### Residual entropy and simulated annealing

R. Ettelaie, M.A. Moore
1985 Journal de Physique Lettres
2014 On montre que la détermination de l'entropie résiduelle, dans la méthode d'optimisation par recuit simulé, foumit des informations utiles sur l'état fondamental vrai. Un verre d'Ising unidimensionnel est étudié pour montrer un exemple de ce procédé et, dans ce cas, l'entropie résiduelle est reliée au nombre d'états métastables qui restent stables par retoumement d'un seul spin. L'entropie résiduelle ne décroît que logarithmiquement vers zéro avec le taux inverse de refroidissement.
more » ... idissement. Abstract. 2014 Determining the residual entropy in the simulated annealing approach to optimization is shown to provide useful information on the true ground state energy. The one-dimensional Ising spin glass is studied to exemplify the procedure and in this case the residual entropy is related to the number of one-spin flip stable metastable states. The residual entropy decreases to zero only logarithmically slowly with the inverse cooling rate. LE JOURNAL DE PHYSIQUE -LETTRES J. Physique Lett. 46 (1985) L-893 -L-900 ler OCTOBRE 1985, Classification Physics Abstracts 05.20 The method of simulated annealing as a general procedure of optimization in problems involving many independent degrees of freedom, was first proposed by S. Kirkpatrick et al. in 1983 [1], and since then has received a great deal of attention. The method is particularly suited to the more difficult optimization problems which are characterized not only by the many degrees of freedom but also by conflicting constraints which cannot be simultaneously satisfied. In such cases one would like to find a solution which is the best compromise between all the different constraints. In order to attach a quantitative meaning to the goodness of a particular solution a cost function is defined. Such a cost function reflects the nature of each constraint and its relative importance. Then, the problem of finding the best solution becomes that of finding the solution which minimizes the cost function. This is not a trivial task. The effect of having a lot of constraints usually introduces many local minima (or metastable states) (often of order exp(N), where N is the number of degrees of freedom). Hence, the amount of computational time required to pick the exact optimal solution increases exponentially with N [1]. (This is strictly time for an NP complete problem. Not all problems with an exponentially large number of local minima are NP complete). Article published online by EDP Sciences and available at http://dx.