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)


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.


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.


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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

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