Optimization of coefficients of lists of polynomials by evolutionary algorithms

J. Rafael Sendra, Stephan M. Winkler

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We here discuss the optimization of coefficients of lists of polynomials using evolutionary computation. The given polynomials have 5 variables, namely t, a1, a2, a3, a4, and integer coefficients. The goal is to find integer values αi , with i ∊ {1, 2, 3, 4}, substituting ai such that, after crossing out the gcd (greatest common divisor) of all coefficients of the polynomials, the resulting integers are minimized in absolute value. Evolution strategies, a special class of heuristic, evolutionary algorithms, are here used for solving this problem. In this paper we describe this approach in detail and analyze test results achieved for two benchmark problem instances; we also show a visual analysis of the fitness landscapes of these problem instances.

Original languageEnglish
Pages (from-to)177-185
Number of pages9
JournalAnnales Mathematicae et Informaticae
Volume44
Publication statusPublished - 2015

Keywords

  • Evolution strategies
  • Evolutionary computation
  • Optimization of parametrizations
  • Symbolic computation

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