Advertisement

Simple Metaheuristics Using the Simplex Algorithm for Non-linear Programming

  • João Pedro Pedroso
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4638)

Abstract

In this paper we present an extension of the Nelder and Mead simplex algorithm for non-linear programming, which makes it suitable for both unconstrained and constrained optimisation. We then explore several extensions of the method for escaping local optima, which make it a simple, yet powerful tool for optimisation of nonlinear functions with many local optima.

A strategy which proved to be extremely robust was random start local search, with a correct, though unusual, setup. Actually, for some of the benchmarks, this simple metaheuristic remained the most effective one. The idea is to use a very large simplex at the begin; the initial movements of this simplex are very large, and therefore act as a kind of filter, which naturally drives the search into good areas.

We propose two more mechanisms for escaping local optima, which, still being very simple to implement, provide better results for some difficult problems.

Keywords

Local Search Local Optimum Tabu Search Simplex Algorithm Direct Search Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Pedroso, J.P.: Simple meta-heuristics using the simplex algorithm for non-linear programming. Technical Report DCC-2007-06, DCC, FC, Universidade do Porto (2007)Google Scholar
  2. 2.
    Nelder, J.A., Mead, R.: A simplex method for function minimization. Computer Journal 7, 308–313 (1965)Google Scholar
  3. 3.
    Lewis, R.M., Torczon, V., Trosset, M.W.: Direct search methods: then and now. Journal of Computational and Applied Mathematics 124(1-2), 191–207 (2000)zbMATHCrossRefGoogle Scholar
  4. 4.
    Pedroso, J.P.: Meta-heuristics using the simplex algorithm for nonlinear programming. In: Proceedings of the 2001 International Symposium on Nonlinear Theory and its Applications, Miyagi, Japan, pp. 315–318 (2001)Google Scholar
  5. 5.
    Audet, C., Dennis Jr., J.: A pattern search filter method for nonlinear programming without derivatives. SIAM Journal on Optimization 14(4), 980–1010 (2004)zbMATHCrossRefGoogle Scholar
  6. 6.
    Chelouah, R., Siarry, P.: A hybrid method combining continuous tabu search and nelder-mead simplex algorithms for the global optimization of multiminima functions. European Journal of Operational Research 161, 636–654 (2005)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • João Pedro Pedroso
    • 1
  1. 1.INESC - Porto and, DCC - Faculdade de Ciências, Universidade do Porto, PortoPortugal

Personalised recommendations