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50 Edson Tadeu Bez, Mirian Buss Gonçalves, and José Eduardo Souza de CursiIn practice, we must choose a value of λ large enough, we generate a finite sample (x 1 , ..., x ns )of elements of S, according to the distribution P and we approximate∑nsx i g(λ, f(x i ))x ∗ ≈ x ∗ ns = i=1∑ns. (10)g(λ, f(x i ))i=1Analogously to [7], we shall use an evolutionary algorithm where the mutation step is performedby using random perturbations of a descent method which iterates as x n+1 = Q n (x n ):the perturbed method iterates as x n+1 = Q n (x n ) + P n , where P n is a convenient randomvariable such as, for instance,P n =a√log(n + b)Z ;ZÑ(0, σId). (11)Equation 10 will be used in order to generate the initial population. The procedure reads asfollows ( [4]):1. Let be given H > 0; three non negative integers NP, NF and NR;2. We generate the initial population S 0 = { x 1 0 , } x2 0 , ..., xNP 0 , by using (Equation 10).3. At step n, S n+1 is derived from S n as follows:Crossover: LetF n ={}yn i = αi n xj n + βi n xk n + γi n : xj n , xk n ∈ S n : i = 1, ..., NF ,where α i n, β i n, γ i n are random values from the uniform distribution on [−H, H]and j and k are randomly chosen;F n contains NF = (2 ∗ NP ) elements;We note B n = S n ∪ F n . B n contains NB = (NP + NF ) elements;Mutation: LetM n = {xp j n = Arg min f(Q n(x j n ) + P j,in ) : xj n ∈ B n : i = 0, ..., NR; j = 1, ..., NB},M n contains NM = (2 ∗ NB) elements; Pn j,0 = 0 e Pnj,1 , ..., Pnj,NR is a sample of NRvalues from P n ;Selection: The elements of A n = B n ∪ M n = S n ∪ F n ∪ M n are increasing orderedaccording to the value of the objective function. The population S n+1 is formed bythe first NP elements of A n , i. e., the best NP elements of S n .In our experiments, the deterministic descent method Q n is the gradient method with optimalstep (steepest descent. See, for instance, [9]). The maximum step is t max =α‖∇f(x , wheren)‖α > 0 is a fixed parameter. Thus, the step t n is defined by the relationf(x n − t n ∇f(x n )) ≤ f(x n − t ∇f(x n )), ∀t ∈ (0, t max ).4. Data SetsWe have tested the method on 4 data sets: three sets of real data and one set of simulated data.The first set of real data comes from the region of Londrina, Brazil,which is divided into 12traffic zones [1]. The second one corresponds to a region that includes part of the State of SantaCatarina, Brazil, divided into 77 zones [5]; The third ones is a subset of the previous region,corresponding to 44 zones of particular interest [5]. The set of simulated data is defined on aregion divided into 30 zones [8].
Calibration of a Gravity–Opportunity Model by Global Optimization 515. ResultsAll the experiments performed use the following set of parameters: NP = 2 (population oftwo elements); ns = 100 (size of the sample for application of the Representation Formula),generated from N(0, 0.5); NR = 5 (Number of random perturbations of the deterministic descentmethod), with a = 0.1, b = 1 and Z generated from N(0, 0.2); initial step size α = 0.7.The determination of the optimal step has been performed by analysis the values of the objectivefunction on a grid of 21 points uniformly distributed on the interval (0, t max ). Furnessiterations have been stopped when either numbers of iterations has reached 100 or the value ofthe objective function has attained 10 −3 : f(β,λ)
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PROCEEDINGS OF THEINTERNATIONAL WOR
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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 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 60 and 61: 52 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
Page 92 and 93: 84 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
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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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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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