A novel selection mechanism for evolutionary algorithms with metameric variable-length representations
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METHODOLOGIES AND APPLICATION
A novel selection mechanism for evolutionary algorithms with metameric variable-length representations Matt Ryerkerk1 · Ron Averill1 · Kalyanmoy Deb1 · Erik Goodman1
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Metameric problems are variable-length optimization problems whose representations take on an at least partially segmented structure. This is referred to as a metameric representation. Frequently, each of these segments defines one of a number of analogous components in the solution. Examples include the nodes in a coverage network or turbines in a wind farm. Locating optimal solutions requires, in part, determining the optimal number of components. Evolutionary algorithms can be applied but require modifications to the traditional fixed-length operators. This study proposes a new selection operator for metameric problems: length niching selection. First, the population is partitioned into several niches based on solution length. A window function determines at which lengths a niche is formed. Local selection is then applied within each niche independently, resulting in a new parent population formed by a diverse set of solution lengths. A coverage and a wind farm problem are used to demonstrate the effectiveness of the new operator. Keywords Metameric representations · Evolutionary algorithms · Variable-length algorithms
1 Introduction Evolutionary algorithms (EAs) have been shown to be effective over a wide range of optimization problems. Typically, the number of design variables is fixed; however, variablelength problems also exist. Frequently, this occurs when solutions are composed of a number of analogous components. For example, designing a wind farm might require determining the positioning of a number of wind turbines. If the number of turbines is allowed to vary then so will the number of design variables. Solutions to such problems can be represented using a segmented genome where each segment represents one comCommunicated by V. Loia.
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Matt Ryerkerk [email protected] Ron Averill [email protected] Kalyanmoy Deb [email protected] Erik Goodman [email protected]
1
Michigan State University, East Lansing, USA
ponent (e.g., a turbine). We have previously proposed the term metameric to describe such representations (Ryerkerk et al. 2017, 2019). Metameric structures in biology are composed of a number of segments which are structurally similar, but not necessarily identical (e.g., vertebrae in a spine). Metameric representations have been applied to many optimization problems for a variety of applications, as shown in a recent survey (Ryerkerk et al. 2019). Examples include the design of wind farms (Mosetti et al. 1994; Grady et al. 2005; González et al. 2012; Ryerkerk et al. 2017), coverage networks (Jourdan and de Weck 2004; Molina et al. 2008; Ting et al. 2009; Ryerkerk et al. 2017), neural networks (Whitley et al. 1990; Stanley and Miikkulainen 2002; Palmes et al. 2005; Sun et al. 2017), and composite laminates (Le Riche and H
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