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New formulations for the kissing number problem

DISCRETE APPLIED MATHEMATICS 2007年第14期155卷 1837-1841页

作者： Kucherenko, Sergei Belotti, Pietro Liberti, Leo Maculan, Nelson Imperial Coll CPSE London SW7 2AZ England Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA Ecole Polytech LIX F-91128 Palaiseau France Univ Fed Rio de Janeiro COPPE BR-21941 Rio De Janeiro Brazil

Determining the maximum number of D-dimensional spheres of radius r that can be adjacent to a central sphere of radius r is known as the Kissing Number Problem (KNP). The problem has been solved for two, three and very recently for four dimensions. We present two nonlinear (nonconvex) mathematical programming models for the solution of the KNP. We solve the problem by using two stochastic global optimization methods: a Multi Level Single Linkage algorithm and a Variable Neighbourhood Search. We obtain numerical results for two, three and four dimensions. (c) 2007 Elsevier B.V. All rights reserved.

关键词： sphere packing NLP global optimization stochastic algorithm multi-level single linkage variable neighbourhood search

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A Python/C plus plus library for bound-constrained global optimization using a biased random-key genetic algorithm

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2015年第3期30卷 710-728页

作者： Silva, R. M. A. Resende, M. G. C. Pardalos, P. M. Univ Fed Pernambuco Ctr Informat CIn Recife PE Brazil AT&T Labs Res Algorithms & Optimizat Res Dept Florham Pk NJ 07932 USA Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA

This paper describes libbrkga, a GNU-style dynamic shared Python/C++ library of the biased random-key genetic algorithm (BRKGA) for bound constrained global optimization. BRKGA (J Heuristics 17:487-525, 2011b) is a general search metaheuristic for finding optimal or near-optimal solutions to hard optimization problems. It is derived from the random-key genetic algorithm of Bean (ORSA J Comput 6:154-160, 1994), differing in the way solutions are combined to produce offspring. After a brief introduction to the BRKGA, including a description of the local search procedure used in its decoder, we show how to download, install, configure, and use the library through an illustrative example.

关键词： Biased random-key genetic algorithm Global optimization Multimodal functions Continuous optimization Heuristic stochastic algorithm stochastic local search Nonlinear programming

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A sum-over-paths impulse-response moment-extraction algorithm for RC IC-interconnect networks

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SOLID-STATE ELECTRONICS 2004年第12期48卷 2133-2145页

作者： Le Coz, YL Krishna, D Petranovic, DM Loh, WM Bendix, P Rensselaer Polytech Inst ECSE Dept Troy NY 12180 USA Log Corp LSI Milpitas CA 95035 USA

We have created a new impulse-response (IR) moment-extraction algorithm for RC circuit networks. It employs a Feynman sum-over-paths postulate. Our approach begins with generation of s-domain nodal-voltage equations. We then perform a Taylor-series expansion of the circuit transfer function. These expansions yield transition diagrams involving mathematical coupling constants, or weight factors, in integral powers of complex frequency s. Our sum-over-paths postulate supports stochastic evaluation of path sums within the circuit transition diagram to any desired order of s. The specific order of sin the sum corresponds, as well, to the order of IR moment we seek to extract. In developing the algorithm, importantly, we maintain computational efficiency and full parallelism. Initial verification studies of uncoupled and coupled RC lines furnished promising results: 5% and 15% approximate I-sigma error for first- and second-order IR moments, respectively, after only 100 sampled path-sum terms. In addition, we observed excellent convergence to exact, analytical moment values with increasing number of samples. Our sum-over-paths postulate, in fact, implies generality for arbitrary RC-interconnect networks, beyond those specific examples presented in this work. We believe, in conclusion, that this type of IR moment-extraction algorithm may find useful application in a massively coupled electrical system, such as that encountered in high-end digital-IC interconnects. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： Feynman sum over paths IC-interconnect modeling impulse response moment extraction RC circuit networks stochastic algorithm

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Multilayer dielectric filter design using a multiobjective evolutionary algorithm

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2005年第11期53卷 3625-3632页

作者： Venkatarayalu, NV Ray, T Gan, YB Natl Univ Singapore Temasek Labs Singapore 119260 Singapore

Design of multilayer dielectric filters involve the identification of suitable dielectric material and appropriate thicknesses of the layers that best satisfies the desired frequency response for the application. Such problems, like any other practical design optimization problem require simultaneous consideration of multiple objectives and constraints. In this paper, we introduce a multiobjective evolutionary algorithm that is capable of handling unconstrained and constrained, single and multiobjective problems without any restriction on the number and nature of variables, constraints and objectives. The algorithm handles constraints and objectives separately using two fitness measures derived out of nondominance, unlike most of its counterparts which use a single fitness measure. Unlike most evolutionary algorithms where only the good parents participate in mating, our algorithm ensures that all solutions participate in mating, which is useful for exploring highly nonlinear search spaces. The diversity of the solutions is controlled by the partner selection scheme that prefers elites with distant neighbors as mating partners. The results of two multiobjective test problems, three multilayer dielectric filter designs (low-pass, bandpass and stopband) and one variable layer low-pass filter design are presented in this paper to highlight the benefits offered by our algorithm in terms of modeling flexibility, computational efficiency and its ability to arrive at competitive nondominated designs. A comparison of our results with those obtained using a single objective aggregated formulation for the stopband filter design is also presented. We have also compared the performance of our algorithm with nondominated sorting genetic algorithm (NSGA-II) for the low-pass filter design where our results are better.

关键词： multiobjective optimization optimization of dielectric filters stochastic algorithm

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Simulation-based optimization of virtual nesting controls for network revenue management

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OPERATIONS RESEARCH 2008年第4期56卷 865-880页

作者： van Ryzin, Garrett Vulcano, Gustavo Columbia Univ Grad Sch Business New York NY 10027 USA NYU Stern Sch Business New York NY 10012 USA

Virtual nesting is a popular capacity control strategy in network revenue management. In virtual nesting, products (itinerary-fare-class combinations) are mapped ("indexed") into a relatively small number of "virtual classes" on each resource (flight leg) of the network. Nested protection levels are then used to control the availability of these virtual classes;specifically, a product request is accepted if and only if its corresponding virtual class is available on each resource required. Bertsimas and de Boer proposed an innovative simulation-based optimization method for computing protection levels in a virtual nesting control scheme [Bertsimas, D., S. de Boer. 2005. Simulation-based booking-limits for airline revenue management. Oper. Res. 53 90-106]. In contrast to traditional heuristic methods, this simulation approach captures the true network revenues generated by virtual nesting controls. However, because it is based on a discrete model of capacity and demand, the method has both computational and theoretical limitations. In particular, it uses first-difference estimates, which are computationally complex to calculate exactly. These gradient estimates are then used in a steepest-ascent-type algorithm, which, for discrete problems, has no guarantee of convergence. In this paper, we analyze a continuous model of the problem that retains most of the desirable features of the Bertsimasde Boer method, yet avoids many of its pitfalls. Because our model is continuous, we are able to compute gradients exactly using a simple and efficient recursion. Indeed, our gradient estimates are often an order of magnitude faster to compute than first-difference estimates, which is an important practical feature given that simulation-based optimization is computationally intensive. In addition, because our model results in a smooth optimization problem, we are able to prove that stochastic gradient methods are at least locally convergent. On several test problems using realisti

关键词： capacity control revenue management stochastic algorithm stochastic gradients

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The impact of uncertain centrifuge capillary pressure on reservoir simulation

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2004年第2期26卷 537-557页

作者： Subbey, S Christie, M Sambridge, M Heriot Watt Univ Inst Petr Engn Edinburgh EH14 4AS Midlothian Scotland Australian Natl Univ Res Sch Earth Sci Inst Adv Studies Canberra ACT 0200 Australia

The capillary pressure in a reservoir determines the saturation distribution, and hence the total in situ volumes of fluids (oil/water/gas). The accurate knowledge of the capillary pressure distribution is one of the primary factors that may be decisive in the reliable estimation of hydrocarbon reserves. The centrifuge procedure provides laboratory data, which can be inverted to derive capillary pressure curves in laboratory conditions. The derived laboratory capillary pressure curves are then scaled up for full-field simulation of petroleum reservoirs. The inversion procedure is uncertain and gives nonunique capillary pressure curves. The standard industrial practice, however, has been to derive a single capillary pressure curve, and ignoring the uncertainty. Since the capillary pressure is uncertain, estimates of important reservoir parameters dependent on capillary pressure distribution are uncertain. This paper shows how the uncertainty in centrifuge capillary pressure can be quantified. It also shows how this uncertainty propagates through the scale-up process and impacts on the estimate of the oil recovery potential. We illustrate using a simple, two-phase (oil/water) synthetic reservoir model.

关键词： uncertainty Volterra linear integral equation inverse ill-posed stochastic algorithm Voronoi cells measured data synthetic data capillary pressure centrifuge

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Solving systems of nonlinear equations with continuous GRASP

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NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 2009年第4期10卷 2000-2006页

作者： Hirsch, Michael J. Pardalos, Panos M. Resende, Mauricio G. C. Raytheon Inc Network Centr Syst St Petersburg FL 33733 USA Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA AT&T Labs Res Algorithms & Optimizat Res Dept Florham Pk NJ 07932 USA

A method for finding all roots of a system of nonlinear equations is described. Our method makes use of C-GRASP, a recently proposed continuous global optimization heuristic. Given a nonlinear system, we solve a corresponding adaptively modified global optimization problem multiple times, each time using C-GRASP, with areas of repulsion around roots that have already been found. The heuristic makes no use of derivative information. We illustrate the approach using systems found in the literature. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Nonlinear systems of equations Global optimization Continuous optimization Heuristic stochastic algorithm stochastic local search Nonlinear programming GRASP C-GRASP

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Application of inverse analysis to determine the geometric configuration of filament heaters for uniform heating

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INTERNATIONAL JOURNAL OF THERMAL SCIENCES 2016年 105卷 1-12页

作者： Lemos, Larissa D. Brittes, Rogerio Franca, Francis H. R. Univ Fed Rio Grande do Sul Dept Mech Engn Rua Sarmento Leite 425 BR-90050170 Porto Alegre RS Brazil Univ Fed Santa Maria Av Presidente Vargas 1958 BR-96506302 Cachoeira Do Sul RS Brazil

In typical designs of ovens, it is often desired to determine the position and geometrical configurations of heaters to attain uniform heating of the materials subjected to thermal processes. In this study, uniform temperature and heat flux are prescribed in one of the surfaces of a radiative system, while the shape and position of filament heaters are left to be found. This is equivalent to the inverse problem of the conventional trial-and-error approach. The oven is modeled as a three-dimensional enclosure formed with diffuse-gray walls, and filled with transparent medium. The inverse problem is solved as an optimization problem. The solution is obtained by the generalized extreme optimization (GEO) algorithm, a stochastic global optimization method. The proposed methodology can lead to filament heaters capable of satisfying the two conditions on the design surface with maximum deviation of about 2% and average deviation less than 0.5%. (C) 2016 Elsevier Masson SAS. All rights reserved.

关键词： Uniform heating Filament heater Inverse design stochastic algorithm

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The vanishing learning rate asymptotic for linear L²-boosting

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ESAIM-PROBABILITY AND STATISTICS 2024年 28卷 227-257页

作者： Dombry, Clement Esstafa, Youssef Univ Franche Comte CNRS LmB F-25000 Besancon France Le Mans Univ Lab Manceau Math Ave Olivier Messiaen F-72085 Le Mans 09 France

We investigate the asymptotic behaviour of gradient boosting algorithms when the learning rate converges to zero and the number of iterations is rescaled accordingly. We mostly consider L-2-boosting for regression with linear base learner as studied in P. B & uuml;hlmann and B. Yu, J. Am. Statist. Assoc. 98 (2003) 324-339 and analyze also a stochastic version of the model where subsampling is used at each step (J.H. Friedman, Computat. Statist. Data Anal. 38 (2002) 367-378). We prove a deterministic limit in the vanishing learning rate asymptotic and characterize the limit as the unique solution of a linear differential equation in an infinite dimensional function space. Besides, the training and test error of the limiting procedure are thoroughly analyzed. We finally illustrate and discuss our result on a simple numerical experiment where the linear L-2-boosting operator is interpreted as a smoothed projection and time is related to its number of degrees of freedom.

关键词： Boosting non parametric regression statistical learning stochastic algorithm Markov chain convergence of stochastic process

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Multi-scale quantum harmonic oscillator algorithm for global numerical optimization

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APPLIED SOFT COMPUTING 2018年 69卷 655-670页

作者： Wang, Peng Ye, Xinggui Li, Bo Cheng, Kun Southwest Univ Nationalities Sch Comp Sci & Technol Chengdu 610225 Sichuan Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China Chinese Acad Sci Chengdu Inst Comp Applicat Chengdu 610041 Sichuan Peoples R China China Unicom Fujian Branch Cloud Comp & Big Data Ctr Fuzhou 350007 Fujian Peoples R China Tangshan Univ Sch Comp Sci & Technol Tangshan 063000 Peoples R China

This paper aims to provide a novel metaheuristic algorithm motivated from quantum motion entitled Multi-scale Quantum Harmonic Oscillator algorithm (MQHOA). The calculation accuracy of MQHOA is adjustable. The physical model and mathematical analysis of the proposed algorithm are detailed and well interpreted in this paper. The structure of MQHOA is very simple, including merely two phases, the quantum harmonic oscillator process (QHO process) and multi-scale process (M process). Experiments are carried out to validate the effectiveness and efficiency of MQHOA by applying it to 30 well defined benchmark functions. We also compare MQHOA with several well-known metaheuristic algorithms, such as genetic algorithm (GA), simulated annealing (SA), particle swarm optimization (PSO) and quantum particle swarm optimization (QPSO). The comparative results indicate the competitive and superior performance of the proposed algorithm in both convergence speed and optimal solution accuracy. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Quantum harmonic oscillator algorithm Quantum algorithm Metaheuristic algorithm stochastic algorithm Global optimization

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