# 4. Representation, Mutation, and Recombination

As explained in Chapter 3, there are two fundamental forces that form the basis of evolutionary systems: variation and selection. In this chapter we discuss the EA components behind the first one.

Since variation operators work at the equivalent of the genetic level, that is to say they work on the representation of solutions, rather than on solutions themselves, this chapter is subdivided into sections that deal with different ways in which solutions can be represented and varied within the overall search algorithm.

Contents
Representation, Mutation, and Recombination . . . . . . . . . . . . . 49
4.1 Representation and the Roles of Variation Operators . . . . . . . . . 49
4.2 Binary Representation …………………………….. 51
4.2.1 Mutation for Binary Representation …………….. 52
4.2.2 Recombination for Binary Representation . . . . . . . . . . . . 52
4.3 Integer Representation …………………………….. 54
4.3.1 Mutation for Integer Representations ……………. 55
4.3.2 Recombination for Integer Representation . . . . . . . . . . . . 56
4.4 Real-Valued or Floating-Point Representation …………… 56
4.4.1 Mutation for Real-Valued Representation . . . . . . . . . . . . . 56
4.4.2 Self-adaptive Mutation for Real-Valued Representation . 57
4.4.3 Recombination Operators for Real-Valued Representation………………….. 65
4.5 Permutation Representation ………………………… 67
4.5.1 Mutation for Permutation Representation . . . . . . . . . . . . 69
4.5.2 Recombination for Permutation Representation . . . . . . . 70
4.6 Tree Representation ………………………………. 75
4.6.1 Mutation for Tree Representation ………………. 77
4.6.2 Recombination for Tree Representation ………….. 78