Genetic Algorithms-Simulations in Statistical Physics-Lecture Slides, Slides of Statistical Physics

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Genetic Algorithms

Part-two

Simulations in

Statistical Physics

Representation of Candidate Solutions

• GAs on primarily two types of representations:
  • Binary-Coded
  • Real-Coded
• Binary-Coded GAs must decode a chromosome into a

CS, evaluate the CS and return the resulting fitness

back to the binary-coded chromosome representing the

evaluated CS.

Genetic Algorithms:

Binary-Coded Representations

• d(ub,lb,l,c) = (ub-lb) decode(c)/2l-1 + lb , where
  • ub = 2,
  • lb = 1,
  • l = the length of the chromosome in bits
  • c = the chromosome
• The parameter, l, determines the accuracy (and resolution of our search).
• What happens when l is increased (or decreased)?

Binary Coded Representations

Individual

Chromosome: 00101 Fitness = ?????

d(2,1,5, 00101 ) = 1.16 f(1.16) = 1.

Individual

Chromosome: 00101 Fitness = 1.

The Fitness Assignment Process for Binary Coded Ch ro mosomes ( ub=2, lb=1, l=5 )

Real-Coded Representations

Individual Chromosome: 1. Fitness = ?????

f( 1.16 ) = 1.

Individual Chromosome: 1. Fitness = 1.

The Fitness Assignment Process for Real Coded Ch ro mosomes

Parent Selection Methods

• GA researchers have used a number of parent selection

methods.

• Some of the more popular methods are:
  • Proportionate Selection
  • Linear Rank Selection
  • Tournament Selection

• Main idea: better individuals get higher chance
  • Chances proportional to fitness
  • Implementation: roulette wheel technique
    • Assign to each individual a part of the roulette wheel
    • Spin the wheel n times to select n individuals

fitness(A) = 3

fitness(B) = 1

fitness(C) = 2

A C

1/6 = 17%

3/6 = 50%

B

2/6 = 33%

Proportionate Selection

Roulette wheel selection

The most commonly used chromosome selection

techniques is the roulette wheel selection.

100 0

49.5 43.

X1: 16.5% X2: 20.2% X3: 6.4% X4: 6.4% X5: 25.3% X6: 24.8%

Linear Rank Selection

• In Linear Rank selection, individuals are assigned

subjective fitness based on the rank within the

population:

• sfi = (P-ri)(max-min)/(P-1) + min
• Where ri is the rank of indvidual i,
• P is the population size,
• Max represents the fitness to assign to the best individual,
• Min represents the fitness to assign to the worst individual.
• pi = sfi / sfj Roulette Wheel Selection can be

performed using the subjective fitnesses.

• One disadvantage associated with linear rank selection

is that the population must be sorted on each cycle.

Tournament Selection

• In Tournament Selection, q individuals are randomly selected from the population and the best of the q individuals is returned as a parent.
• Selection Pressure increases as q is increased and decreases a q is decreased.

Genetic Procreation Operators

• However, there are a number of crossover operators

that have been used on binary and real-coded GAs:

• Single-point Crossover,
• Two-point Crossover,
• Uniform Crossover

Single-Point Crossover

• Given two parents, single-point crossover will generate

a cut-point and recombines the first part of first parent

with the second part of the second parent to create

one offspring.

• Single-point crossover then recombines the second part

of the first parent with the first part of the second

parent to create a second offspring.

Two-Point Crossover

• Example:
  • Parent 1: X X | X X X | X X
  • Parent 2: Y Y | Y Y Y | Y Y
  • Offspring 1: X X Y Y Y X X
  • Offspring 2: Y Y X X X Y Y

Two-Point crossover is very similar to single-point crossover except that two cut-points are generated instead of one.

Uniform Crossover

• In Uniform Crossover, a value of the first parent’s gene is assigned to the first offspring and the value of the second parent’s gene is to the second offspring with probability 0.5.
• With probability 0.5 the value of the first parent’s gene is assigned to the second offspring and the value of the second parent’s gene is assigned to the first offspring.
• Example:
  • Parent 1: X X X X X X X
  • Parent 2: Y Y Y Y Y Y Y
  • Offspring 1: X Y X Y Y X Y
  • Offspring 2: Y X Y X X Y X