Hysteretic optimization for the Sherrington–Kirkpatrick spin glass

Pál, Károly F.

doi:10.1016/j.physa.2005.11.013

Cited by 35 publications

(16 citation statements)

References 27 publications

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“…In this paper, we will set up a general formalism which will be amenable to an analytical treatment and derive the upper bound µ ≤ 1 4 . The details of the calculation will be published elsewhere [9].Numerically, the sample-to-sample fluctuations in the mean-field model have been investigated extensively in the literature [7,10,11,12,13,14]. In all of these cases the study was restricted to zero temperature.…”

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confidence: 99%

Free-Energy Fluctuations and Chaos in the Sherrington-Kirkpatrick Model

Aspelmeier

2008

Phys. Rev. Lett.

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The sample-to-sample fluctuations ∆FN of the free energy in the Sherrington-Kirkpatrick model are shown rigorously to be related to bond chaos. Via this connection, the fluctuations become analytically accessible by replica methods. The replica calculation for bond chaos shows that the exponent µ governing the growth of the fluctuations with system size N , ∆FN ∼ N µ , is bounded by µ ≤ 1 4 .The sample-to-sample fluctuations of the free energy in the mean-field Ising spin glass [1] are a long standing unsolved problem in spin glass physics. In addition to their intrinsic interest as a finite size effect in spin glasses, they are of fundamental importance for the physics of finite-dimensional spin glasses. It has been shown [2] that the finite-size scaling of the free energy fluctuations ∆F N in the mean-field spin glass is equal to the scaling of the domain wall energy ∆F DW in finite dimensionswhere N is the total system size and L its linear dimension (in the case of a finite dimensional system). This implies the relationship θ = dµ between the domain wall exponent θ and the fluctuation exponent µ. This highly nontrivial equivalence between a mean-field quantity and a finitedimensional quantity provides a strong test for replica field theory which was used in Ref. 2 to derive this result.Chaos is also a very important aspect of spin glasses. Chaos refers to the property that an infinitesimal change of, for instance, the temperature or the bond strengths results in a complete change of the equilibrium state. Chaos was first suggested in the context of the droplet picture and finite dimensional spin glasses [3] but has also been studied in the mean field model [4,5,6].In this paper we derive a new and exact connection between the free energy fluctuations and the seemingly unrelated phenomenon of chaos. Such a connection has been suggested by Bouchaud et al. [7] as part of a heuristic argument to obtain the free energy fluctuations. Our results partly corroborate the argument but we will see that a crucial ingredient seems to be missing from it. In addition to making the heuristic argument precise, our results provide a new way to access the fluctuations analytically. The fluctuations are a subextensive quantity such that their calculation usually requires higher order terms in the loop expansion. These are, however, inaccessible due to the massless modes present throughout the spin glass phase. Here we will show that it is sufficient to calculate chaos to zero loop order (which is possible) to obtain the fluctuations. We demonstrate this explicitly above and at the critical temperature but believe and present evidence that it also works in the low temperature phase.The method we use to derive the connection between fluctuations and chaos is a variation of the interpolating Hamiltonian method. Our approach is inspired by the work of Billoire [8] where a similar method was introduced to study the finite size corrections to the free energy numerically. In this paper, we will set up a general formalism which will b...

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confidence: 99%

Free-Energy Fluctuations and Chaos in the Sherrington-Kirkpatrick Model

Aspelmeier

2008

Phys. Rev. Lett.

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“…HO. HO [18] is inspired by the demagnetization process of a magnetic sample. A magnetic sample comes to a very stable low-energy state called ground state, when it is demagnetized by an oscillating magnetic field of slowly decreasing amplitude.…”

Section: Glass-demagnetization-based Algorithmsmentioning

confidence: 99%

“…Based on Newton's gravitational law and laws of motion algorithms emerged such as CFO [14] by Formato in 2007, GSA by Rashedi et al [15], APO by Xie et al [16] in 2009, and GIO by Flores et al [17] in 2011. Hysteretic Optimization (HO) [18] based on demagnetization process was proposed in 2008. In 2010, Kaveh and Talatahari proposed CSS [19] based on electrostatic theorems such as Coulomb's law, Gauss's law, and superposition principle from electrostatics and Newton's laws of motion.…”

Section: Introductionmentioning

confidence: 99%

Physics-Inspired Optimization Algorithms: A Survey

Biswas

Mishra

Tiwari

et al. 2013

Journal of Optimization

109

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Natural phenomenon can be used to solve complex optimization problems with its excellent facts, functions, and phenomenon. In this paper, a survey on physics-based algorithm is done to show how these inspirations led to the solution of well-known optimization problem. The survey is focused on inspirations that are originated from physics, their formulation into solutions, and their evolution with time. Comparative studies of these noble algorithms along with their variety of applications have been done throughout this paper.

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“…Hysteretic optimization (HO) algorithm was originally proposed in Zaránd et al (2002), Pál (2003Pál ( , 2004Pál ( , 2006a. To implement the HO algorithm, the following steps need to be performed (Zaránd et al 2002;Gonçalves and Boettcher 2008;Pál 2004):…”

Section: Fundamentals Of Hysteretic Optimization Algorithmmentioning

confidence: 99%

Emerging Physics-based CI Algorithms

Xing

Gao²

2013

Innovative Computational Intelligence: A Rough Guide to 134 Clever Algorithms

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In this chapter, a set of (more specifically 22 in total) emerging physicsbased computational intelligence (CI) algorithms are introduced. We first, in Sect. 24.1, describe the organizational structure of this chapter. Then, from Sects. 24.2 to 24.23, each section is dedicated to a specific algorithm which falls within this category. The fundamentals of each algorithm and their corresponding performances compared with other CI algorithms can be found in each associated section. Finally, the conclusions drawn in Sect. 24.24 closes this chapter. IntroductionSeveral novel physics-based algorithms were detailed in previous chapters. In particular, Chap. 18 detailed the big bang-big crunch algorithm, Chap. 19 was dedicated to central force optimization algorithm, Chap. 20 discussed the charged system search algorithm, Chap. 21 introduced the electromagnetism-like mechanism algorithm, Chap. 22 was devoted to the gravitational search algorithm, and Chap. 23 described the intelligent water drops algorithm. Apart from this quasimature physics principles inspired CI methods, there are some emerging algorithms also fall within this category. This chapter collects 22 of them that are currently scattered in the literature and organizes them as follows: The effectiveness of these newly developed algorithms are validated through the testing on a wide range of benchmark functions and engineering design problems, and also a detailed comparison with various traditional performance leading CI algorithms, such as particle swarm optimization (PSO), genetic algorithm (GA), differential evolution (DE), evolutionary algorithm (EA), fuzzy system (FS), ant colony optimization (ACO), and simulated annealing (SA). Artificial Physics Optimization AlgorithmIn this section, we will introduce an emerging CI algorithm that is based on artificial physics or physicomimetics, a concept which was introduced in Spears et al. (2004a, b); Spears and Gordon (1999); Spears and Spears (2012). Fundamentals of Artificial Physics Optimization AlgorithmArtificial physics optimization (APO) algorithm was recently proposed in Xie et al. ( , b, 2010aXie et al. ( , b, 2011a, . Several APO applications and variants can also be found in the literature Popov 2012, 2013; Zeng 2009b, 2011;Mo and Zeng 2009; Wang and Zeng 2010a, b;Yang et al. 2010;Yin et al. 2010; Xie et al. 2011c, d;Wang et al. 2011). To implement the APO algorithm, the following steps need to be performed Biswas et al. 2013):• Initialization step: At this step, a swarm of individuals is randomly generated in the n-dimensional decision space. 376 24 Emerging Physics-based CI Algorithms• Force calculation step: At this step, according to the masses and distances between individual particles, the total force exerted on each particle is computed. In APO, the mass is defined via Eq. 24.1 Biswas et al. 2013):The force is then calculated through Eq. 24.2 Biswas et al. 2013):ð24:2ÞThe kth component of the total force F i;k exerted on individual i by all other individuals is acquired via Eq. 24.3...

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Hysteretic optimization for the Sherrington–Kirkpatrick spin glass

Cited by 35 publications

References 27 publications

Free-Energy Fluctuations and Chaos in the Sherrington-Kirkpatrick Model

Free-Energy Fluctuations and Chaos in the Sherrington-Kirkpatrick Model

Physics-Inspired Optimization Algorithms: A Survey

Emerging Physics-based CI Algorithms

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