Simple metaheuristics using the simplex algorithm for non-linear programming

Authors:
João Pedro Pedroso
Affiliations:
INESC - Porto and DCC - Faculdade de Ciências, Universidade do Porto, Porto, Portugal
Venue:
SLS'07 Proceedings of the 2007 international conference on Engineering stochastic local search algorithms: designing, implementing and analyzing effective heuristics
Year:
2007

Citing 2
Cited 1

Direct search methods: then and now

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
A Pattern Search Filter Method for Nonlinear Programming without Derivatives

SIAM Journal on Optimization

The Effect of Re-sampling on Incremental Nelder-Mead Simplex Algorithm: Distributed Regression in Wireless Sensor Networks

WASA '08 Proceedings of the Third International Conference on Wireless Algorithms, Systems, and Applications

Quantified Score

Hi-index	0.00

Visualization

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.