[...]... introduction into the field of representations for genetic and evolutionary algorithms The chapter provides the basis and definitions which are essential for understanding the content of this work Genetic and evolutionary algorithms (GEAs) are nature-inspired optimization methods that can be advantageously used for many optimization problems GEAs imitate basic principles of life and apply genetic operators like... performance increases if optimal solutions are similar to the MST Analyzing and developing direct representations nicely illustrates the trade-off between designing either problem-specific representations or problem-specific operators For efficient GEAs, it is necessary either to design problem-specific representations and to use standard operators like one-point or uniform crossover, or to develop problem-specific... optimization problem separately For more information about direct representations we refer to Chap 7 2.2 Genetic and Evolutionary Algorithms In this section, we introduce genetic and evolutionary algorithms We illustrate basic principles and outline the basic functionality of GEAs The schema theorem stated by Holland (1975) explains the performance of selectorecombinative GAs and leads us to the building... that genetic search is independent of the structure of the optimal solution Although no explicit genotype-phenotype mapping exists for edge-sets and the framework for the design of representations cannot be directly applied, the framework is useful for structuring the analysis of edge-sets Similarly to non-uniformly redundant representations, edge-sets overrepresent some specific types of tree and GEA... 1 2 4 2 Representations for Genetic and Evolutionary Algorithms 2.1 Genetic Representations 2.1.1 Genotypes and Phenotypes 2.1.2 Decomposition of the Fitness Function 2.1.3 Types of Representations 2.2 Genetic and Evolutionary Algorithms 2.2.1 Principles... 178 6.4.1 Motivation and Functionality 179 6.4.2 Bias and Non-Uniformly Redundant Representations 183 6.4.3 The Node-Biased Encoding 184 6.4.4 A Concept for the Analysis of Redundant Representations 187 6.4.5 Population Sizing for the Link-Biased Encoding 191 6.4.6 The Link -and- Node-Biased Encoding ... that the reasons for problem difficulty depend on the used optimization method, we describe some common measurements of problem complexity Finally, in Sect 2.4 we review some former recommendations for the design of efficient representations 2.1 Genetic Representations This section introduces representations for genetic and evolutionary algorithms When using GEAs for optimization purposes, representations. .. framework for the analysis and design of tree representations For tree representations, standard crossover and mutation operators are applied to tree-specific genotypes However, finding or defining tree-specific genotypes and genotype-phenotype mappings is a difficult task because there are no intuitive genotypes for trees Therefore, researchers have proposed a variety of different, more or less tricky representations. .. were used for the design of genetic and evolutionary algorithms 2.2.2 Functionality Genetic and evolutionary algorithms imitate the principles of life outlined in the previous subsection and use it for optimization purposes Researchers have proposed many different variants of GEAs in the literature For illustrating the basic functionality of GEAs we want to use the traditional standard simple genetic. .. a string This type of representation can be used for binary, integer, and real-valued representations and allows an encoding which is independent of the position of the alleles in the chromosome Later, Goldberg et al (1989) used this position-independent representation for the messy genetic algorithm 2.2 Genetic and Evolutionary Algorithms 15 Direct Representations In Sect 2.1.2, we have seen that . x0 y0 w0 h0" alt="" Representations for Genetic and Evolutionary Algorithms Franz Rothlauf Representations for Genetic and Evolutionary Algorithms ABC Dr. Franz Rothlauf Universität Mannheim 68131. significance and importance of the presented represen- tation framework on the performance of GEAs, the framework is used for analyzing the performance of binary representations of integers and tree rep- resentations are presented for redundant and non-uniformly scaled encodings. Furthermore, it is shown that low-locality representations can change the difficulty of the problem. For low-locality en- codings,