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NEW ENERGETIC SELECTION PRINCIPLE IN DIFFERENTIAL EVOLUTION Vitaliy Feoktistov Centre de Recherche LGI2P, Site EERIE, EMA Parc Scientifique Georges Besse, 30035 Nimes, France Vitaliy.Feoktistov@ema.fr Stefan Janaqi Centre de Recherche LGI2P, Site EERIE, EMA Parc Scientifique Georges Besse, 30035 Nimes, France Stefan.Janaqi@ema.fr Keywords: differential evolution, evolutionary algorithms, heuristics, optimization, selection. Abstract: The Differential Evolution algorithm goes back to the class of Evolutionary Algorithms and inherits its philosophy and concept. Possessing only three control parameters (size of population, differentiation and recombination constants) Differential Evolution has promising characteristics of robustness and convergence. In this paper we introduce a new principle of Energetic Selection. It consists in both decreasing the population size and the computation efforts according to an energetic barrier function which depends on the number of generation. The value of this function acts as an energetic filter, through which can pass only individuals with lower fitness. Furthermore, this approach allows us to initialize the population of a sufficient (large) size. This method leads us to an improvement of algorithm convergence. 1 INTRODUCTION Evolutionary Algorithms increasingly become the primary method of choice for optimization problems that are too complex to be solved by deterministic techniques. They are universal, robust, easy to use and inherently parallel. The huge number of applications and continuous interest prove it during several decades (Heitkötter and Beasley, 2000; Beasley, 1997). In comparison with the deterministic methods Evolutionary Algorithm require superficial knowledge about the problem being solved. Generally, the algorithm only needs to evaluate the cost function for a given set of input parameters. Nevertheless, in most cases such heuristics take less time to find the optimum than, for example, gradient methods. One of the latest breakthroughs in the evolutionary computation is the Differential Evolution algorithm. 2 DIFFERENTIAL EVOLUTION Differential Evolution (DE) is a recently invented global optimization technique (Storn and Price, 1995). It can be classified as an iterative stochastic method. Enlarging the Evolutionary Algorithms’ group, DE turns out to be one of the best populationbased optimizers (Storn and Price, 1996; Feoktis- I. Seruca et al. (eds.), Enterprise Information Systems VI, © 2006 Springer. Printed in the Netherlands. 151 151–157. tov and Janaqi, 2004c; Feoktistov and Janaqi, 2004a; Feoktistov and Janaqi, 2004b). In the following lines we give a brief description of DE algorithm. An optimization problem is represented by a set of variables. Let these variables form a D-dimensional vector in continuous space X = (x1,...,xD) ∈ IR D . Let there be some criterion of optimization f :IR D → IR, usually named fitness or cost function. Then the goal of optimization is to find the values of the variables that minimize the criterion, i.e. to find X ∗ : f(X ∗ ) =minf(X) (1) X Often, the variables satisfy boundary constraints L ≤ X ≤ H : L, H ∈ IR D (2) As all Evolutionary Algorithms, DE deals with a population of solutions. The population IP of a generation g has NP vectors, so-called individuals of population. Each such individual represents a potential optimal solution. IP g = X g i , i = 1,...,NP (3) In turn, the individual contains D variables, so called genes. X g i = xgi,j , j = 1,...,D (4) The population is initialized by randomly generating individuals within the boundary constraints, IP 0 = x 0 i,j = randi,j · (hj − lj)+lj (5)
152 ENTERPRISE INFORMATION SYSTEMS VI where rand function generates values uniformly in the interval [0, 1]. Then, for each generation the individuals of the population are updated by means of a reproduction scheme. Thereto for each individual ind a set of other individuals π is randomly extracted from the population. To produce a new one the operations of Differentiation and Recombination are applied one after another. Next, the Selection is used to choose the best. Now briefly consider these operations. Here, we show the typical model of the Differentiation, others can be found in (Feoktistov and Janaqi, 2004a; Feoktistov and Janaqi, 2004c). For that, three different individuals π = {ξ1,ξ2,ξ3} are randomly extracted from a population. So, the result, a trial individual, is τ = ξ3 + F · (ξ2 − ξ1) , (6) where F>0 is the constant of differentiation. After, the trial individual τ is recombined with updated one ind. The Recombination represents a typical case of a genes’ exchange. The trial one inherits genes with some probability. Thus, � τj if randj
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vi TABLE OF CONTENTS PART 1 - DATAB
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viii TABLE OF CONTENTS A WIRELESS A
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CONFERENCE COMMITTEE Honorary Presi
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Hung, P. (AUSTRALIA) Jahankhani, H.
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Invited Papers
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2 ENTERPRISE INFORMATION SYSTEMS VI
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EVOLUTIONARY PROJECT MANAGEMENT: MU
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MANAGING COMPLEXITY OF ENTERPRISE I
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ASSESSING EFFORT PREDICTION MODELS
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ORGANIZATIONAL AND TECHNOLOGICAL CR
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since it means changing the relevan
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ACME-DB: AN ADAPTIVE CACHING MECHAN
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ACME-DB: AN ADAPTIVE CACHING MECHAN
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Hit Rate (%) ACME-DB: AN ADAPTIVE C
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5.3.6 Effect on all Policies by Int
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ACKNOWLEDGEMENTS We would like to t
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This paper describes the data sampl
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The major limit A of the operation
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RELATIONAL SAMPLING FOR DATA QUALIT
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TOWARDS DESIGN RATIONALES OF SOFTWA
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((Brown et al., 1998), pp. 159-190,
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sive data filtering, presentation (
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• implementation changes in servi
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MEMORY MANAGEMENT FOR LARGE SCALE D
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Page 169 and 170: AN EXPERIENCE IN MANAGEMENT OF IMPR
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TOWARDS A META MODEL FOR DESCRIBING
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elementary message (ae-message) can
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problems on a pragmatic level, whic
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TOWARDS A META MODEL FOR DESCRIBING
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INTRUSION DETECTION SYSTEMS USING A
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INTRUSION DETECTION SYSTEMS USING A
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(k� 1) (k) (k�1) (k) p � w
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Table 5: Performance Comparison of
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A USER-CENTERED METHODOLOGY TO GENE
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carries out the second phase of the
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1 1 1 1 2 PROCESS STORE ENTITY EDGE
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constraints rules. KOGGE (Ebert et
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PART 4 Software Agents and Internet
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CABA 2 L A BLISS PREDICTIVE COMPOSI
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Figure 4: Symbols emission in DAR-H
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A METHODOLOGY FOR INTERFACE DESIGN
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and mobility loss coupled with redu
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Tradeoff: The default input is poss
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Sessions on the VABS which are held
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A CONTACT RECOMMENDER SYSTEM FOR A
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A CONTACT RECOMMENDER SYSTEM FOR A
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- "Going to the sources". The user
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Here are the matrix W and P for our
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EMOTION SYNTHESIS IN VIRTUAL ENVIRO
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theme turns out to be surprisingly
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6 FROM FEATURES TO SYMBOLS 6.1 Face
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Electronic Imaging 2000 Conference
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to the accessibility problem for th
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Figure 3: Hierarchical View of the
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4 CONCLUSIONS AND FUTURE WORK On th
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PERSONALISED RESOURCE DISCOVERY SEA
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profile, the user defines his curre
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Abdelkafi, N. .....................
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