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International Conference on Machine Learning and Cybernetics

作者： Zheng, H Zheng, ZB Xiang, Y Wuhan Univ Sch Elect Informat Wuhan 430079 Hubei Peoples R China

ISBN: (纸本)0780378652

This paper presents a novel ant system based optimisation method which integrates genetic algorithms and simplex algorithms. This method is able to not only speed up the search process for solutions, but also improve the quality of the solutions. In this paper, the proposed method is applied to set up a learning model for the "Tuned" mask, which is used to texture classification. Experimental results on aerial images and comparisons with genetic algorithms and genetic simplex algorithms are presented to illustrate the merit and feasibility of the proposed method.

关键词： ant colony system genetic algorithms simplex algorithms texture classification

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Pivot versus interior point methods:: Pros and cons

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2002年第2期140卷 170-190页

作者： Illés, T Terlaky, T McMaster Univ Dept Comp & Software Hamilton ON L8S 4L7 Canada Eotvos Lorand Univ Dept Operat Res Budapest Hungary

Linear optimization (LO) is the fundamental problem of mathematical optimization. It admits an enormous number of applications in economics, engineering, science and many other fields. The three most significant classes of algorithms for solving LO problems are: pivot, ellipsoid and interior point methods. Because ellipsoid methods are not efficient in practice we will concentrate on the computationally successful simplex and primal-dual interior point methods only. and summarize the pros and cons of these algorithm classes. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： linear programming linear optimization pivot methods simplex algorithms interior point methods complexity sensitivity analysis

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Pivot versus interior point methods:: Pros and cons

Pivot versus interior point methods:: Pros and cons

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EURO 2000 Conference

作者： Illés, T Terlaky, T McMaster Univ Dept Comp & Software Hamilton ON L8S 4L7 Canada Eotvos Lorand Univ Dept Operat Res Budapest Hungary

关键词： linear programming linear optimization pivot methods simplex algorithms interior point methods complexity sensitivity analysis

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simplex optimization of protein crystallization conditions

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JOURNAL OF CRYSTAL GROWTH 1999年第2-4期196卷 674-684页

作者： Prater, BD Tuller, SC Wilson, LJ E Tennessee State Univ Dept Chem Johnson City TN 37614 USA

simplex algorithms have been used to optimize for size, number and morphology of lysozyme and apoferritin crystals. This approach requires fewer experiments than the single-factor-at-a-time method or factorial designs and will be useful in conserving materials on the International Space Station. The simplex method has the possible advantage that it conserves on materials by reducing the number of experiments required to optimize a crystallization system. The process is iterative and exploratory and should allow optimum microgravity conditions to be determined which might very well be different from the optimum conditions on Earth. Because the simplex method uses simple mathematical operations to calculate the next set of crystallization conditions it will be easier for crystal growers to implement than factorial designs. Factorial experiments are based on varying all factors simultaneously at a limited number of factor levels. This results in a model that is used to determine the influence of each factor and their interactions. Factorial design experiments are especially useful at the beginning of an experimental study and as a screening tool to investigate a large number of factors. The simplex method is an optimization method which is model-independent and requires no fitting of models to data. Also, when applied to protein crystal growth the simplex method does not rely on an absolute quality score. Instead, with each iteration a comparison is made to the last experiment and the results are assigned as being "better or worse". In this study, commercially obtained apoferritin was purified from 65% monomeric apoferritin to 92% monomeric apoferritin by size exclusion chromatography. simplex optimization found the best apoferritin crystals were obtained at 15 mg/ml apoferritin, 2.0% CdSO4, 25 degrees C using the hanging drop vapor diffusion method of crystallization and at 24 mg/ml apoferritin, 1.5% CdSO4, 25 degrees C using the containerless crystallization method.

关键词： protein crystal growth lysozyme ferritin simplex algorithms factorial designs chemometrics

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A simplex ALGORITHM WHOSE AVERAGE NUMBER OF STEPS IS BOUNDED BETWEEN 2 QUADRATIC-FUNCTIONS OF THE SMALLER DIMENSION

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JOURNAL OF THE ACM 1985年第4期32卷 871-895页

作者： ADLER, I MEGIDDO, N TEL AVIV UNIV IL-69978 TEL AVIV ISRAEL IBM ALMADEN RES CTR SAN JOSE CA 95120 USA

It has been a challenge for mathematicians to confirm theoretically the extremely good performance of simplex-type algorithms for linear programming. In this paper the average number of steps performed by a simplex algorithm, the so-called self-dual method, is analyzed. The algorithm is not started at the traditional point (1, … , l)T, but points of the form (1, ϵ, ϵ2, …)T, with ϵ sufficiently small, are used. The result is better, in two respects, than those of the previous analyses. First, it is shown that the expected number of steps is bounded between two quadratic functions c1(min(m, n))2 and c2(min(m, n))2 of the smaller dimension of the problem. This should be compared with the previous two major results in the field. Borgwardt proves an upper bound of O(n4m1/(n-1)) under a model that implies that the zero vector satisfies all the constraints, and also the algorithm under his consideration solves only problems from that particular subclass. Smale analyzes the self-dual algorithm starting at (1, … , 1)T. He shows that for any fixed m there is a constant c(m) such the expected number of steps is less than c(m)(ln n)m(m+1); Megiddo has shown that, under Smale's model, an upper bound C(m) exists. Thus, for the first time, a polynomial upper bound with no restrictions (except for nondegeneracy) on the problem is proved, and, for the first time, a nontrivial lower bound of precisely the same order of magnitude is established. Both Borgwardt and Smale require the input vectors to be drawn from spherically symmetric distributions. In the model in this paper, invariance is required only under certain

关键词： Lexicographic pivoting probabilistic analysis of algorithms simplex algorithms

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