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2 Parameter Study

2.1 Initial Configuration

To investigate the influence of some important configuration parameters of the Genetic Programming kernel, a problem which can be quickly calculated was selected: the lawn-mower problem (See Koza's book).

The lawn-mower problem can be described as follows. Consider an autonomous mower which must evolve the ability to mow the lawn it is placed upon. The lawn in question is a ten times ten grid toriodal world. Toriodal means that if the mower moves outside the lawn, it automatically comes in again on the opposite side. The mower has no sensors. It can move forward, turn left, and jump.

Starting from a reasonably good configuration, some parameters were modified. The starting configuration was:

PopulationSize                  = 100
NumberOfGenerations             = (depends on parameter)
CreationType                    = 2
CreationProbability             = 2.0
CrossoverProbability            = 98.0
MaximumDepthForCreation         = 6
MaximumDepthForCrossover        = 17
SelectionType                   = 1
TournamentSize                  = 10
DemeticGrouping                 = 0
DemeSize                        = 20
DemeticMigProbability           = 100.0
SwapMutationProbability         = 3.0
ShrinkMutationProbability       = 3.0
SteadyState                     = 0
LengthFactor                    = 0.001

As many as 50 runs were made for each parameter value. The average fitness values of the best performing genetic programs were recorded for each generation.

This study was done to determine the influence of the Genetic Programming control parameters. The conclusions that can be drawn from the study are, however, not generally applicable to all problems.

2.2 Results

Picture (Parameter study: population size)
Parameter study: population size

Picture (Parameter study: large population size versus large number of generations)
Parameter study: large population size versus large number of generations

Picture (Parameter study: steady state)
Parameter study: steady state

Picture (Parameter study: maximum depth for creation)
Parameter study: maximum depth for creation

Picture (Parameter study: selection method)
Parameter study: selection method

Picture (Parameter study: crossover probability)
Parameter study: crossover probability

Picture (Parameter study: demetic grouping)
Parameter study: demetic grouping

Picture (Parameter study: deme size)
Parameter study: deme size. Demetic grouping=1

Picture (Parameter study: demetic migration probability)
Parameter study: demetic migration probability. Demetic grouping=1

Picture (Parameter study: swap mutation)
Parameter study: swap mutation

Picture (Parameter study: shrink mutation)
Parameter study: shrink mutation

Picture (Parameter study: tournament size)
Parameter study: tournament size

Picture (Parameter study: creation type)
Parameter study: creation type

2.3 Conclusions

There are some conclusions that can be drawn from the parameter study:


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