# Genetic Algorithms and Genetic Programming: Modern Concepts and Practical Applications (Numerical Insights)

## Michael Affenzeller

Language: English

Pages: 379

ISBN: 1584886293

Format: PDF / Kindle (mobi) / ePub

**Genetic Algorithms and Genetic Programming: Modern Concepts and Practical Applications** discusses algorithmic developments in the context of genetic algorithms (GAs) and genetic programming (GP). It applies the algorithms to significant combinatorial optimization problems and describes structure identification using HeuristicLab as a platform for algorithm development.

The book focuses on both theoretical and empirical aspects. The theoretical sections explore the important and characteristic properties of the basic GA as well as main characteristics of the selected algorithmic extensions developed by the authors. In the empirical parts of the text, the authors apply GAs to two combinatorial optimization problems: the traveling salesman and capacitated vehicle routing problems. To highlight the properties of the algorithmic measures in the field of GP, they analyze GP-based nonlinear structure identification applied to time series and classification problems.

Written by core members of the HeuristicLab team, this book provides a better understanding of the basic workflow of GAs and GP, encouraging readers to establish new bionic, problem-independent theoretical concepts. By comparing the results of standard GA and GP implementation with several algorithmic extensions, it also shows how to substantially increase achievable solution quality.

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, and f3 as mse(E1 , T ), mse(E2 , T ), and mse(E3 , T ), respectively yielding f itness(f1) = 26.0 (2.12) f itness(f2) = 100.5 f itness(f3) = 9.0 (2.13) (2.14) Whereas the search for formulas that minimize a given error function (or maximize some other given ﬁtness function) is the major goal of GP-based regression, the shape and the size of the solution could also be integrated into the ﬁtness estimation function. The number and values of coeﬃcients used is another issue that is tackled in.

Actual population size between the two borders (lower and upper limit of population size) displaying also the identical chromosomes that occur especially in the last iterations. the traveling salesman problem taken from the TSPLib [Rei91]. More sophisticated studies analyzing the characteristics of RAPGA will be presented in Chapter 7. 4.4 Consequences Arising out of Offspring Selection and RAPGA Typically, GAs operate under the implicit assumption that parent individuals of above average.

Tours (a b c d e f g h i j) and (c f g a j b d i e h). The PMX operator creates an oﬀspring in the following way: First, it randomly selects two cutting points along the strings. As indicated in Figure 8.4, suppose that the ﬁrst cut point is selected between the ﬁfth © 2009 by Taylor & Francis Group, LLC 134 Genetic Algorithms and Genetic Programming a b c d e f g h i j Parent 1 c f g a j b d i e h Parent 2 c fb gd a j bf dg ih e hi Offspring FIGURE 8.4:.

Customers and ﬁnally with every single customer. Once a better solution has been found, the operator starts again with three consecutive customers and continues until no further improvement is possible. Local search methods can improve solutions on the one hand, but on the other hand they also might reduce the diversity in a population when applied to several individuals which could end in the same local minimum. © 2009 by Taylor & Francis Group, LLC Chapter 9 Evolutionary System.

But also which ones are activated and which ones are not, and an initial weighting factor is also given for each deﬁnition denoting its relative probability to be chosen when it comes to selecting a randomly chosen function or terminal. 9.2.4 9.2.4.1 Solution Representation Representing Formulas by Structure Trees As we have now described how function and terminal deﬁnitions are managed, we shall take a look at the representation of solution candidates for GP-based system identiﬁcation. The.