A Multiagent Genetic Algorithm for Global Numerical Optimization

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A Multiagent Genetic Algorithm for Global
Numerical Optimization

• Li Gang Mar 29, 2007

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Outline

• Motivation
• Structure
• Operators
• Experiments
• Dicussion

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Motivation

• Genetic Algorithm is good approach for global
  numerical optimization problems when they cannot
  be solved analytically
• The major drawback of standard GA is that it may
  be trapped in local optima. Therefore, high
  diversity is necessary for successful evolution.

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MAGA architecture

• The individuals are placed on a grid, which
  induces a neighborhood relation, so the
  interaction is restricted
• The inter-individual operators are applied to an
  individual and the best individual among is
  neighbors, called the winner, and the individual
  is replaced by the offspring.
• An individual can also be replaced by its own
  offspring

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Structure

• The structure is very similar to Cellular Genetic
  Algorithm. The major difference is the genetic
  operators.

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Inter-individual Operators

• An individual is replaced by the offspring
  between it and its best neighbor (winner)
• A certain operator is used with a predefined
  probability
• Some notation
• L(i,j) (l1,l2,,ln)
• Max(i,j) (m1,m2,,mn)
• New(i,j) (e1,e2,,en)

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Occupy Strategy 1
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Occupy Strategy 2
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Orthogonal Crossover

• It generates new individuals by the orthogonal
  design
• A small number of individuals are scattered
  uniformly over the space
• The best is selected

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Self Operator

• Mutation
• Self-Learning a small scale MAGA is applied on
  the best individual in the grid and its mutants
• The best is selected

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Experiments setting

• L 5 X 5 sL 3 X 3
• Po 0.2 Pc 0.1 Pm 0.1
• Gen 150 sGen 10
• 50 runs

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Problems

• Multimodal
• High dimension
• But independent

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Comparison with other GAs
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Complexity in dimension
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Complexity in dimension cont.

• MAGA obtained better solutions than BGA AEA

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Problems of 10000 dimensions!

• O(na) is the approximated complexity of dimension
  (better than linear)

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Approximating Linear System

• Given a high-order transfer function G(s), it is
  desired to find an approximate model H(s) such
  that it contains the desired characteristic of
  the original system
• It needs to optimize the error function J, whose
  variables are not independent

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Stable Linear System

• The problem has 5 dimensions.
• It requires 19735 individuals to converge

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Unstable Linear System

• The problem has 4 dimensions
• The number of evaluations averaged over 10 trials
  of MAGA is 2775.

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Discussion

• MAGA is very similar to Cellular GA.
• I think its main advantages are the genetic
  operators, which are carefully designed, tailored
  for the problems of independent variables
• Nevertheless, its performance is very impressive.
  It can even find close-to-optimum solution
  efficiently
• It is the state-of-art algorithm. Very difficult
  to beat, but we can use it in practical problems.