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Barriers and local minima in energy landscapes of stochastic local search [article]

Petteri Kaski
2006 arXiv   pre-print
These results paint a grim picture of the worst-case topography of k-SAT for local search, and constitute apparently the first rigorous analysis of the growth of energy barriers in a random ensemble of  ...  ., the typical k-SAT energy landscape induced by an instance drawn from the ensemble has a set of 2^Ω(n) local energy minima, each separated by an unconditional Ω(n) energy barrier from each of the O(1  ...  A local search algorithm can now be viewed as a stochastic process that traverses a sequence of adjacent states in the energy landscape associated with the problem instance.  ... 
arXiv:cs/0611103v1 fatcat:3kjsdqlf7zatlphryii7duulyq

Stochastic Tunneling Approach for Global Minimization of Complex Potential Energy Landscapes

W. Wenzel, K. Hamacher
1999 Physical Review Letters  
We investigate a novel stochastic technique for the global optimization of complex potential energy surfaces (PES) that avoids the freezing problem of simulated annealing by allowing the dynamical process  ...  to tunnel energetically inaccessible regions of the PES by way of a dynamically adjusted nonlinear transformation of the original PES.  ...  of high energy barriers that separate local minima of the PES.  ... 
doi:10.1103/physrevlett.82.3003 fatcat:qjolsnnk5fby3f6ahskoolthsq

Scaling behavior of stochastic minimization algorithms in a perfect funnel landscape

K. Hamacher, W. Wenzel
1999 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
Generalized Monte-Carlo methods(MCM, STUN) avoid an enumerative search of the PES and thus provide a natural resolution of the Levinthal paradox.  ...  We determined scaling laws for the numerical effort to find the optimal configurations of a simple model potential energy surface (PES) with a perfect funnel structure that reflects key characteristics  ...  Our investigation of a novel stochastic tunnelling technique, which removes the kinetic barriers between local minima of the PES, demonstrates that the scaling exponents α is determined by the thermodynamic  ... 
doi:10.1103/physreve.59.938 fatcat:6gfklu25dbgy7jywl57fkml2pq

Stochastic tunneling minimization by molecular dynamics: an application to heteropolymer models

A Baumketner, H Shimizu, M Isobe, Y Hiwatari
2002 Physica A: Statistical Mechanics and its Applications  
By using molecular dynamics simulations, we examined low-energy conformational space of the two models by means of standard simulated annealing (SA) and stochastic tunneling techniques.  ...  In the case of the protein, the stochastic tunneling method is able to locate about 5 times more low-energy conformations at short simulation times than the SA method while for the polyampholyte the achieved  ...  This work was supported by the Research and Development Applying Advanced Computational Science and Technology, Japan Science and Technology Corporation (JST).  ... 
doi:10.1016/s0378-4371(02)00738-0 fatcat:byzwpo4fxjcglhezcwqpqos7eq

Nanomaterials - what energy landscapes can tell us

Johann Schön
2015 Processing and Application of Ceramics  
Thus, a study of their energy landscape is needed to determine or predict possible structures, and analyse their stability, via the determination of the minima on the landscape and the generalized barriers  ...  In this contribution, we introduce the major concepts of energy landscapes for chemical systems, and present summaries of four applications to nano-materials: a MgO monolayer on a sapphire substrate, possible  ...  Heard and S. Neelamraju, who have contributed to the development of the G42+ algorithm, and D. Zagorac for helpful advice in preparing the structure figures.  ... 
doi:10.2298/pac1503157s fatcat:fzexejbwujckbfrjrj3bo45kcy

Structure Prediction for PbS and ZnO at Different Pressures and Visualization of the Energy Landscapes

D. Zagorac, J.C. Schön, K. Doll, M. Jansen
2011 Acta Physica Polonica. A  
Based on the barrier and minima information 2-D models of the energy landscape were constructed.  ...  This requires the global exploration of the energy landscape of the chemical system, since each stable phase corresponds to a locally ergodic region of the landscape.  ...  Regarding the barrier structure of the energy landscape, wurtzite and sphalerite appear to exhibit the largest barriers and thus the highest kinetic stability.  ... 
doi:10.12693/aphyspola.120.215 fatcat:q7irch56gfeejnbtbsxiglugd4

Multicanonical jump walk annealing: An efficient method for geometric optimization

Huafeng Xu, B. J. Berne
2000 Journal of Chemical Physics  
Namely, a stochastic global optimization method must favor the global minimum thermodynamically and at the same time be able to cross the high energy barriers.  ...  The method efficiently finds the global minima of these systems. In four comparative studies, MJWA greatly outperforms the conventional simulated annealing in locating the global minima.  ...  Wales of Cambridge University for helpful correspondence and Y. H. Lee of Columbia University and A. Roitberg of NIST for informative discussions. This work was supported by a grant from NIH.  ... 
doi:10.1063/1.480844 fatcat:ueak34frtnaonhlgalbowshlnm

Glassy Phase of Optimal Quantum Control

Alexandre G. R. Day, Marin Bukov, Phillip Weinberg, Pankaj Mehta, Dries Sels
2019 Physical Review Letters  
Across the transition, the control landscape features an exponential number of clusters separated by extensive barriers, which bears a strong resemblance with replica symmetry breaking in spin glasses  ...  Using a machine learning (ML) inspired framework based on the manifold learning algorithm t-SNE, we are able to visualize the geometry of the high-dimensional control landscape in an effective low-dimensional  ...  The authors are pleased to acknowledge that the computational work reported on in this paper was performed on the Shared Computing Cluster which is administered by Boston University's Research Computing  ... 
doi:10.1103/physrevlett.122.020601 fatcat:wl3hnjrw6vb4phd4jeveedkoma

Energy landscape paving simulations of the trp-cage protein

Alexander Schug, Wolfgang Wenzel, Ulrich H. E. Hansmann
2005 Journal of Chemical Physics  
Especially, we introduce a temperature-free variant of the method and demonstrate that it allows a fast scanning of the energy landscape.  ...  We evaluate the efficiency of multiple variants of energy landscape paving in all-atom simulations of the trp-cage protein using a recently developed new force field.  ...  Hansmann spent part of his sabbatical at the Institute for Nanotechnology ͑Forschungszentrum Karlsruhe͒. He thanks the institute and especially W. Wenzel and his group for kind hospitality.  ... 
doi:10.1063/1.1899149 pmid:16161610 fatcat:big3fo4bejaihm24kku2zlinea

Stochastic Local Search Using the Search Space Smoothing Meta-Heuristic:A Case Study

Sheqin Dong, Fan Guo, Jun Yuan, Rensheng Wang, Xianlong Hong
2006 Proceedings of the 9th Joint Conference on Information Sciences (JCIS)  
We design a novel algorithm which runs stochastic local search under the SSS framework.  ...  The function determining the accepting probability of uphill moves is designed so that the algorithm can take advantage of the local smoothing effect ignored in original SSS.  ...  Such stochastic local search can make use of local smoothing effect.  ... 
doi:10.2991/jcis.2006.213 dblp:conf/jcis/DongGYWH06a fatcat:so55jfdtwzeuncfuruwcuczaou

Ab initioenergy landscape of LiF clusters

K. Doll, J. C. Schön, M. Jansen
2010 Journal of Chemical Physics  
In addition, the threshold algorithm is employed to determine the energy barriers for the transitions among these structures, for the cluster (LiF)4, again on the ab initio level; and the corresponding  ...  A global search for possible LiF cluster structures is performed, up to (LiF)8. The method is based on simulated annealing, where all the energies are evaluated on the ab initio level.  ...  This way, the energy barriers separating the minima of the energy landscape of this cluster were computed, and a tree graph representation of the energy landscape of LiF 4 was constructed.  ... 
doi:10.1063/1.3455708 pmid:20632748 fatcat:fcbdyisgavbb5bgqnwhuwqhlva

Understanding the Continuous-Time Dynamics of Phase-Transition Nano-Oscillator-based Ising Hamiltonian Solver

Sourav Dutta, Abhishek Khanna, Suman Datta
2020 IEEE Journal on Exploratory Solid-State Computational Devices and Circuits  
We highlight the formation of stable attractor states in the phase space of the coupled PTNO network using secondharmonic injection locking (SHIL) that corresponds to the minima of the Ising Hamiltonian  ...  Many combinatorial optimization problems can be mapped onto the ground-state search problem of an Ising model.  ...  Stochasticity also plays a critical role in affecting the likelihood of the oscillator network to escape the local energy minima and reach the global optimum.  ... 
doi:10.1109/jxcdc.2020.3045074 fatcat:rjn6bxbvezgehcgdff4zn6xpzi

Determination of the energy landscape of Pd12Pt1 using a combined genetic algorithm and threshold energy method

Rafael Pacheco-Contreras, Dora J. Borbón-González, Maribel Dessens-Félix, Lauro Oliver Paz-Borbón, Roy L. Johnston, J. Christian Schön, Martin Jansen, Alvaro Posada-Amarillas
2013 RSC Advances  
of local minima, with an icosahedral motif found to be the putative global minimum for Pd 12 Pt 1 .  ...  and the threshold method for global optimization and exploration of the barrier structure, employing the semiempirical Gupta many-body potential for modeling the interatomic interactions.  ...  Acknowledgements RPC and MDF are grateful to CONACYT for the award of a PhD scholarship. APA acknowledges financial support from CONACYT through grants 24060 and 180424.  ... 
doi:10.1039/c3ra41477a fatcat:hphv7zqffvdtdbarjgpwvoq5x4

A Conformational Analysis Method for Understanding the Energy Landscapes of Clusters

Longjiu Cheng, Wensheng Cai, Xueguang Shao
2007 ChemPhysChem  
In most of the stochastic optimization methods, the search for new solutions is based on perturbations, and local minimization is necessary after each perturbation.  ...  [8] 13] [14] [15] An inherent structure network (ISN) was also employed to represent the topology of energy landscapes, with which local minima and transition states can be represented by nodes and  ... 
doi:10.1002/cphc.200600604 pmid:17285660 fatcat:7fshmt2fbzgmbitoyee3mqdfvm

Discovering Unique, Low-Energy Pure Water Isomers: Memetic Exploration, Optimization, and Landscape Analysis

Harold Soh, Yew-Soon Ong, Quoc Chinh Nguyen, Quang Huy Nguyen, Mohamed Salahuddin Habibullah, Terence Hung, Jer-Lai Kuo
2010 IEEE Transactions on Evolutionary Computation  
Further numerical results show that AMMA and ABHA outperformed a baseline stochastic multi-start local search (SMSL) algorithm in terms of convergence and isomer archival.  ...  The discovery of low-energy stable and meta-stable molecular structures remains an important and unsolved problem in search and optimization.  ...  Experimental results show that AMMA and ABHA performed similarly but were superior to a baseline stochastic multi-start local search (SMSL) algorithm in terms of convergence and number of low-energy isomers  ... 
doi:10.1109/tevc.2009.2033584 fatcat:nfcfegiuorcbrd74vbj2mhsxou
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