Download Parallel Genetic Algorithms

Parallel Genetic Algorithms
By Larry Hale and Trevor McCasland
Introduction to Genetic Algorithms
• Genetic algorithms are search algorithms that use the principles of
natural selection to find more optimal solutions to modeling,
simulation, and optimization problems.
• Generate “good but not optimal” solutions to brute-forceable
problems
• They then recombine these in an attempt to find an optimal or near
optimal solution
• These candidate solutions are then evaluated for “fitness”.
• Fitness is computationally expensive to evaluate
Biological Background
•
•
•
•
•
•
•
Individual - Any possible solution
Population - The working group of all individuals
Gene - A particular trait of an individual
Chromosome - A set of genes that make a model for an individual
Genome - Set of all chromosomes of an individual
Genotype - Particular set of genes in a genome of an individual
Phenotype - Physical and mental characteristics of an individual
Search Space
• All possible solutions
Fitness
Solution
Selection
• Deciding which members of
the population that will be
used to generate new
solutions through either of
the following
• Random selection
• Selection proportional to
fitness
Evaluation
• Fitness - each individual is evaluated for its effectiveness
• For example, fitness of the following individual is 23 - 10 = 13
• 23 - best possible fitness
• 10 - inferior genes
• 13 - resulting fitness score
Solution
10010101000010101010100
Individual
10100101010101010010101
Evaluation Continued
• A good fitness evaluation
gives a fitness that is
proportional to how close to
the optimal solution it is
• A more practical example,
• 12 total possible
conflicts
• 2 conflicts
• fitness = 12 - 2 = 10
Recombination (or Crossover)
• Selected solutions are recombined in various ways to generate new
solutions
• The most common solution to this is called a one-point crossover
Parent 1
Parent 2
10110001 1010010101001101
10011010 0100101010100111
Child 1
Child 2
10011010 1010010101001101
10110001 0100101010100111
Mutation
• Random changes introduced to aid in finding a better solution
• Chance of mutation is usually between 1 and 2 tenths of a percent
Before:
101100011010010101001101
After:
101100011010110101001101
Genetic Algorithm Process
Initialize
Population
Evaluate
End?
Next Generation
No
Yes
Mutate
Select
Solution
Recombine
Advantages of Parallel Genetic Algorithms
•
•
•
•
•
•
Shares all of the advantages of a serial GA
Higher efficiency and efficacy
Less likely to find suboptimal solutions
Parallel search from multiple points in search space
Can yield alternative solutions to a problem
Robust and not very restrictive because they run independently
Classification of Parallel Genetic Algorithms
• Classification relies of the computation/communication ratio
• Ratio is low for fine grain
parallel GAs
• Fine grain examples
• Master-slave
• Toroidal cluster
• Ratio is high for coarse grain
parallel GAs
• Coarse grain examples
• Ring GA (hypercube or
other topology)
• Dual Species GA
Master-Slave
• Global single-population
• Evaluation of fitness is distributed among slaves
• Selection, recombination, and mutation are all done in the master
processor
Genetic Operators
Master
Individuals
Slaves
Calculate
Fitness
Calculate
Fitness
Fitness
Calculate
Fitness
Calculate
Fitness
Toroidal Cluster
• Separated single-population
• Population is distributed
over processors of a 2D
mesh
• Neighbors share members
of their population for parent
selection
Island
Ring GA
• Multiple populations
• Each processor is assigned
a simple GA and there is
little communication
between populations
• This also restricts the size of
the selection and mating
pools
Migration
Island
Island
Dual Species Genetic Algorithm
• A coarse grained GA with only two subpopulations
• The populations exploit the use of different crossover probability and
mutation operators to prevent premature convergence
• Migration occurs when one of the populations have converged
• Population 1 favors
• crossovers of parents
that are high in similarity
• low mutation rate
• Population 2 favors
• crossovers of parents
that are low in similarity
• high mutation rate
DSGA Process
Initialize
Populations
Evaluate
Populations
End?
Yes
Solution
No
Migrate
Yes
Migrate?
Mutation 1
Crossover 1
Selection 1
Mutation 2
Crossover 2
Selection 2
No
Yes
Migrate?
No
Parallel GA Hybrids
Coarse and fine grain
Coarse grain and master slave
Coarse grain and coarse
grain
Coarse Grained Vs Fine Grained (Rastrigin function)
• Generally coarse grained
genetic algorithms perform
better because of their
efficiency and global
population
• Fine grained genetic
algorithms are favored when
fitness calculation time is
large
MAXSAT FGA Vs SGA
Number of fitness
evaluations: 30000
Population size: 30
Offspring size: 200
Speedup: 43/40 = 1.08
MAXSAT FGA Vs SGA
Number of fitness
evaluations: 30000
Population size: 30
Offspring size: 600
Speedup: 117/75 = 1.56
MAXSAT FGA Vs SGA
Number of fitness
evaluations: 50000
Population size: 30
Offspring size: 1000
Speedup: 211/115 = 1.83
MAXSAT FGA Vs SGA
Number of fitness
evaluations: 100000
Population size: 30
Offspring size: 2000
Speedup: 416/240 = 1.83
Sources
http://neo.lcc.uma.es/Articles/albatroyaxx_2.pdf
http://tracer.uc3m.es/tws/cEA/documents/cant98.pdf
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.45.8861&rep=rep1&ty
pe=pdf
http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4636604
http://neo.lcc.uma.es/cEA-web/documents/hiroyasu.pdf