Facts, conjectures, and improvements for simulated annealing

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Descombes, X.

Peter Salamon - Google Scholar Citations

Fachat, A. Gelfand, S. Geman, S. Geyer, C.

The simulated annealing algorithm explained with an analogy to a toy

In: Barndoff Nielsen, O. Stochastic Geometry, Likelihood and Computation. Chapmann and Hall, London Google Scholar. Gougeon, F. In: Hill, D. Green, P.

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Facts, Conjectures and Improvements for Simulated Annealing

Ingber, L. Kirkpatrick, S. Larsen, M. In: Proc. In fact, even for studies with a few dozen species, finding the most plausible phylogeny would require examining more trees than there are atoms in the universe; an impossible task! Therefore, in practice heuristic search algorithms are used which seek to come close to the optimum through clever sampling of the search space. While heuristic searches give reasonable solutions within feasible run-times, they ignore a large part of the search space, so that we only obtain limited information about how close our solution is to the optimum, and if there are potentially several equally good optima.

During a number of summer project Daniel and I worked on further understanding the search characteristics of the simulated annealing heuristic. This algorithm mimics the cooling of a liquid and is a widely used search strategy.

On simulated annealing phase transitions in phylogeny reconstruction

When a liquid cools, the atoms sample a series of spatial arrangements always adopting those which improve their free energy but occasionally also adopting arrangements which are worse. Analogously, the algorithm generates a candidate solution from the current solution and then chooses whether to accept it as the new solution using the following rules: Is the solution better than the previous solution?

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The temperature is a parameter that decreases over time according to a cooling schedule and regulates how likely the search accepts worse solutions. Initially it is high allowing the algorithm to move almost freely in the search space.

ISBN 10: 0898715083

As the temperature decreases, the search is confined to smaller and smaller areas until it homes in on the final and hopefully optimal solution. When a liquid cools it goes through a phase transition at which the state of the system fundamentally changes from a liquid to a solid. Intriguingly, a similar transition occurs when we run simulated annealing on the computer. Daniel and I were curious if we could use these transitions to learn something about the search space structure. Specifically: Melting temperatures allow us to distinguish between materials and give insights into the material properties.

Can simulated annealing phase transitions be used in the same way to characterise optimisation problems and learn about the search landscape?

https://carpfinssorcons.tk In order to investigate this hypothesis, Daniel and I recorded the phase transitions in 30 different phylogeny inference problems we obtained from the literature. Our study Link , which to the best of our knowledge is the most comprehensive study on phase transitions so far, showed that there is a considerable difference between the phase transitions in different problems. This supports the idea that it might be possible to use the phase transitions to learn about the search space landscape. Account Options Anmelden.

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