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Modelling the dynamics of stochastic local search on k-SAT

JOURNAL OF HEURISTICS 2007年第6期13卷 587-639页

作者： Fournier, Nicolas G. EPO Munich Germany

A new analytical tool is presented to provide a better understanding of the search space of k-SAT. This tool, termed the local value distribution, describes the probability of finding assignments of any value q' in the neighbourhood of assignments of value q. The local value distribution is then used to define a Markov model to model the dynamics of a corresponding stochastic local search algorithm for k-SAT. The model is evaluated by comparing the predicted algorithm dynamics to experimental results. In most cases the fit of the model to the experimental results is very good, but limitations are also recognised.

关键词： algorithm analysis experimental evaluation stochastic algorithms local search k-SAT

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How to assess and report the performance of a stochastic algorithm on a benchmark problem: mean or best result on a number of runs?

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OPTIMIZATION LETTERS 2007年第3期1卷 309-311页

作者： Birattari, Mauro Dorigo, Marco Univ Libre Bruxelles IRIDIA CoDE Brussels Belgium

Some authors claim that reporting the best result obtained by a stochastic algorithm in a number of runs is more meaningful than reporting some central statistic. In this short note, we analyze and refute the main arg... 详细信息

关键词： Assessment of performance Experimental methodology stochastic algorithms Metaheuristics

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An alternative way of presenting statistical test results when evaluating the performance of stochastic approaches

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NEUROCOMPUTING 2015年第1期147卷 235-238页

作者： Weise, Thomas Chiong, Raymond Univ Sci & Technol China USTC Birmingham Joint Res Inst Intelligent Comput Hefei 230027 Anhui Peoples R China Univ Newcastle Sch Design Commun & Informat Technol Callaghan NSW 2308 Australia

stochastic approaches such as evolutionary algorithms have been widely used in various science and engineering problems. When comparing the performance of a set of stochastic algorithms, it is necessary to statistically evaluate which algorithms are the most suitable for solving a given problem. The outcome of statistical tests comparing N >= 2 processes, where N is the number of algorithms, is often presented in tables. This can become confusing for larger numbers of N. Such a scenario is, however, very common in both numerical and combinatorial optimization as well as in the domain of stochastic algorithms in general. In this letter, we introduce an alternative way of visually presenting the results of statistical tests for multiple processes in a compact and easy-to-read manner using a directed acyclic graph (DAG), in the form of a simplified Hasse diagram. The rationale of doing so is based on the fact that the outcome of the tests is always at least a strict partial order, which can be appropriately presented via a DAG. The goal of this brief communication is to promote the use of this approach as a means for presenting the results of comparisons between different optimization methods. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Statistical tests Directed acyclic graph Hasse diagram stochastic algorithms Optimization

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stochastic analysis of the Least Mean Kurtosis algorithm for Gaussian inputs

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DIGITAL SIGNAL PROCESSING 2016年 54卷 35-45页

作者： Bershad, Neil J. Bermudez, Jose C. M. Univ Calif Irvine Dept Elect & Comp Engn Irvine CA 92717 USA Univ Fed Santa Catarina Dept Elect & Elect Engn BR-88040970 Florianopolis SC Brazil

The Least Mean Kurtosis (LMK) algorithm was initially proposed as an adaptive algorithm that is robust to the observation noise distribution. Good performances of this algorithm have been shown for non Gaussian additive measurement noise. However, the complexity of the algorithm imposes difficulties for the development of a reasonably complete theoretical stochastic model for its behavior. The purpose of this paper is to contribute to the development of such a model. We study the stochastic behavior of Least Mean Kurtosis (LMK) algorithm for Gaussian inputs and for additive noises with even probability density functions. Deterministic recursions are derived for the adaptive weight error covariance matrix in a very novel manner, leading to a recursive model for the excess mean square error (EMSE) behavior that is shown to be accurate for Gaussian, uniform and binary noise distributions. The analysis results are then used to compare the performances of LMK with the least mean squares (LMS) and least mean fourth (LMF) algorithms under different circumstances. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Adaptive filters Analysis LMK algorithm stochastic algorithms

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Deterministic and stochastic modeling of heterogeneous catalytic selective hydrogenation of vegetable oil

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CHEMICAL ENGINEERING JOURNAL 2024年 488卷

作者： Pellegrino, Enza Di Giuliano, Andrea Cancrini, Nicoletta Gallucci, Katia Univ Aquila Dept Ind & Informat Engn & Econ DIIIE Piazzale E Pontieri 1 loc Monteluco di Roio Laquila 67100 AQ Italy

Vegetable oils (VO) can provide sustainable feedstock to substitute chemicals currently obtained from petrol. VO are majorly composed of saturated or unsaturated fatty acids with 18 carbon atoms (C18), free or esterifying glycerol. The monounsaturated C18 fatty acid (C18:1, oleic acid) is of industrial interest. Heterogeneous catalytic selective hydrogenation of VO is studied to maximize the fraction of C18:1 in VO. The current work investigates hydrogenation from the modelling point of view, examining the relation between deterministic models (based on classical ordinary differential equations) and stochastic models (implemented by dedicated algorithms). The investigation starts from experimental data of canola oil treated with H 2 in presence of commercial Lindlar catalyst. Two reaction schemes were considered to develop the deterministic models. Two algorithms (Gillespie's stochastic simulation algorithm and tau-leaping) were implemented for stochastic simulations. The whole simulative work was carried out by MATLAB (R) 2023b. The deterministic model shows that consecutive hydrogenations of one double bond per step with pseudo-first order rate laws - the most straightforward reaction scheme considered in this work - interpret the experimental data well, provided that variable selectivity values are introduced. The stochastic simulations at different numbers of initial molecules allow a multiscale analysis of the system, confirming the reliability of the chosen reaction scheme and suggesting that the experimental system is in its thermodynamic limit, in the sense of statistical-mechanics, at all investigated conditions.

关键词： Selective Hydrogenation Vegetable oil Deterministic Modelling stochastic algorithms Heterogeneous Catalysis Lindlar Catalyst

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A stochastic algorithm finding p-means on the circle

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BERNOULLI 2016年第4期22卷 2237-2300页

作者： Arnaudon, Marc Miclo, Laurent Univ Bordeaux UMR 5251 Inst Math Bordeaux 351 Cours Liberat F-33405 Talence France CNRS 351 Cours Liberat F-33405 Talence France Univ Toulouse 3 UMR 5219 Inst Math Toulouse 118 Route Narbonne F-31062 Toulouse 9 France CNRS 118 Route Narbonne F-31062 Toulouse 9 France

A stochastic algorithm is proposed, finding some elements from the set of intrinsic p-mean(s) associated to a probability measure nu on a compact Riemannian manifold and to p epsilon [1, infinity). It is fed sequentially with independent random variables (Y-n)n epsilon N distributed according to nu, which is often the only available knowledge of nu. Furthermore, the algorithm is easy to implement, because it evolves like a Brownian motion between the random times when it jumps in direction of one of the Y-n, n epsilon N. Its principle is based on simulated annealing and homogenization, so that temperature and approximations schemes must be tuned up (plus a regularizing scheme if nu does not admit a Holderian density). The analysis of the convergence is restricted to the case where the state space is a circle. In its principle, the proof relies on the investigation of the evolution of a time-inhomogeneous L-2 functional and on the corresponding spectral gap estimates due to Holley, Kusuoka and Stroock. But it requires new estimates on the discrepancies between the unknown instantaneous invariant measures and some convenient Gibbs measures.

关键词： Gibbs measures homogenization instantaneous invariant measures intrinsic p-means probability measures on compact Riemannian manifolds simulated annealing spectral gap at small temperature stochastic algorithms

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stochastic, analytic and numerical aspects of coagulation processes

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MATHEMATICS AND COMPUTERS IN SIMULATION 2003年第3-6期62卷 265-275页

作者： Wagner, W Weierstrass Inst Appl Anal & Stochast D-10117 Berlin Germany

In this paper, we review recent results concerning stochastic models for coagulation processes and their relationship to deterministic equations. Open problems related to the gelation effect are discussed. Finally, we present some new conjectures based on numerical experiments performed with stochastic algorithms. (C) 2003 IMACS. Published by Elsevier Science B.V. All rights reserved.

关键词： coagulation gelation effect stochastic algorithms

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Monte Carlo simulation and genetic algorithm for optimising supply chain management in a stochastic environment

Monte Carlo simulation and genetic algorithm for optimising ...

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IEEE International Conference on Systems, Man and Cybernetics (SMC)

作者： Jellouli, O Chatelet, E Univ Technol Troyes Syst Modeling & Dependabil Lab F-10010 Troyes France

ISBN: (纸本)0780370872

Open market and e-commerce change the environment of the manufacturing system. In fact, nowadays, vendors are facing a more and more flexible demand. A the same time, we have more accurate tools to study demand evolution and characteristics. This paper reports a methodology to adopt for optimizing the supply chain inventory management (SCIM) taking into account parameters characterizing this uncertain environment. This approach tends to reduce the cost of parameters changing when dealing with a flexible demand. We focus on the management of stochastic parameters characterizing the demand such as stochastic lead time, quantity and rate and other parameters such as delivery time. The objective fixed is to optimize the profit composed of unsatisfied demand, backlog, inventory and production costs. Since an analytical formula of the profit isn't possible, we use Monte Carlo simulation and genetic algorithms. Numerical results are given for two cases.

关键词： stochastic algorithms supply chain Monte Carlo simulation cost optimization

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stochastic Neuromorphic Circuits for Solving MAXCUT 37

Stochastic Neuromorphic Circuits for Solving MAXCUT

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37th IEEE International Parallel and Distributed Processing Symposium (IPDPS)

作者： Theilman, Bradley H. Wang, Yipu Parekht, Ojas Severa, William Smith, J. Darby Aimone, James B. Sandia Natl Labs Neural Explorat & Res Lab POB 5800 Albuquerque NM 87185 USA Sandia Natl Labs Discrete Math & Optimizat Albuquerque NM USA

ISBN: (纸本)9798350337662

Finding the maximum cut of a graph (MAXCUT) is a classic optimization problem that has motivated parallel algorithm development. While approximate algorithms to MAXCUT offer attractive theoretical guarantees and demonstrate compelling empirical performance, such approximation approaches can shift the dominant computational cost to the stochastic sampling operations. Neuromorphic computing, which uses the organizing principles of the nervous system to inspire new parallel computing architectures, offers a possible solution. One ubiquitous feature of natural brains is stochasticity: the individual elements of biological neural networks possess an intrinsic randomness that serves as a resource enabling their unique computational capacities. By designing circuits and algorithms that make use of randomness similarly to natural brains, we hypothesize that the intrinsic randomness in microelectronics devices could be turned into a valuable component of a neuromorphic architecture enabling more efficient computations. Here, we present neuromorphic circuits that transform the stochastic behavior of a pool of random devices into useful correlations that drive stochastic solutions to MAXCUT. We show that these circuits perform favorably in comparison to software solvers and argue that this neuromorphic hardware implementation provides a path for scaling advantages. This work demonstrates the utility of combining neuromorphic principles with intrinsic randomness as a computational resource for new computational architectures.

关键词： discrete optimization MAXCUT neuromorphic computing stochastic algorithms

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A stochastic Approach to Solving Bilevel Natural Gas Cash-Out Problems

A Stochastic Approach to Solving Bilevel Natural Gas Cash-Ou...

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16th Annual International Conference on Computational Science (ICCS)

作者： Kalashnikov, Vyacheslav Alexandrov, Vassil Kalashnykova, Nataliya Tecnol Monterrey ITESM Campus Monterrey Monterrey Mexico Cent Econ & Math Inst CEMI Moscow Russia Sumy State Univ Sumy Ukraine ICREA BSC C Jordi Girona 29 Barcelona Spain Univ Autonoma Nuevo Leon UANL Monterrey Mexico

We study a special bilevel programming problem that arises in transactions between a Natural Gas Shipping Company and a Pipeline Operator. Because of the business relationships between these two actors, the timing, and objectives of their decision-making process are different. In order to model that, bilevel programming was traditionally used. Apart from the theoretical studies of the problem to facilitate its solution a linear reformulation is required, as well as heuristic approaches, and branch-and-bound techniques may be applied. We present a linear programming reformulation of the latest version of the model, which is easier and faster to solve numerically. This reformulation makes it easier to theoretically analyze the problem, allowing us to draw some conclusions about the nature of the solution. Since elements of uncertainty are definitely present in the bilevel natural gas cash-out problem, its stochastic formulation is developed in the form of a bilevel multi-stage stochastic programming model with recourse. After reducing the original formulation to a bilevel linear problem, a stochastic scenario tree is defined by its node events, and time series forecasting is used to produce stochastic values for data of natural gas price and demand. Numerical experiments were run to compare the stochastic solution with the perfect information solution and the expected value solutions.

关键词： Operations Research Big Data natural gas cash-out problems stochastic algorithms

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