Optimization in AutoMod

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Optimization in AutoMod

• Jerry Banks

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Evolution strategies algorithm

• Looks at a population of solutions at each
  iteration
• Avoids a local optimum

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Survival of the fittest

• Theory of evolution
• Initial population (parents) combines to create
  the next generation (children)
• Children inherit traits from their parents
• But they also have differences (mutations)
• The fittest children (as defined by the fitness
  function) survive to become parents the next
  generation

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In AutoMod terms

• Initial population is made up of sets of factor
  values
• Then, the children would be defined by factor
  values

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Optimization process

• First generation
• Step 1 Randomly create the first generation of
  children
• Each generation contains 7N children
• N is the number of parents per generation
• N 3 is a good number
• Each child is randomly assigned factor values

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Optimization process

• Step 1, cont.
• Example
• Assume that there are 3 factors
• Each factor has value varied from 1 to 4

 
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Optimization process

• For each generation, including the first
• Step 2 Make the runs for each child
• Step 3 Based on the fitness score for each
  child, pick the best N children to use as parents
  for the next generation

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Optimization process

• Step 4 To create each child in the new
  generation, randomly pick two of the parents
  (selected in Step 3), combine them (i.e., take
  some of the factors values from one parent and
  some factor values from the other), then mutate
  the factor values slightly within the factors
  set of defined values
• Create 7N children which is the number of parents
  per generation

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Optimization process

• Since parents are chosen randomly, it is possible
  that the two parents for a generation may
  occasionally be the same
• Step 5 Repeat steps 2 4 until either the
  termination criteria are met or the runs are
  stopped

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Optimization options

• Optimization parameters
• Maximum replications per solution
• The number of times to repeat runs for a set of
  values
• Each run uses a different set of random numbers

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Optimization options

• Optimization parameters
• Maximum number of parents per generation
• The number of sets of factor values that are used
  to create the next generation of children
• The higher the number of parents, the less of a
  chance of converging on a local optimum, but the
  slower the search
• lt 4 factors, N 2 is sufficient
• gt 4 factors, N gt 3 is recommended

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Termination options

• Runs continue until stopped or termination
  criteria are met
• The best solution is provided given the number of
  runs made
• If mutations are essentially identical, runs will
  be stopped automatically

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Termination options

• Stopped when either of the following conditions
  occurs
• N generations P improvement
• Compares the best fitness score of the current
  generation to the best score of the previous Nth
  generation
• If the improvement is lt P, runs are stopped
• Maximum number of generations is reached

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Progress graph

• Check to see if the lines have converged
• If not, continue searching
• Progress graph is discussed later

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Do some runs

• Optimization analyses make runs until the
  termination criteria are met
• Could be many hundreds of runs
• So, select Do some runs

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Fitness function

• Describes the factors and responses to be
  optimized
• Each factor or term is called a response
• Terms can have a relative importance

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Example
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Direction

• Usually want to maximize terms that generate
  money
• ThruPut
• Usually want to minimize terms that cost money
• NumOps
• Need to indicate whether high or low scores are
  desired

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Progress graph

• Best fitness
• Max (Min) so far in any generation
• Best fitness in this generation
• Max (Min) of a child in this generation
• Parents average fitness
• Avg fitness of all the parents of the generation
• Childrens average fitness
• Avg fitness of all the children of the generation

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Progress graph
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Progress graph

• First generation of children produced a fitness
  function value that was positive
• Terms being maximized in the fitness function
  were bigger than the terms being minimized
• Optimization became negative as more runs were
  made
• Factors and response values for the optimal
  scenario
• See summary statistics