Chapter 5: Implementing a GA

Section 5.1: When Should a GA Be Used?

• Search space is large
• Search space is not well understood
• Fitness function is noisy
• Satisficing is acceptable

Section 5.2: Encoding a Problem for a GA

• Typically fixed length
• Typically fixed ordering

Binary Encodings

• There are variants, such as Gray coding

Many-Character and Real-Valued Encodings

Tree Encodings

• Variable length
• Example: Koza's Lisp programs

Section 5.3: Adapting the Encoding

• A potential solution for the linkage problem enabling related loci to be close together
• A variable length encoding presents a larger solution space

Inversion

• Idea: if the original string is abcdefgh, the new string after inversion might be abfedcgh
• The position of each gene now needs to be explicitly represented, for example {(1, a) (2, b) (3, c) (4, d) (5, e) (6, f) (7, g) (8, h)}
• What is a potential problem with single point crossover?
• One potential solution is to use a master / slave approach

Exploring Crossover "Hot Spots"

• ! represents a crossover spot
• Parent 1: 1 0 0 1 ! 1 1 1 ! 1
• Parent 2: 0 0 0 0 0 0 ! 0 0
• Child 1: 1 0 0 1 ! 0 0 ! 1 ! 0
• Child 2: 0 0 0 0 1 1 0 1

Messy GAs

• Goldberg et. al.
• Loci can be overspecified
• Loci can be underspecified
• For example a binary chromosome of length four might be {(1, 0) (2, 0) (4, 1) (4, 0)}
• For overspecified positions, read off the leftmost value
• For underspecified positions, do one bit hill climbing and use the fitness of the local optimum
• Phase 1: Primordial Phase. Guess(!!) the order of a solution, k. Generate all(!!) possible solutions of size k. Reduce the size of the population using fitness based selection.
• Phase 2: Juxtaposition Phase. Use "cut" and "splice" to produce the next generation. No mutation.
• The approach worked well on a 30 bit "deceptive problem" where f(000) = 28, f(001) = 26, f(010) = 22, f(011) = 0, f(100) = 14, f(101) = 0, f(110) = 0, f(111) = 30