Potential Transformation Method for Global Optimization

  • Robert A. Donnelly
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 94)


Several techniques for global optimization treat the objective function f as a force-field potential. In the simplest case, trajectories of the differential equation \(m\ddot x = - \nabla f\) sample regions of low potential while retaining the energy tosurmount passes which might block the way to regions of even lower local minima. A potential transformation is an increasing function V: R → R. It determines a new potential g = V(f), with the same minimizers as f, and new trajectories satisfying \(m\ddot x = - \nabla g = - \frac{{dV}}{{df}}\nabla f.\)We discuss a class of potential transformations that greatly increase the attractiveness of low local minima. As a special case, this provides a new approach to an equation proposed by Griewank for global optimization. Practical methods for implementing these ideas are discussed, and the method is applied to three test problems.


Simulated Annealing Global Optimization Global Optimization Algorithm Potential Transformation Steep Descent Direction 
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 Science+Business Media New York 1997

Authors and Affiliations

  • Robert A. Donnelly
    • 1
  1. 1.Chemistry DepartmentAuburn UniversityAuburnUSA

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