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Hiding Solutions in Random Satisfiability Problems: A Statistical Mechanics Approach

W. Barthel, A. K. Hartmann, M. Leone, F. Ricci-Tersenghi, M. Weigt, R. Zecchina
2002 Physical Review Letters  
A major problem in evaluating stochastic local search algorithms for NP-complete problems is the need for a systematic generation of hard test instances having previously known properties of the optimal  ...  The design of the hardest problem instances is based on the existence of a first order ferromagnetic phase transition and the glassy nature of excited states.  ...  These states are dynamically favored and trap the system for very long times during a stochastic local search.  ... 
doi:10.1103/physrevlett.88.188701 pmid:12005728 fatcat:lbqrp62sgjhlrjf5bhnamgzgyi

Chemical Reaction Networks and Stochastic Local Search [chapter]

Erik Winfree
2019 Lecture Notes in Computer Science  
Stochastic local search can be an effective method for solving a wide variety of optimization and constraint satisfaction problems.  ...  While not of use for practical computing, the constructions emphasize that exploiting the stochasticity inherent in chemical reaction network dynamics is not inherently inefficient -and indeed I propose  ...  The sixth perspectivethat stochastic CRNs inherently perform stochastic local search -is developed in the rest of this paper.  ... 
doi:10.1007/978-3-030-26807-7_1 fatcat:fo4p66657vg3hbqztimmm4jzbu

Solution space heterogeneity of the randomK-satisfiability problem: Theory and simulations

Haijun Zhou
2010 Journal of Physics, Conference Series  
In this paper we review our recent efforts on the solution space fine structures of the random K-SAT problem.  ...  The existence of solution communities in the solution space is confirmed by numerical simulations of solution space random walking, and the effect of solution space heterogeneity on a stochastic local  ...  This work was partially supported by the National Science Foundation of China (Grant numbers 10774150 and 10834014) and the China 973-Program (Grant number 2007CB935903).  ... 
doi:10.1088/1742-6596/233/1/012011 fatcat:k2j54j47afgajcfscj3euzpee4

The Boolean Satisfiability Problem [article]

Yu Geng
2020 Figshare  
A problem is NP-complete if it belongs to the set (or "class" if you prefer) of the hardest problems in NP-hardest in the sense that every problem ever exists in NP can be reduced to them.  ...  The Boolean Satisfiability Problem is also the first problem proven to be NP-complete.  ...  ) -Search-based -Basis for current most successful solvers • Stalmarck's algorithm -More of a "breadth first" search, proprietary algorithm • Stochastic search -Local search, hill climbing,  ... 
doi:10.6084/m9.figshare.12331172.v1 fatcat:ky6vwo7gm5h3vfovcrpoknfovm

Solving satisfiability problems by fluctuations: The dynamics of stochastic local search algorithms

Wolfgang Barthel, Alexander K. Hartmann, Martin Weigt
2003 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems.  ...  We find two different dynamical regimes, depending on the number of constraints per variable: For low constraintness, the problems are solved efficiently, i.e. in linear time.  ...  of stochastic local search.  ... 
doi:10.1103/physreve.67.066104 pmid:16241301 fatcat:pr4wbesanve5dgk35emkruxuna

Unweighted Stochastic Local Search can be Effective for Random CSP Benchmarks [article]

Christopher D. Rosin
2014 arXiv   pre-print
We present ULSA, a novel stochastic local search algorithm for random binary constraint satisfaction problems (CSP).  ...  ULSA is many times faster than the prior state of the art on a widely-studied suite of random CSP benchmarks.  ...  The stochastic local search state in NuMVC is based on a current candidate subset of the vertices.  ... 
arXiv:1411.7480v1 fatcat:h6iaioluqrde5mo7knj43xyxpy

A Hybrid Quantum Genetic Algorithm and Local Search based DPLL for Max 3-SAT Problems

Abdesslem Layeb, Djamel-Eddine Saidouni
2014 Applied Mathematics & Information Sciences  
A new local search based on DPLL algorithm has been embodied in the quantum genetic algorithm leading to an efficient hybrid framework which achieves better balance between diversification and intensification  ...  The underlying idea is to harness the optimization capabilities of quantum genetic algorithm to achieve good quality solutions for Max SAT problem.  ...  The quantum dynamic is enhanced by a local search procedure based on DPLL algorithm.  ... 
doi:10.12785/amis/080109 fatcat:qmyh7erwejaovbuaxp4xe4gohi

An Evolutionary Local Search Method for Incremental Satisfiability [chapter]

Mohamed El Bachir Menaï
2004 Lecture Notes in Computer Science  
It has only one free parameter and had proved competitive with the more elaborate stochastic local search methods on many hard optimization problems such as MAXSAT problem.  ...  Since stochastic local search algorithms have been proved highly efficient for SAT, it is valuable to investigate their application to solve ISAT.  ...  Acknowledgment The author is grateful to the anonymous referees for their valuable comments and suggestions.  ... 
doi:10.1007/978-3-540-30210-0_13 fatcat:63vcfygkujhwtid44d5wqslwpq

Portfolios in Stochastic Local Search: Efficiently Computing Most Probable Explanations in Bayesian Networks

Ole J. Mengshoel, Dan Roth, David C. Wilkins
2010 Journal of automated reasoning  
for the satisfiability (SAT) problem.  ...  In this article we investigate the use of portfolios (or collections) of heuristics when solving computationally hard problems using stochastic local search.  ...  David Fried and Song Han are also acknowledged for their co-development of the Raven software, with which much of the experimental work reported here was performed.  ... 
doi:10.1007/s10817-010-9170-5 fatcat:2nylfad3fvawnowtz7vlje4abi

Glassy behavior and jamming of a random walk process for sequentially satisfying a constraint satisfaction formula

Haijun Zhou
2010 European Physical Journal B : Condensed Matter Physics  
In this paper we investigate the influence of the solution space landscape to a simple stochastic local search process SEQSAT, which satisfies a K-SAT formula in a sequential manner.  ...  Random K-satisfiability (K-SAT) is a model system for studying typical-case complexity of combinatorial optimization.  ...  CONCLUSION AND FURTHER DISCUSSIONS In this work the dynamic behavior of a simple stochastic search algorithm SEQSAT for the random K-SAT problem were investigated by computer simulations.  ... 
doi:10.1140/epjb/e2010-00021-x fatcat:ajfvop7pfjfvjc5gjzadlpwlm4

The state of SAT

Henry Kautz, Bart Selman
2007 Discrete Applied Mathematics  
The papers in this special issue originated at SAT 2001, the Fourth International Symposium on the Theory and Applications of Satisfiability Testing.  ...  This foreword reviews the current state of satisfiability testing and places the papers in this issue in context.  ...  We implicitly assumed in this challenge, as was common at the time, that stochastic search refers to some form of local search.  ... 
doi:10.1016/j.dam.2006.10.004 fatcat:uouc5yqwlbhpbpd5g25ka3mdia

Improving Configuration Checking for Satisfiable Random k-SAT Instances

André Abramé, Djamal Habet, Donia Toumi
2014 International Symposium on Artificial Intelligence and Mathematics  
Local search methods based on Configuration Checking (CC) have shown their efficiency in solving random k-SAT instances.  ...  The main idea behind CC is to consider the neighborhood of variables in the SAT formula to avoid cycling problem in local search.  ...  (Dynamic) Stochastic Local Search for SAT For a given CNF formula F, a basic Stochastic Local Search (SLS) algorithm for SAT starts by randomly generating a complete assignment I which may falsify some  ... 
dblp:conf/isaim/AbrameHT14 fatcat:cl4k2uhbnbfwbjzwupqre2luvq

Multifractal Dynamics of the QREM [article]

Tommaso Parolini, Gianni Mossi
2020 arXiv   pre-print
The scaling of the value of this entropy at saturation with the volume of the system identifies the three known dynamical phases of the model.  ...  We study numerically the population transfer protocol on the Quantum Random Energy Model and its relation to quantum computing, for system sizes of n≤ 20 quantum spins.  ...  P. would like to thank the Institute for the Theory of Quantum Technologies (TQT) of Trieste for support, the QuAIL group at NASA Ames and the Universities Space Research Association (USRA) for the kind  ... 
arXiv:2007.00315v1 fatcat:46hcst4pe5gthgyjg3j6sgaw3m

Approaching the ground states of the random maximum two-satisfiability problem by a greedy single-spin flipping process

Hui Ma, Haijun Zhou
2011 Physical Review E  
For the ± J Viana-Bray spin glass model, however, the greedy single-spin dynamics quickly gets trapped to a local minimal region of the energy landscape.  ...  In this brief report we explore the energy landscapes of two spin glass models using a greedy single-spin flipping process, Gmax.  ...  In this brief report we explore the energy landscapes of two mean-field spin glass models using stochastic local dynamics.  ... 
doi:10.1103/physreve.83.052101 pmid:21728591 fatcat:lejl5jxeb5ebvlt6jgrtthpghm

Ten Challenges Redux: Recent Progress in Propositional Reasoning and Search [chapter]

Henry Kautz, Bart Selman
2003 Lecture Notes in Computer Science  
In this paper we review recent progress towards each of these challenges, including our own work on the power of clause learning and randomized restart policies.  ...  In 1997 we presented ten challenges for research on satisfiability testing [1] .  ...  Randomized Systematic Search We implicitly assumed in this challenge, as was common at the time, that stochastic search refers to some form of local search.  ... 
doi:10.1007/978-3-540-45193-8_1 fatcat:a6eqq3kh6nalpfowg4pfc3xkhu
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