The ground state energy of the Edwards-Anderson Ising spin glass with a hybrid genetic algorithm

Pál, Károly F.

doi:10.1016/0378-4371(95)00348-7

Cited by 85 publications

(61 citation statements)

References 23 publications

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“…Hysteretic optimization is not really effective for magnetic systems of low connectivity. It does find very low lying states, but even our best attempts [3] were unable to locate the true ground state of Edwards-Anderson spin glasses of sizes that can be handled reliably and often even easily by some other algorithms [6,7,8,9,10,11,12,13]. The method is also not effective for the random field Ising model [14].…”

Section: Introductionmentioning

confidence: 97%

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Hysteretic optimization for the Sherrington–Kirkpatrick spin glass

Pál

2006

Physica A: Statistical Mechanics and its Applications

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Hysteretic optimization is a heuristic optimization method based on the observation that magnetic samples are driven into a low energy state when demagnetized by an oscillating magnetic field of decreasing amplitude. We show that hysteretic optimization is very good for finding ground states of Sherrington-Kirkpatrick spin glass systems. With this method it is possible to get good statistics for ground state energies for large samples of systems consisting of up to about 2000 spins. The way we estimate error rates may be useful for some other optimization methods as well. Our results show that both the average and the width of the ground state energy distribution converges faster with increasing size than expected from earlier studies.

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Section: Introductionmentioning

confidence: 97%

“…The present algorithm about two orders of magnitude faster. It is also much more effective than hybrid genetic algorithm, which is very good for the Edwards-Anderson case [6,7]. Exact algorithm [16] presently only affordable for quite small systems.…”

Section: Introductionmentioning

confidence: 99%

Hysteretic optimization for the Sherrington–Kirkpatrick spin glass

Pál

2006

Physica A: Statistical Mechanics and its Applications

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“…In this form, genetic algorithms have been applied to the Ising spin glass, but, unless for very small systems, true ground states could not be found with high reliability [59,60]. Only hybrids combining genetic crossover with some downhill optimization procedure such as local spin flips or the "cluster-exact approximation" [19], restricting the search space to metastable states, led to more successful approaches [20,61].…”

Section: B Genetic Matchingmentioning

confidence: 99%

“…Correspondingly, heuristic optimization techniques for finding low-lying or ground states are called for. These might include generic approaches, such as simulated annealing [16], multicanonical [17] or parallel tempering [18] Monte Carlo simulations, but also a number of methods specifically tailored to the problem [19,20,21,22,23], the latter generally showing the best performance [3,24]. Insofar as these methods make use of some type of relaxational (quasi-) dynamics, they to some extent also suffer from the slowness of relaxation entailed by the structure of free-energy minima and separating barriers.…”

Section: Introductionmentioning

confidence: 99%

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

Weigel¹

2007

Phys. Rev. E

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Due to an extremely rugged structure of the free energy landscape, the determination of spinglass ground states is among the hardest known optimization problems, found to be N P-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.

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“…that there is a critical slowing down [14]. In this letter we show our results for the direct calculation of spin glass ground states using a hybrid of genetic algorithms [15,16] and Cluster-Exact Approximation (CEA) [17]. Because the computation of spin glass ground states belongs to the class of NP-hard problems, it is a tough computational task.…”

Section: Introductionmentioning

confidence: 99%