1532-1551, 2000.[7] M.R. Garey and D.S. Johnson. Computers and Intractability (A Guide to the theory of NP-Completeness). W.H.Freeman and Company, San Francisco, 1979.[8] E.F. Grove. Online bin packing with lookahead. SODA 1995: 430–436.[9] G. Gutin, T. Jensen, and A. Yeo. Batched bin packing. Discrete Optimization, 2(1): 71-82, 2005.[10] E. Hansen. Global Optimization Using Interval Analysis. Marcel Dekker, New York, 1992.[11] Z. Ivkovič and E.L. Lloyd. A fundamental restriction on fully dynamic maintenance of bin packing. InformationProcessing Letters, 59(4): 229-232, 1996.[12] Z. Ivkovič and E.L. Lloyd. Fully Dynamic Algorithms for Bin Packing: Being (Mostly) Myopic Helps. SIAMJ. Computing, 28(2): 574-611, 1998.[13] M.Cs. Markót, T. Csendes, and A.E. Csallner. Multisection in interval branch-and-bound methods for globaloptimization. II. Numerical tests. Journal of Global Optimization, 16(3): 219-228, 2000.[14] R.E. Moore. Interval Analysis. Prentice–Hall, Englewood Cliffs, 1966.[15] H. Ratschek and J. Rokne. New Computer Methods for Global Optimization. Ellis Horwood, Chichester, 1988.[16] S.S. Seiden. On the online bin packing problem. Journal of the ACM, 49(5): 640-671, 2002.[17] A. Van Vliet. An improved lower bound for online bin packing algorithms. Information Processing Letters,43(5): 277-284, 1992.
Proceedings of GO 2005, pp. 35 – 37.A global optimization model for locating chaos: numericalresults ∗Balázs Bánhelyi, 1 Tibor Csendes, 1 and Barnabás Garay 21 University of Szeged, Szeged, Hungary, banhelyi|csendes@inf.u-szeged.hu2 Budapest University of Technology, Budapest, Hungary, garay@math.bme.huAbstractKeywords:We present a computer assisted proofs for the existence of so-called horseshoes of the different iteratesof the classical Hénon map (H(x, y) = (1 + y − αx 2 , βx)). An associated abstract providesalgorithms and the theoretical basis for the checking of three geometrical conditions to be fulfilled byall points of the solution region. The method applies interval arithmetic and recursive subdivision.This verified technique proved to be fast on the investigated problem instances. So we were able tosolve some unsolved problems, the present talk will summarize these computational results.Chaos, Hénon-mapping, Computer-aided proof.After having introduced our computational methodology to locate chaotic regions (see theassociated abstract and the papers [4] and [1]), now we concentrate on the obtained numericalresults. First we have checked the reported chaotic region [6] by our checking routine.We have investigated the seventh iterate of the Hénon mapping with the parameters ofA = 1.4 and B = 0.3. The checked region consists of two parallelograms with sides parallel tothe x-axis, the first coordinates of the lower corner points were 0.460, 0.556, 0.588, and 0.620,while the second coordinates were the same, 0.01. The common y coordinate for the uppercorner points was 0.28. The tangent of the sides was 2. We have set the ε threshold value forthe checking routine to be 10 −10 .First the algorithm determined the starting interval, that contains the region to be checked:[0.46000000000, 0.75500000000] × [0.01000000000, 0.28000000000].Then the three conditions were checked one after the other. All of these proved to be valid— as expected. The amount of function evaluations (for the transformation, i.e. for the seventhiterate of the Hénon mapping in each case) were 273, 523, and 1613, respectively. Thealgorithm stores those subintervals for which it was impossible to prove whether the givencondition holds, these required further subdivision to achieve a conclusion. The depth of thestack necessary for the checking was 11, 13, and 14, respectively. The CPU time used provedto be negligible, only a few seconds.Then, We have applied the global optimization model for the 5th iterate Hénon mapping.Note that the less the iteration number, the more difficult the related problem: no chaoticregions were reported for the iterates less than 7 till now. We have solved the optimizationproblem with a clustering method [2]. After some experimentation, the search domain set for∗ This work has been partially supported by the Bilateral Austrian-Hungarian project öu56011 as well as by the HungarianNational Science Foundation Grants OTKA No. T 037491, T 032118, T 034350, T 048377, and T 046822.
Page 1: PROCEEDINGS OF THEINTERNATIONAL WOR
Page 5 and 6: ContentsPrefaceiiiPlenary TalksYaro
Page 7 and 8: ContentsviiFuh-Hwa Franklin Liu, Ch
Page 9: PLENARY TALKS
Page 12 and 13: 4 Yaroslav D. Sergeyevto work with
Page 15: EXTENDED ABSTRACTS
Page 18 and 19: 10 Bernardetta Addis and Sven Leyff
Page 24 and 25: 16 Bernardetta Addis, Marco Locatel
Page 26 and 27: 18 April K. Andreas and J. Cole Smi
Page 32 and 33: 24 Charles Audet, Pierre Hansen, an
Page 38 and 39: 30 János Balogh, József Békési,
Page 40 and 41: 32 János Balogh, József Békési,
Page 44 and 45: 36 Balázs Bánhelyi, Tibor Csendes
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Page 49 and 50: MGA Pruning Technique 41Figure 1. A
Page 51 and 52: MGA Pruning Technique 43O(n) = k 2
Page 53: MGA Pruning Technique 45one), while
Page 56 and 57: 48 Edson Tadeu Bez, Mirian Buss Gon
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 77: Globally optimal prototypes 69Refer
Page 80 and 81: 72 Leocadio G. Casado, Eligius M.T.
Page 82 and 83: 874 Leocadio G. Casado, Eligius M.T
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
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84 Tibor Csendes, Balázs Bánhelyi
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86 Bernd DachwaldFor spacecraft wit
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88 Bernd Dachwaldcurrent target sta
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90 Bernd Dachwaldreference launch d
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92 Mirjam Dür and Chris TofallisMo
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94 Mirjam Dür and Chris Tofallis2.
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96 Mirjam Dür and Chris Tofallis[3
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98 José Fernández and Boglárka T
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100 José Fernández and Boglárka
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102 José Fernández and Boglárka
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104 Erika R. Frits, Ali Baharev, Zo
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110 Juergen Garloff and Andrew P. S
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112 Juergen Garloff and Andrew P. S
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Proceedings of GO 2005, pp. 115 - 1
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Global multiobjective optimization
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Global multiobjective optimization
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Conditions for ε-Pareto Solutions
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Conditions for ε-Pareto Solutions
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128 Eligius M.T. Hendrix1.1 Effecti
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130 Eligius M.T. Hendrix4h(x)3.532.
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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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Page 196 and 197:
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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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Page 272 and 273:
264 Yinfeng Xu and Wenqiang Daiopti
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266 Yinfeng Xu and Wenqiang DaiThe
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Author IndexAddis, BernardettaDipar
Page 279:
Author Index 271Nasuto, S.J.Departm
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