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Simulated annealing-based algorithms for the studies of the thermoelastic scaling behavior

IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART C-APPLICATIONS AND REVIEWS 2000年第4期30卷 506-516页

作者： Wong, YC Leung, KS Wong, CK Chinese Univ Hong Kong Dept Comp Sci & Engn Shatin Hong Kong Peoples R China

Simulated annealing is a robust and easy-to-implement algorithm for material simulation, However, it consumes a huge amount of computational time, especially on the studies of percolation networks. To reduce the running time, we parallelize the simulated annealing algorithm in our studies of the thermoelastic scaling behavior of percolation networks. The critical properties of the thermoelastic moduli of percolation networks near the threshold p(c) are investigated by constructing a square percolation network. The properties are tested by simulations of a series of two-dimensional (2-D) percolation networks near p(c). The simulations are performed using a novel parallelizing scheme on the simulated annealing algorithm. To further accelerate the computational speed, we also propose a new conjectural method to generate better initial configurations, which speeds up the simulation significantly. Preliminary simulation results show surprisingly that the percolating phenomenon of thermal expansion does exist under certain conditions. The behavior seems to be governed by the elastic properties of a percolation network.

关键词： composite materials percolation networks scaling behavior simulated annealing stochastic algorithms

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Stability of annealing schemes and related processes

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SYSTEMS & CONTROL LETTERS 2000年第5期41卷 325-331页

作者： Borkar, VS Tata Inst Fundamental Res Sch Technol & Comp Sci Bombay 400005 Maharashtra India

An approach for establishing stability of annealing schemes and related processes is described. This extends the approach developed in Borkar and Meyn (SIAM J. Control Optim. 38 (2000) 447) for stochastic approximation algorithms. The proof uses a possibly degenerate stochastic differential equation obtained as a scaling limit of the interpolated algorithm. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： stochastic algorithms stochastic stability annealing processes scaling limits

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Global optimization requires global information

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1998年第3期96卷 575-588页

作者： Stephens, CP Baritompa, W Univ Canterbury Dept Math & Stat Christchurch 1 New Zealand

There are many global optimization algorithms which do not use global information. We broaden previous results, showing limitations on such algorithms, even if allowed to run forever. We show that deterministic algorithms must sample a dense set to find the global optimum value and can never be guaranteed to converge only to global optimizers. Further, analogous results show that introducing a stochastic element does not overcome these limitations. An example is simulated annealing in practice. Our results show that there are functions for which the probability of success is arbitrarily small.

关键词： global optimization convergence stochastic algorithms deterministic algorithms

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A Numerical Scheme for Invariant Distributions of Constrained Diffusions

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MATHEMATICS OF OPERATIONS RESEARCH 2014年第2期39卷 262-289页

作者： Budhiraja, Amarjit Chen, Jiang Rubenthaler, Sylvain Univ N Carolina Dept Stat & Operat Res Chapel Hill NC 27599 USA Univ Nice Sophia Antipolis CNRS LJAD UMR 7351 F-06108 Nice 02 France

Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady-state performance of the corresponding stochastic networks, and thus it is important to develop reliable and efficient algorithms for numerical computation of such distributions. In this work we propose and analyze a Monte-Carlo scheme based on an Euler type discretization of the reflected stochastic differential equation using a single sequence of time discretization steps which decrease to zero as time approaches infinity. Appropriately weighted empirical measures constructed from the simulated discretized reflected diffusion are proposed as approximations for the invariant probability measure of the true diffusion model. Almost sure consistency results are established That, in particular, show that weighted averages of polynomially growing continuous functionals evaluated on the discretized simulated system converge a.s. to the corresponding integrals with respect to the invariant measure. Proofs rely on constructing suitable Lyapunov functions for tightness and uniform integrability and characterizing almost sure limit points through an extension of Echeverria's criteria for reflected diffusions. Regularity properties of the underlying Skorohod problems play a key role in the proofs. Rates of convergence for suitable families of test functions are also obtained. A key advantage of Monte-Carlo methods is the ease of implementation, particularly for high-dimensional problems. A numerical example of an eight-dimensional Skorohod problem is presented to illustrate the applicability of the approach.

关键词： reflected diffusions heavy traffic theory stochastic networks Skorohod problem invariant measures stochastic algorithms

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An introduction to MCMC for machine learning

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MACHINE LEARNING 2003年第1-2期50卷 5-43页

作者： Andrieu, C de Freitas, N Doucet, A Jordan, MI Univ Bristol Dept Math Stat Grp Bristol BS8 1TW Avon England Univ British Columbia Dept Comp Sci Vancouver BC V6T 1Z4 Canada Univ Melbourne Dept Elect & Elect Engn Parkville Vic 3052 Australia Univ Calif Berkeley Dept Comp Sci Berkeley CA 94720 USA Univ Calif Berkeley Dept Stat Berkeley CA 94720 USA

This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of this special issue. Lastly, it discusses new interesting research horizons.

关键词： Markov chain Monte Carlo MCMC sampling stochastic algorithms

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Electricity Cost Minimization for Interruptible Workload in Datacenter Servers

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IEEE TRANSACTIONS ON SERVICES COMPUTING 2020年第6期13卷 1059-1071页

作者： Zhang, Wei Wen, Yonggang Lai, Loi Lei Liu, Fang Fan, Rui Nanyang Technol Univ Sch Comp Sci & Engn 50 Nanyang Ave Singapore 639798 Singapore Guangdong Univ Technol Sch Automat Guangzhou 510006 Guangdong Peoples R China Shanghai Tech Univ Sch Informat Sci & Technol Shanghai 200031 Peoples R China

Datacenters have experienced dramatic growth in recent years, and the cost for powering them has become a significant problem. This paper proposes methods to minimize the energy cost for performing a task on a datacenter server before a deadline. We observe that energy prices fluctuate over time, and schedule the task to execute in periods of relatively low cost, despite not having knowledge of future costs during the execution. This problem is studied in several models, starting with an online setting where electricity prices can change arbitrarily. A root phi-competitive algorithm is proposed, where phi is the ratio between the maximum and minimum electricity prices, and this algorithm is also shown to be optimal by proving a matching lower bound. Next, we consider a stochastic setting in which prices vary in a Markovian fashion and propose an optimal algorithm based on dynamic programming. We then study the performance of our algorithms in practice using prices derived from real world data. The results show that the stochastic algorithm is very effective, and achieves cost that is within 3.4 percent of the optimum. Moreover, it performs well compared to several heuristics used in practice.

关键词： Servers Heuristic algorithms stochastic processes Energy consumption Minimization Quality of service Energy cost datacenters online algorithms stochastic algorithms

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Optimal placements of flexible objects .1. Analytical results for the unbounded case

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IEEE TRANSACTIONS ON COMPUTERS 1997年第8期46卷 890-904页

作者： Albrecht, A Cheung, SK Hui, KC Leung, KS Wong, CK CHINESE UNIV HONG KONG DEPT MECH & AUTOMAT ENGNSHATINNTHONG KONG

We consider optimal placements of two-dimensional flexible (elastic, deformable) objects. The objects are discs of equal size placed within a rigid boundary. The paper is divided into two parts. In the first part, analytical results for three types of regular, periodic arrangements-the hexagonal, square, and triangular placements-are presented. The regular arrangements are analyzed for rectangular boundaries and radii of discs that are small compared to the area of the placement region, because, in this case, the influence of boundary conditions can be neglected. This situation is called the unbounded case. We show that, for the unbounded case among the three regular placements, the type of hexagonal arrangements provides the largest number of placed units for the same deformation depth. Furthermore, it can be proved that these regular placements are not too far from the truly optimal arrangements. For example, hexagonal placements differ at most by the factor 1.1 from the largest possible number of generally shaped units in arbitrary arrangements. These analytical results are used as guidances for testing stochastic algorithms optimizing placements of flexible objects. In the second part of the paper, mainly two problems are considered: The underlying physical model and a simulated annealing algorithm maximizing the number of flexible discs in equilibrium placements. Along with the physical model, an approximate formula is derived, reflecting the deformation/force relationship for a large range of deformations. This formula is obtained from numerical experiments which were performed for various sizes of discs and several elastic materials. The potential applications of the presented approach are in the design of new amorphous polymeric and related materials as well as in the design of package cushioning systems.

关键词： combinatorial optimization placement problems stochastic algorithms simulated annealing composite materials

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Zeroth-order optimization with orthogonal random directions

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MATHEMATICAL PROGRAMMING 2023年第1-2期199卷 1179-1219页

作者： Kozak, David Molinari, Cesare Rosasco, Lorenzo Tenorio, Luis Villa, Silvia Solea Energy Overland Pk KS 66210 USA Ist Italiano Tecnol Genoa Italy Univ Genoa MIT Ist Italiano Tecnol DIBRIS MaLGaCBMM Genoa Italy Colorado Sch Mines Dept Appl Math & Stat Golden CO USA Univ Genoa DIMA MaLGa Genoa Italy

We propose and analyze a randomized zeroth-order optimization method based on approximating the exact gradient by finite differences computed in a set of orthogonal random directions that changes with each iteration. A number of previously proposed methods are recovered as special cases including spherical smoothing, coordinate descent, as well as discretized gradient descent. Our main contribution is proving convergence guarantees as well as convergence rates under different parameter choices and assumptions. In particular, we consider convex objectives, but also possibly non-convex objectives satisfying the Polyak-Lojasiewicz (PL) condition. Theoretical results are complemented and illustrated by numerical experiments.

关键词： Zeroth-order optimization Derivative-free methods stochastic algorithms Polyak-Lojasiewicz inequality Convex programming Finite differences approximation Random search

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Discrete Optimization Algorithm Based on Probability Distribution with Transformation of Target Values

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PROGRAMMING AND COMPUTER SOFTWARE 2024年第6期50卷 445-456页

作者： Sarin, K. S. Tomsk State Univ Control Syst & Radioelect Tomsk 634050 Russia

Problems of search optimization in a discrete space, particularly, in a binary space where a variable can take only two values, are of great practical importance. This paper proposes a new population-based discrete optimization algorithm that uses probability distributions of variables. The distributions determine the probability of taking one or another discrete value and are generated by transforming target values of solutions into their weight coefficients. The performance of the algorithm is evaluated using unimodal and multimodal test functions with binary variables. The experimental results demonstrate the high efficiency of the proposed algorithm in terms of convergence rate and stability.

关键词： optimization methods discrete optimization binary optimization metaheuristics stochastic algorithms and probability distribution

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A simulated annealing version of the EM algorithm for non-Gaussian deconvolution

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STATISTICS AND COMPUTING 1997年第4期7卷 229-236页

作者： Lavielle, M Moulines, E UNIV PARIS 05 F-75270 PARIS 06FRANCE UNIV PARIS SUD PARISFRANCE TELECOM PARIS URA 820F-75634 PARIS 13FRANCE

The Expectation-Maximization (EM) algorithm is a very popular technique for maximum likelihood estimation in incomplete data models. When the expectation step cannot be performed in closed form, a stochastic approximation of EM (SAEM) can be used. Under very general conditions, the authors have shown that the attractive stationary points of the SAEM algorithm correspond to the global and local maxima of the observed likelihood. In order to avoid convergence towards a local maxima, a simulated annealing version of SAEM is proposed. An illustrative application to the convolution model for estimating the coefficients of the filter is given.

关键词： EM algorithm deconvolution linear filters stochastic algorithms simulated annealing

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