56:
that lie above the best minimum found are suppressed. If the dynamical process can escape the well around the current minimum estimate it will not be trapped by other local minima that are higher. Wells with deeper minima are enhanced. The dynamical process is accelerated by
39:
of the function to be objective minimized in which the function is nonlinearly transformed to allow for easier tunneling among regions containing function minima. Easier tunneling allows for faster exploration of sample space and faster convergence to a good solution.
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Schematic one-dimensional test function (black) and STUN effective potential (red & blue), where the minimum indicated by the arrows is the best minimum found so far. All
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This goal is achieved by Monte Carlo sampling of a transformed function that lacks this slow dynamics. In the "standard-form" the transformation reads
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798:
578:
K. Hamacher & W. Wenzel (1999). "The
Scaling Behaviour of Stochastic Minimization Algorithms in a Perfect Funnel Landscape".
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185:
The general idea of STUN is to circumvent the slow dynamics of ill-shaped energy functions that one encounters for example in
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36:
540:
K. Hamacher (2006). "Adaptation in
Stochastic Tunneling Global Optimization of Complex Potential Energy Landscapes".
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by randomly "hopping" from the current solution vector to another with a difference in the function value of
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W. Wenzel & K. Hamacher (1999). "A Stochastic tunneling approach for global minimization".
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is then adjusted to tunnel out of the minimum and pursue a more globally optimum solution.
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290:{\displaystyle f_{STUN}:=1-\exp \left(-\gamma \cdot \left(E(x)-E_{o}\right)\right)}
479:
A variation on always tunneling is to do so only when trapped at a local minimum.
462:{\displaystyle \min \left(1;\exp \left(-\beta \cdot \Delta f_{STUN}\right)\right)}
91:. The acceptance probability of such a trial jump is in most cases chosen to be
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773:
186:
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IEEE Transactions on
Computer-Aided Design of Integrated Circuits and Systems
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is the lowest function value found so far. This transformation preserves the
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151:{\displaystyle \min \left(1;\exp \left(-\beta \cdot \Delta E\right)\right)}
756:"Improving FPGA Placement with Dynamically Adaptive Stochastic Tunneling"
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is the recommended way of determining if trapped at a local minimum.
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in the original algorithm giving a new acceptance probability of
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688:"Equation of State Calculations by Fast Computing Machines"
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The effect of such a transformation is shown in the graph.
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745:: CS1 maint: multiple names: authors list (
64:-based optimization techniques sample the
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475:Dynamically adaptive stochastic tunneling
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162:criterion) with an appropriate parameter
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16:Stochastic method of global optimization
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189:by tunneling through such barriers.
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696:The Journal of Chemical Physics
501:Detrended fluctuation analysis
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1:
754:Mingjie Lin (December 2010).
660:10.1103/PhysRevLett.82.3003
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774:10.1109/tcad.2010.2061670
678:, Arianna W. Rosenbluth,
563:10.1209/epl/i2006-10058-0
366:is then used in place of
27:(STUN) is an approach to
682:, Augusta H. Teller and
359:{\displaystyle f_{STUN}}
84:{\displaystyle \Delta E}
799:Stochastic optimization
612:10.1103/PhysRevE.59.938
492:{\displaystyle \gamma }
680:Marshall N. Rosenbluth
528:Differential evolution
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175:{\displaystyle \beta }
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317:{\displaystyle E_{o}}
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25:stochastic tunneling
709:1953JChPh..21.1087M
676:Nicholas Metropolis
652:1999PhRvL..82.3003W
604:1999PhRvE..59..938H
555:2006EL.....74..944H
513:Simulated annealing
29:global optimization
518:Parallel tempering
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66:objective function
62:Monte Carlo method
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33:Monte Carlo method
21:numerical analysis
768:(12): 1858–1869.
717:10.1063/1.1699114
636:(15): 3003–3007.
523:Genetic algorithm
379:{\displaystyle E}
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703:(6): 1087–1092.
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588:(1): 938–941.
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686:(June 1953).
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684:Edward Teller
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31:based on the
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187:spin glasses
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534:References
160:Metropolis
620:119096368
571:250761754
487:γ
428:Δ
425:⋅
422:β
419:−
411:
265:−
245:⋅
242:γ
239:−
231:
225:−
170:β
133:Δ
130:⋅
127:β
124:−
116:
76:Δ
793:Category
37:sampling
782:8706692
733:1046577
725:4390578
705:Bibcode
668:5113626
648:Bibcode
600:Bibcode
551:Bibcode
780:
731:
723:
666:
618:
569:
297:where
778:S2CID
729:S2CID
691:(PDF)
664:S2CID
638:arXiv
616:S2CID
590:arXiv
567:S2CID
57:that.
54:wells
747:link
721:OSTI
326:loci
44:Idea
770:doi
713:doi
656:doi
608:doi
559:doi
408:exp
394:min
228:exp
113:exp
99:min
19:In
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35:-
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