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A Robbins-Monro-type algorithm for computing global minimizer of generalized conic functions

OPTIMIZATION 2015年第9期64卷 1999-2020页

作者： Barczy, Matyas Nagy, Abris Noszaly, Csaba Vincze, Csaba Univ Debrecen Fac Informat Dept Appl Math & Probabil Debrecen Hungary Hungarian Acad Sci Inst Math MTA DE Res Grp Equat Funct & Curves Debrecen Hungary Univ Debrecen Debrecen Hungary Univ Debrecen Inst Math Debrecen Hungary

We generalize the notion and some properties of the conic function introduced by Vincze and Nagy in 2012. We provide a stochastic algorithm for computing the global minimizer of generalized conic functions, we prove a... 详细信息

关键词： global optimization Markov process conic function stochastic algorithm Robbins-Monro algorithm 90C25 60D05

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Importance sampling and statistical Romberg method

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BERNOULLI 2015年第4期21卷 1947-1983页

作者： Ben Alaya, Mohamed Hajji, Kaouther Kebaier, Ahmed Univ Paris 04 Univ Paris 13 CNRS LAGAUMR 7539 Villetaneuse France

The efficiency of Monte Carlo simulations is significantly improved when implemented with variance reduction methods. Among these methods, we focus on the popular importance sampling technique based on producing a parametric transformation through a shift parameter theta. The optimal choice of theta is approximated using Robbins Monro procedures, provided that a nonexplosion condition is satisfied. Otherwise, one can use either a constrained Robbins Monro algorithm (see, e.g., Arouna (Monte Carlo Methods Appl. 10 (2004) 1-24) and Lelong (Statist. Probab. Lett. 78 (2008) 2632-2636)) or a more astute procedure based on an unconstrained approach recently introduced by Lemaire and Pages in (Ann. AppL Probab. 20 (2010) 1029-1067). In this article, we develop a new algorithm based on a combination of the statistical Romberg method and the importance sampling technique. The statistical Romberg method introduced by Kebaier in (Ann. AppL Probab. 15 (2005) 2681-2705) is known for reducing efficiently the complexity compared to the classical Monte Carlo one. In the setting of discritized diffusions, we prove the almost sure convergence of the constrained and unconstrained versions of the Robbins Monro routine, towards the optimal shift theta* that minimizes the variance associated to the statistical Romberg method. Then, we prove a central limit theorem for the new algorithm that we called adaptive statistical Romberg method. Finally, we illustrate by numerical simulation the efficiency of our method through applications in option pricing for the Heston model.

关键词： central limit theorem Euler scheme Heston model Robbins-Monro statistical Romberg method stochastic algorithm variance reduction

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GOLAY CODE AND RANDOM PACKING

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 1986年第3期38卷 583-588页

作者： ITOH, Y INST STAT MATH TOKYO JAPAN

SummaryA random sequential packing by Hamming distance is applied to study Golay code. The probability of getting Golay code is estimated by computer simulation. A histogram of number of packed points is given to show... 详细信息

关键词： Random sequential packing Hamming distance stochastic algorithm Golay binary code clusters of histogram

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On recursive estimation in incomplete data models

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STATISTICS 2000年第1期34卷 27-51页

作者： Yao, JF Univ Paris 01 SAMOS F-75634 Paris France

We consider a new recursive algorithm for parameter estimation from an independent incomplete data sequence. The algorithm can be viewed as a recursive version of the well-known EM algorithm, augmented with a Monte-Carlo step which restores the missing data. Based on recent results on stochastic algorithms, we give conditions for the a.s. convergence of the algorithm. Moreover, asymptotical variance of this estimator is reduced by a simple averaging. Application to finite mixtures is given with a simulation experiment.

关键词： incomplete data EM algorithm recursive estimation mixtures stochastic algorithm

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Parallel-Chiller Optimization Using Continuous Barnacles Mating Optimizer Considering Chiller Availability and Cooling Load Variations

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PROCESS INTEGRATION AND OPTIMIZATION FOR SUSTAINABILITY 2024年 1-17页

作者： Thou, Edwin Mun Chuen Wong, Basil T. Chong, Kok Hing Bong, Victor Nee Shin Boniface, Christopher J. Swinburne Univ Technol Sarawak Campus Fac Engn Comp & Sci Dept Mech Engn Kuching Malaysia Publ Works Dept Sarawak Kuching Sarawak Malaysia

Heating, ventilation, and air conditioning systems are known for their high energy consumption, and the operation of parallel chillers is an important way to increase the energy efficiency of these systems. In the field of optimal chiller loading, algorithms are used to find the best loading combinations of chillers for different systems. Existing studies assume that all chillers in a case study are available and included for optimization. Furthermore, due to the iterative nature of stochastic algorithms used for optimal chiller loading, they can present huge variations between results, leading to suboptimal performance. This study aims to solve these problems by modifying an existing optimization algorithm, which is the barnacle mating optimizer. By allowing manual overriding of the on and off statuses of each chiller, these modifications improve practical applications in cases of chiller maintenance or breakdown. Furthermore, optimization precision was increased by introducing continuous cycles in each optimization procedure, followed by filtering and sorting of the best loading distributions. With numerical testing, the proposed continuous barnacles mating optimizer performed on par with its native counterpart at high cooling loads while providing up to 11% energy savings and reliably following optimization constraints at lower loads. Manual chiller switching functions of the modified algorithm also demonstrated good stability despite having fewer chillers during high-load situations. This study encourages improvements other than power consumption in the optimal chiller loading field to improve their feasibility in practical applications while addressing the 11th goal of the Sustainable Development Goals, prompting another step towards more sustainable buildings and cities.

关键词： Optimal chiller loading stochastic algorithm Chiller switching Part load ratio Downtime

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Spinal constructions for continuous type-space branching processes with interactions

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ELECTRONIC JOURNAL OF PROBABILITY 2024年第none期29卷 1-46页

作者： Medous, Charles Univ Grenoble Alpes CNRS IF F-38000 Grenoble France Univ Grenoble Alpes INRIA F-38000 Grenoble France

We consider branching processes describing structured, interacting populations in continuous time. Dynamics of each individual's characteristics and branching properties can be influenced by the entire population. We propose a Girsanov-type result based on a spinal construction, and establish a many-to-one formula. By combining this result with the spinal decomposition, we derive a generalized continuous-time version of the Kesten-Stigum theorem that incorporates interactions. Additionally, we propose an alternative approach of the spine construction for exact simulations of stochastic size-dependent populations.

关键词： non-local branching processes interacting populations spine Many-to-One formula Kesten-Stigum theorem stochastic algorithm

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Adaptive importance sampling for multilevel Monte Carlo Euler method

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stochasticS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND stochastic PROCESSES 2023年第2期95卷 303-327页

作者： Ben Alaya, Mohamed Hajji, Kaouther Kebaier, Ahmed Univ Rouen Normandie St Etienne Du Rouvray France Univ Sorbonne Paris Nord Villetaneuse France Univ Evry Univ Paris Saclay Lab Math & Modelisat Evry CNRS Evry France

This paper focuses on the study of an original combination of the Multilevel Monte Carlo method introduced by Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56(3) (2008), pp. 607-617.] and the popular importance sampling technique. To compute the optimal choice of the parameter involved in the importance sampling method, we rely on Robbins-Monro type stochastic algorithms. On the one hand, we extend our previous work [M. Ben Alaya, K. Hajji and A. Kebaier, Importance sampling and statistical Romberg method, Bernoulli 21(4) (2015), pp. 1947-1983.] to the Multilevel Monte Carlo setting. On the other hand, we improve [M. Ben Alaya, K. Hajji and A. Kebaier, Importance sampling and statistical Romberg method, Bernoulli 21(4) (2015), pp. 1947-1983.] by providing a new adaptive algorithm avoiding the discretization of any additional process. Furthermore, from a technical point of view, the use of the same stochastic algorithms as in [M. Ben Alaya, K. Hajji and A. Kebaier, Importance sampling and statistical Romberg method, Bernoulli 21(4) (2015), pp. 1947-1983.] appears to be problematic. To overcome this issue, we employ an alternative version of stochastic algorithms with projection (see, e.g. Laruelle, Lehalle and Pages [Optimal posting price of limit orders: learning by trading, Math. Financ. Econ. 7(3) (2013), pp. 359-403.]). In this setting, we show innovative limit theorems for a doubly indexed stochastic algorithm which appear to be crucial to study the asymptotic behaviour of the new adaptive Multilevel Monte Carlo estimator. Finally, we illustrate the efficiency of our method through applications from quantitative finance.

关键词： Multilevel Monte Carlo stochastic algorithm Robbins-Monro variance reduction Lindeberg-Feller central limit theorem Euler scheme finance

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UNCONSTRAINED RECURSIVE IMPORTANCE SAMPLING

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ANNALS OF APPLIED PROBABILITY 2010年第3期20卷 1029-1067页

作者： Lemaire, Vincent Pages, Gilles Univ Paris 06 Lab Probabil & Modeles Aleatoires UMR 7599 F-75252 Paris 5 France

We propose an unconstrained stochastic approximation method for finding the optimal change of measure (in an a priori parametric family) to reduce the variance of a Monte Carlo simulation. We consider different parametric families based on the Girsanov theorem and the Esscher transform (exponential-tilting). In [Monte Carlo Methods Appl. 10 (2004) 1-24], it described a projected Robbins-Monro procedure to select the parameter minimizing the variance in a multidimensional Gaussian framework. In our approach, the parameter (scalar or process) is selected by a classical Robbins-Monro procedure without projection or truncation. To obtain this unconstrained algorithm, we extensively use the regularity of the density of the law without assuming smoothness of the payoff. We prove the convergence for a large class of multidimensional distributions as well as for diffusion processes. We illustrate the efficiency of our algorithm on several pricing problems: a Basket payoff under a multidimensional NIG distribution and a barrier options in different markets.

关键词： stochastic algorithm Robbins-Monro importance sampling Esscher transform NIG distribution barrier options

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An effective construction method for multi-level uniform designs

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2013年第9期143卷 1583-1589页

作者： Tang, Yu Xu, Hongquan Soochow Univ Sch Math Sci Suzhou 215006 Jiangsu Peoples R China Univ Calif Los Angeles Dept Stat Los Angeles CA 90095 USA

Uniform designs are widely used in various applications. However, it is computationally intractable to construct uniform designs, even for moderate number of runs, factors and levels. We establish a linear relationship between average squared centered L-2-discrepancy and generalized wordlength pattern, and then based on it, we propose a general method for constructing uniform designs with arbitrary number of levels. The main idea is to choose a generalized minimum aberration design and then permute its levels. We propose a novel stochastic algorithm and obtain many new uniform designs that have smaller centered L-2-discrepancies than the existing ones. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Fractional factorial design Generalized minimum aberration Generalized wordlength pattern Level permutation stochastic algorithm Uniform design

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Improved Salp Swarm algorithm with Space Transformation Search for Training Neural Network

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ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2020年第4期45卷 2743-2761页

作者： Panda, Nibedan Majhi, Santosh Kumar Veer Surendra Sai Univ Technol Dept Comp Sci & Engn Burla 768018 Odisha India

Swarm-based algorithm is best suitable when it can perform smooth balance between the exploration and exploitation as well as faster convergence by successfully avoiding local optima entrapment. At recent time, salp swarm algorithm (SSA) is developed as a nature-inspired swarm-based algorithm. It can solve continuous, nonlinear and complex in nature day-to-day life optimization problems. Like many other optimization algorithms, SSA suffers with the problem of local stagnation. This paper introduces an improved version of the SSA, which improves the performance of the existing SSA by using space transformation search (STS). The proposed algorithm is termed as STS-SSA. The STS-SSA enhances the exploration and exploitation capability in the search space and successfully avoids local optima entrapment. The STS-SSA is evaluated by considering the IEEE CEC 2017 standard benchmark function set. The efficiency and robustness of the proposed STS-SSA are measured using performance metrics, convergence analysis and statistical significance. A demonstration is given as an application of the proposed algorithm for solving a real-life problem. For this purpose, the multi-layer feed-forward network is trained using the proposed STS-SSA. The experimental results demonstrate that the developed STS-SSA can be used for solving optimization problems effectively.

关键词： Salp swarm algorithm Space transformation search (STS) stochastic algorithm Optimization Classification Neural network

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