Journal of Global Optimization

, Volume 47, Issue 2, pp 293–325

The oracle penalty method


DOI: 10.1007/s10898-009-9477-0

Cite this article as:
Schlüter, M. & Gerdts, M. J Glob Optim (2010) 47: 293. doi:10.1007/s10898-009-9477-0


A new and universal penalty method is introduced in this contribution. It is especially intended to be applied in stochastic metaheuristics like genetic algorithms, particle swarm optimization or ant colony optimization. The novelty of this method is, that it is an advanced approach that only requires one parameter to be tuned. Moreover this parameter, named oracle, is easy and intuitive to handle. A pseudo-code implementation of the method is presented together with numerical results on a set of 60 constrained benchmark problems from the open literature. The results are compared with those obtained by common penalty methods, revealing the strength of the proposed approach. Further results on three real-world applications are briefly discussed and fortify the practical usefulness and capability of the method.


Constrained optimization Global optimization Penalty function Stochastic metaheuristic Ant colony optimization MIDACO-Solver Mixed integer nonlinear programming (MINLP) 

Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  1. 1.Theoretical and Computational Optimization Group, School of MathematicsUniversity of BirminghamEdgbaston, BirminghamUK
  2. 2.Department of MathematicsUniversity of WürzburgWürzburgGermany

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