Adaptation of Length in a Nonstationary Environment

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Adaptation of Length in a Nonstationary
Environment
Han Yu, Annie S. Wu, Kuo-Chi Lin, and Guy
Schiavone University of Central
Florida, Orlando, Fl, 32816, USA
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Introduction

• Early study indicates that GA tends to favor
  longer individuals in period of heavy search,
  because longer individuals provide more resources
  to the search process.
• We study the behavior of variable length GA in a
  changing environment, using a multi-processor
  scheduling problem

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Variable Length Representation

• Early work
• LS-1 learning system (Smith, 1980)
• Messy GA (Goldberg, 1989)
• Genetic Programming (GP) (Koza, 1992)
• SAGA (Harvey, 1992)

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Variable Length Representation

• Recent findings
• Exploration of cause of bloat (Langdon and Poli,
  1997)
• Investigation of code growth in GP (Soule et al.,
  1996)
• Study on the impact of parsimony pressure (Burke
  et al., 1998)

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GA in a Changing Environment

• Maintain population diversity
• Random immigrants (Grefenstette, 1992)
• Hyper-mutation (Cobb 1990)
• Adaptive GA operators (Grefenstette, 1999)
• TDGA (Mori et al., 1996)
• Redundant representation schemes (Goldberg and
  Smith, 1987, Ng and Wang, 1995)
• Additional memory systems (Branke, 1999)

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Test Bed
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Solution Representation

• Variable length representation

(4,1)(2,4)(3,3)(2,3)(4,1)(5,4)(6,3)(1,1)(3,2)
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Genetic Operators

• Crossover
• Random one-point crossover
• Crossover point chosen between adjacent genes
• Length of offspring may be different from their
  parents
• Mutation
• Either task or processor number is changed for a
  mutated gene

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Fitness Function

• Consists of task_fitness and processor_ fitness
• task_fitness
• Evaluate the order of the tasks assigned to the
  same processor
• Check if all tasks in the problem appear in the
  solution
• processor_fitness
• Evaluate the execution time of tasks in a valid
  schedule

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Fitness Function (continued)
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Raw Fitness

• Give partial credit to solutions that contain
  some valid sequences
• Size of task groups is determined by era
• Starts from checking every pair of adjacent tasks
  (era 0) assigned to the same processor
• Gradually checking larger task groups by
  increasing era

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Parameter Settings
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Test Settings
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Experiments

• Fixed length GA, era not reset after problem
  changes
• Fixed length GA, era reset after problem changes
• Variable length GA, era not reset after problem
  changes
• Variable length GA, era reset after problem
  changes

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Fixed Length, era Not Reset
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Fixed Length, era Reset
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Variable Length, era Not Reset
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Variable Length, era Not Reset
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Variable Length, era Reset
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Variable Length, era Reset
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Average Fitness for Individual Length, before
Target Changes
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Average Fitness for Individual Length, after
Target Changes
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Average Fitness for Coding Length, before Target
Change
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Average Fitness for Coding Length, after Target
Change
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Short vs. Long Solutions
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Valid Sequences of Tasks in the Long Solution
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Conclusions

• A variable length GA is quicker to adapt to a new
  environment
• GA favors better quality resources rather than
  more resources right after problem changes
• The flexibility in the representation enables
  variable length GA to better recognize and retain
  good build blocks