Stochastic tunneling
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Stochastic tunneling (STUN) is one approach to global optimization among several others and is based on the Monte Carlo method-sampling of the function to be minimized.
[edit] Idea
Monte Carlo method-based optimization techniques sample the objective function by randomly "hopping" from the current solution vector to another with a difference in the function value of ΔE. The acceptance probability of such a trial jump is in most cases chosen to be 
(Metropolis criterion) with an appropriate parameter β.
The general idea of STUN is to circumvent the slow dynamics of ill-shaped energy functions that one encounters for example in spin glasses by tunneling through such barriers.
This goal is achieved by Monte-Carlo-sampling of a transformed function that lacks this slow dynamics. In the "standard-form" the transformation reads 
where fo is the lowest function value found so far. This transformation preserves the loci of the minima.
The effect of such a transformation is shown in the graph.
[edit] Other approaches
[edit] References
- K. Hamacher. Adaptation in Stochastic Tunneling Global Optimization of Complex Potential Energy Landscapes, Europhys.Lett. 74(6):944, 2006.
- K. Hamacher and W. Wenzel. The Scaling Behaviour of Stochastic Minimization Algorithms in a Perfect Funnel Landscape. Phys. Rev. E, 59(1):938-941, 1999.
- W. Wenzel and K. Hamacher. A Stochastic tunneling approach for global minimization. Phys. Rev. Lett., 82(15):3003-3007, 1999.
- Metropolis et al., J.Chem.Phys. 1954.
