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Comparison of Constraint-Handling Mechanisms for the (1,λ)-ES on a Simple Constrained Problem.

Michael Hellwig1, Dirk V Arnold2

  • 1Research Center Process and Product Engineering, Vorarlberg University of Applied Sciences, Dornbirn, 6850, Austria michael.hellwig@fhv.at.

Evolutionary Computation
|October 17, 2014
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Summary

This study compares two constraint-handling techniques, reflection and truncation, in evolution strategies for linear programming. Both methods effectively manage constraints, with cumulative step size adaptation explaining their distinct behaviors.

Keywords:
Evolution strategiesconstrained optimizationconstraint-handling techniques.cumulative step size adaptation

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Area of Science:

  • Evolutionary Computation
  • Optimization Techniques
  • Mathematical Modeling

Background:

  • Non-elitist single-parent evolution strategies are explored for constrained optimization.
  • Constraint-handling is crucial for evolutionary algorithms applied to real-world problems.
  • Existing repair mechanisms for infeasible solutions are compared.

Purpose of the Study:

  • To investigate and compare two specific repair mechanisms: reflection and truncation.
  • To analyze the behavior of evolution strategies with these repair methods under a single linear constraint.
  • To extend theoretical understanding of constraint-handling in evolutionary computation.

Main Methods:

  • Analytical investigation of two repair mechanisms (reflection and truncation) in evolution strategies.
  • Comparison of analytical results with earlier repair approaches.
  • Calculation of one-generation behavior distributions for strategy analysis.
  • Development of a zeroth-order model for steady-state analysis with fixed step size.

Main Results:

  • The study provides analytical results for reflection and truncation repair mechanisms.
  • Qualitative differences in algorithm variant behavior are explained by cumulative step size adaptation.
  • The performance of the two repair methods is compared within the same fitness environment.

Conclusions:

  • The research enhances theoretical knowledge of constraint-handling methods in evolutionary computation.
  • The findings have implications for designing effective constraint-handling techniques.
  • Cumulative step size adaptation plays a key role in understanding strategy behavior.