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interval algorithm for global numerical optimization

ENGINEERING OPTIMIZATION 2008年第9期40卷 849-868页

作者： Zhang, Xiaowei Liu, Sanyang Xidian Univ Dept Math Sci Xian 710071 Peoples R China

The interval optimization algorithm shows great advantages in bound constrained global optimization. An interval algorithm is presented in this article based on a new selection criterion. The selection criterion is proposed based on numerical experiments and the parameter pf* designed by Casado, Garcia and Csendes in 2000. The proposed criterion at each iteration selects some intervals of which the number is not greater than a constant so that the possible memory problem during the implementation of the algorithm is avoided and the running time of the algorithm is decreased, when the dimension of the problem is increasing. Based on the selection criterion, the proposed algorithm is implemented for a wide set of tested functions which includes easy and hard problems. Numerical experiments show that the proposed algorithm is efficient.

关键词： selection criterion interval algorithm global optimization

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interval algorithm for Random Number Generation: Information Spectrum Approach

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IEEE TRANSACTIONS ON INFORMATION THEORY 2020年第3期66卷 1691-1701页

作者： Watanabe, Shun Han, Te Sun Tokyo Univ Agr & Technol Dept Comp & Informat Sci Tokyo 1848588 Japan Natl Inst Informat & Commun Technol Quantum ICT Lab Tokyo 1848795 Japan

The problem of exactly generating a general random process (target process) by using another general random process (coin process) is studied. The performance of the interval algorithm, introduced by Han and Hoshi, is analyzed from the perspective of information spectrum approach. When either the coin process or the target process has one point spectrum, the asymptotic optimality of the interval algorithm among any random number generation algorithms is proved, which demonstrates utility of the interval algorithm beyond the ergodic process. Furthermore, the feasibility condition of exact random number generation is also elucidated. Finally, the obtained general results are illustrated by the case of generating a Markov process from another Markov process.

关键词： Random number generation Random variables Random processes Markov processes Performance analysis Entropy Convergence Information spectrum approach interval algorithm random number generation

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interval algorithm for random number generation

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IEEE TRANSACTIONS ON INFORMATION THEORY 1997年第2期43卷 599-611页

作者： Han, TS Hoshi, M Sch. of Inf. Syst. Univ. of Electro-Commun. Tokyo Japan Graduate School of Information Systems University of Electro-Communications Chofu Tokyo Japan

The problem of generating a random number with an arbitrary probability distribution by using a general biased M-coin is studied, An efficient and very simple algorithm based on the successive refinement of partitions of the unit interval [0, 1), which we call the interval algorithm, is proposed, A fairly tight evaluation on the efficiency is given, Generalizations of the interval algorithm to the following cases are investigated: 1) output sequence is independent and identically distributed (i.i.d.);2) output sequence is Markov;3) input sequence is Markov;4) input sequence and output sequence are both subject to arbitrary stochastic processes.

关键词： random number generation interval algorithm partitions entropy biased coin arithmetic coding

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interval algorithm for homophonic coding

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IEEE TRANSACTIONS ON INFORMATION THEORY 2001年第3期47卷 1021-1031页

作者： Hoshi, M Han, TS Univ Electrocommun Grad Sch Informat Syst Chofu Tokyo 1828585 Japan

It is shown that the idea of the successive refinement of interval partitions, which plays the key role in the interval algorithm for random number generation by Han and Hoshi, is also applicable to the homophonic coding. An interval algorithm for homophonic coding is introduced which produces an independent and identically distributed (i.i.d.) sequence with probability p, Lower and upper bounds for the expected codeword length are given. Based on this, an interval algorithm for fixed-to-variable homophonic coding is established, The expected codeword length per source letter converges to H(X) / H(p) in probability as the block length tends to infinity, where H(X) is the entropy rate of the source X. The algorithm is asymptotically optimal. An algorithm for fixed-to-fixed homophonic coding is also established. The decoding error probability tends to zero as the block length tends to infinity. Homophonic coding with cost is generally considered. The expected cost of the codeword per source letter converges to (c) over bar (X) / H (p) in probability as the block length tends to infinity, where (c) over bar denotes the verage cost of a source letter. The main contribution of this paper can be regarded as a novel application of Elias' coding technique to homophonic coding. Intrinsic relations among these algorithms, the interval algorithm for random number generation and the arithmetic code are also discussed.

关键词： arithmetic coding cost coding Elias coding homophonic coding interval algorithm random number generation

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interval algorithm for a Kind of Nonsmooth Global Optimization

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Chinese Quarterly Journal of Mathematics 1999年第2期14卷 63-68,页

作者：申培萍河南师范大学河南新乡 453 0 0 2

Based on the interval analysis,a practical interval algorithm is developed for finding all global minimizers of a nonsmooth function on a closed domain XR n, which is given by defining a special derivative to the function and using the interval inclusion of derivative. Both theoretical analysis and numerical results show that this method is practical and effective.

关键词： global minimizer nonsmooth function interval algorithm

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Performance Analysis of the interval algorithm for Random Number Generation Based on Number Systems

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IEEE TRANSACTIONS ON INFORMATION THEORY 2011年第3期57卷 1177-1185页

作者： Oohama, Yasutada Univ Tokushima Dept Informat Sci & Intelligent Syst Tokushima 7708506 Japan

In this paper we analyze the interval algorithm for random number generation proposed by Han and Hoshi using the expression of real numbers on the interval [0, 1). We first establish an explicit representation of the interval algorithm with the representation of real numbers on the interval [0, 1) based on number systems. Next, using the expression of the interval algorithm, we give a rigorous analysis of the interval algorithm. We discuss the difference between the expected number of the coin tosses in the interval algorithm and their upper bound derived by Han and Hoshi and show that it can be characterized explicitly with the established expression of the interval algorithm.

关键词： Generating tree interval algorithm number systems performance analysis random number generation

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Performance Analysis of the interval algorithm for Random Number Generation in the Case of Markov Coin Tossing

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2020年第12期E103A卷 1325-1336页

作者： Oohama, Yasutada Univ Electrocommun Chofu Tokyo 1828585 Japan

In this paper we analyze the interval algorithm for random number generation proposed by Han and Hoshi in the case of Markov coin tossing. Using the expression of real numbers on the interval [0,1), we first establish an explicit representation of the interval algorithm with the representation of real numbers on the interval [0,1) based one number systems. Next, using the expression of the interval algorithm, we give a rigorous analysis of the interval algorithm. We discuss the difference between the expected number of the coin tosses in the interval algorithm and their upper bound derived by Han and Hoshi and show that it can be characterized explicitly with the established expression of the interval algorithm.

关键词： random number generation interval algorithm Markov coin tossing number systems performance analysis

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An interval algorithm for sensitivity analysis of coupled vibro-acoustic systems

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APPLIED MATHEMATICAL MODELLING 2017年 50卷 394-413页

作者： Li, Yunlong Wang, Xiaojun Zhang, Haohui Chen, Xianjia Xu, Menghui Wang, Chong Beihang Univ Inst Solid Mech Beijing 100191 Peoples R China Univ Illinois Dept Mech Sci & Engn Urbana IL 61801 USA Ningbo Univ Fac Mech Engn & Mech Ningbo 315211 Zhejiang Peoples R China Tech Univ Carolo Wilhelmina Braunschweig Inst Sci Comp D-38106 Braunschweig Germany

Sensitivity analysis is a vital part in the optimization design of coupled vibro-acoustic systems. A new interval sensitivity-analysis method for vibro-acoustic systems is proposed in this paper. This method relies on only interval perturbation analysis instead of partial derivatives and difference operations. For strongly nonlinear systems, in particular, this methodology requires parameter variation over narrower ranges in comparison with other methods. To implement sensitivity analysis based on this method, the interval ranges of the responses of the vibro-acoustic system with interval parameters should first be obtained. Therefore, an interval perturbation-analysis method is presented for obtaining the interval bounds of the sound-pressure responses of a coupled vibro-acoustic system with interval parameters. The interval perturbation method is then compared with the Monte Carlo method, which can be taken as the benchmark for comparative accuracy. Two numerical examples involving sensitivity analysis of vibro-acoustic systems illustrate the feasibility and effectiveness of the proposed interval-based method. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Sensitivity analysis interval perturbation method Vibro-acoustic system interval algorithm Design optimization

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Channel simulation by interval algorithm: A performance analysis of interval algorithm

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IEEE TRANSACTIONS ON INFORMATION THEORY 1999年第6期45卷 2121-2129页

作者： Uyematsu, T Kanaya, F Tokyo Inst Technol Dept Elect & Elect Engn Meguro Ku Tokyo 1528552 Japan Shonan Inst Technol Dept Informat Sci Fujisawa Kanagawa 2510046 Japan

This correspondence deals with the problem of simulating a discrete memoryless channel and proposes two algorithms for channel simulation by using the interval algorithm. The first algorithm provides exact channel simulation and the number of fair random bits per input sample approaches the conditional resolvability of the channel with probability one. The second algorithm provides approximate channel simulation and the approximation error measured bg the variational distance vanishes exponentially as the block length tends to infinity, when the number of fair random bits per input sample is above the conditional resolvability. Further, some asymptotic properties of these algorithms as well as the original interval algorithm for random number generation are clarified.

关键词： channel simulation conditional entropy conditional resolvability interval algorithm random number generation

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Generating stochastic processes based on the finitary interval algorithm

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2008年第9期E91A卷 2482-2488页

作者： Fujisaki, Hiroshi Kanazawa Univ Grad Sch Nat Sci & Technol Kanazawa Ishikawa 9201192 Japan

We point out that the interval algorithm can be expressed in the form of a shift on the sequence space. Then we clarify that, by using a Bernoulli process, the interval algorithm can generate only a block of Markov chains or a sequence of independent blocks of Markov chains but not a stationary Markov process. By virtue of the finitary coding constructed by Hamachi and Keane, we obtain the procedure, called the finitary interval algorithm, to generate a Markov process by using the interval algorithm. The finitary interval algorithm also gives maps, defined almost everywhere, which transform a Markov measure to a Bernoulli measure.

关键词： random number generation interval algorithm induced transformation Bernoulli shift Markov process finitary coding

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