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On the behaviour of the (1, λ)-ES for conically constrained linear problems.

Dirk V Arnold1

  • 1Faculty of Computer Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4R2 dirk@cs.dal.ca.

Evolutionary Computation
|March 11, 2014
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This study analyzes a novel evolutionary strategy (ES) for constrained linear optimization. The research provides insights into convergence speed and step size adaptation for problems with conical constraints.

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Evolution strategiesconstraint handlingcumulative step size adaptation

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Area of Science:

  • Optimization
  • Evolutionary Computation
  • Mathematical Programming

Background:

  • Constrained optimization problems are common in various scientific and engineering fields.
  • Existing evolutionary strategies often struggle with conically constrained feasible regions.
  • Generalizing analysis beyond specific cone orientations is crucial for broader applicability.

Purpose of the Study:

  • To analyze the behavior of an evolutionary strategy (ES) that resamples infeasible solutions for linear optimization.
  • To generalize the analysis of such strategies to arbitrary orientations of conical constraints.
  • To determine the convergence speed and characterize step size adaptation in this context.

Main Methods:

  • Derivation of expressions for the strategy's single-step behavior.
  • Utilizing a zeroth-order model with scale-invariant mutation strength adaptation.
  • Deriving approximate expressions for average step size and convergence rate with cumulative step size adaptation.

Main Results:

  • The study provides a generalized analysis of an ES for conically constrained linear optimization.
  • Expressions characterizing single-step behavior and convergence speed were derived.
  • The performance of cumulative step size adaptation was analyzed and compared to optimal values.

Conclusions:

  • The developed evolutionary strategy effectively handles constraints in linear optimization problems with conical feasible regions.
  • The analysis offers a theoretical framework for understanding and improving the performance of such strategies.
  • The findings contribute to the development of more robust and efficient optimization algorithms.