We investigate skew-symmetric sequences with chain lengths up to N = 71, giving a complete table of all merit factors F≥7 and their associated configurations. We also calculate the exact thermodynami-cal properties of shorter chains (N≤55). We then introduce an evolutionary strategy, describing the properties of our search algorithm and comparing our results to those of other heuristic methods such as simulated annealing. We find the highest merit factors ever reached for chains of length 81≤N≤201.

Low autocorrelation binary sequences: exact enumeration and optimization by evolutionary strategies

We study the static as well as the glassy or dynamical transition in the mean-field p-state Potts glass. By numerical solution of the saddle-point equations we investigate the static and dynamical transitions for all values of p in the non-perturbative regime p>4. The static and dynamical Edwards-Anderson parameter increase with p logarithmically. This makes the glassy transition temperature lie very close to the static one. We compare the main predictions of the theory with numerical simulations.

On the static and dynamical transition in the mean-field Potts glass

We consider combinatorial optimization problems defined over random ensembles and study how solution cost increases when the optimal solution undergoes a small perturbation delta. For the minimum spanning tree, the increase in cost scales as delta2. For the minimum matching and traveling salesman problems in dimension d >/= 2, the increase scales as delta3; this is observed in Monte Carlo simulations in d = 2, 3, 4 and in theoretical analysis of a mean-field model. We speculate that the scaling exponent could serve to classify combinatorial optimization problems of this general kind into a small number of distinct categories, similar to universality classes in statistical physics.

/pdf/scaling-and-universality-in-continuous-length-combinatorial-1jdsu3ufez.pdf

Scaling and universality in continuous length combinatorial optimization.

Due to an extremely rugged structure of the free energy landscape, the determination of spin-glass ground states is among the hardest known optimization problems, found to be NP hard in the most general case. Owing to the specific structure of local (free) energy minima, general-purpose optimization strategies perform relatively poorly on these problems, and a number of specially tailored optimization techniques have been developed in particular for the Ising spin glass and similar discrete systems. Here, an efficient optimization heuristic for the much less discussed case of continuous spins is introduced, based on the combination of an embedding of Ising spins into the continuous rotators and an appropriate variant of a genetic algorithm. Statistical techniques for insuring high reliability in finding (numerically) exact ground states are discussed, and the method is benchmarked against the simulated annealing approach.

http://www.martin-weigel.org/fileadmin/media/pdf/pre_76_066706.pdf

Genetic embedded matching approach to ground states in continuous-spin systems.

Simulated annealing with a more complicated set of moves than single-spin flips is applied to the one-dimensional Ising spin glass. The explicit connection between the residual entropy at T=0 in the simulated annealing and the number of metastable states, found previously for single-spin flips, is shown to be also true for these more complicated moves. This result together with a zero-temperature scaling argument is used to derive the degree of improvement that the inclusion of more complicated moves can produce. The results are in accord with the observations made for a number of problems in combinatorial optimization Application de la technique du recuit simule au verre de spin d'Ising 1D avec une dynamique plus compliquee que le renversement d'un seul spin, etudie precedemment, et mise en evidence de la conservation de la validite de la relation entre l'entropie residuelle a T=0 et le nombre d'etats metastables; utilisation de ce resultat en conjonction avec un argument de loi d'echelle a temperature nulle pour caracteriser l'amelioration produite par l'inclusion d'une dynamique plus compliquee

Moore Ma

Papers

Zero-temperature scaling and combinatorial optimization.