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128 Eligius M.T. Hendrix1.1 EffectivenessFocusing on effectiveness there are several targets a user of the algorithm may have:1. To discover all global minimum points. This of course can only be realised when thenumber of global minimum points is finite.2. To detect at least one global optimal point.3. To find a solution with a function value as low as possible.4. To produce a uniform covering: This idea as introduced by [3], can be relevant for populationbased algorithms.The first and second targets are typical satisfaction targets; was the search successful or not?What are good measures of success? In the older literature, often convergence was used i.e.x k → x ∗ , where x ∗ is one of the minimum points. Alternatively one observes f(x k ) → f(x ∗ ).In tests and analyses, to make results comparable, one should be explicit in the definitions ofsuccess. We need not only to specify ɛ and/or δ such that‖x k − x ∗ ‖ < ɛ and/or f(x k ) < f(x ∗ ) + δ (2)but we should also specify whether success means that there is an index K such that (2) is truefor all k > K. Alternatively, a record min k f(x k ) may have reached level f(x ∗ ) + δ and this canbe considered a success. Whether the algorithm is effective also depends on the stochastic natureof it. When we are dealing with stochastic algorithms, the effectiveness can be expressedas the probability that a success has been reached. In analysis, this probability can be derivedwhen having sufficient assumptions on the behaviour of the algorithm and in numerical experimentsit can be estimated by looking over repeated runs how many times the algorithmleads to convergence. We will give some examples of such analysis.1.2 EfficiencyGlobally efficiency is defined as the effort the algorithm needs to be successful. A usual indicatorfor algorithms is the (expected) number of function evaluations necessary to reach theoptimum. This indicator depends on many factors such as the shape of the test function andthe termination criteria used. The indicator more or less suggests that the calculation effortof function evaluations dominates the other calculation effort of the algorithm. Several otherindicators appear in literature that can be considered to be derived from the main indicator.In nonlinear programming (e.g. [5] and [2]) the concept of convergence speed is common.It is a limiting concept on the convergence of the series x k . Let x 0 , x 1 , . . . , x k , . . . converge topoint x ∗ . The largest number α for which‖x k+1 − x ∗ ‖limk→∞ ‖x k − x ∗ ‖ α = β < ∞ (3)gives the order of convergence, whereas β is called the convergence factor. In this terminology,among others the following concepts appearlinear convergence means α = 1 and β < 1quadratic convergence means α = 2 and 0 < β < 1superlinear convergence: 1 < α < 2 and β < 1, i.e. β = 0 for α = 1.Mainly in deterministic GO algorithms, information on the past evaluations is stored in thecomputer memory. This requires efficient data handling for looking up necessary information
On the goodness of Global Optimisation Algorithms 129during the iterations. As well memory requirement as retrieving actions become a part of thecomputational burden that cannot be neglected compared to the computational effort due tofunction evaluations. These aspects become important from the perspective of efficiency ofalgorithms.In stochastic GO algorithms an efficiency indicator is the success rate defined as the probabilitythat the next iterate is an improvement on the record value found thus far P (f(x k )
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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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36 Balázs Bánhelyi, Tibor Csendes
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Proceedings of GO 2005, pp. 39 - 45
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MGA Pruning Technique 41Figure 1. A
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MGA Pruning Technique 43O(n) = k 2
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MGA Pruning Technique 45one), while
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48 Edson Tadeu Bez, Mirian Buss Gon
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54 R. Blanquero, E. Carrizosa, E. C
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56 R. Blanquero, E. Carrizosa, E. C
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58 Sándor Bozókiwhere for any i,
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60 Sándor Bozóki[6] Budescu, D.V.
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62 Emilio Carrizosa, José Gordillo
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64 Emilio Carrizosa, José Gordillo
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Globally optimal prototypes 69Refer
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72 Leocadio G. Casado, Eligius M.T.
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874 Leocadio G. Casado, Eligius M.T
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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
Page 108 and 109: 100 José Fernández and Boglárka
Page 110 and 111: 102 José Fernández and Boglárka
Page 112 and 113: 104 Erika R. Frits, Ali Baharev, Zo
Page 118 and 119: 110 Juergen Garloff and Andrew P. S
Page 120 and 121: 112 Juergen Garloff and Andrew P. S
Page 123 and 124: Proceedings of GO 2005, pp. 115 - 1
Page 125 and 126: Global multiobjective optimization
Page 127 and 128: Global multiobjective optimization
Page 131 and 132: Conditions for ε-Pareto Solutions
Page 133: Conditions for ε-Pareto Solutions
Page 138 and 139: 130 Eligius M.T. Hendrix4h(x)3.532.
Page 140 and 141: 132 Eligius M.T. Hendrixneighbourho
Page 142 and 143: 134 Kenneth Holmströmcomputed by R
Page 144 and 145: 136 Kenneth Holmströmα(x) =∑i=1
Page 146 and 147: 138 Kenneth HolmströmGL-step Phase
Page 148 and 149: 140 Kenneth Holmströmsurrogate mod
Page 150 and 151: 142 Dario Izzo and Mihály Csaba Ma
Page 156 and 157: 148 Leo Liberti and Milan DražićV
Page 158 and 159: 150 Leo Liberti and Milan Dražićs
Page 163 and 164: Set-covering based p-center problem
Page 165 and 166: Set-covering based p-center problem
Page 169 and 170: On the Solution of Interplanetary T
Page 171 and 172: On the Solution of Interplanetary T
Page 175 and 176: Parametrical approach for studying
Page 177 and 178: Parametrical approach for studying
Page 181 and 182: An Interval Branch-and-Bound Algori
Page 183 and 184: 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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