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Calculating the exact bounds of optimal values in LP with interval coefficients

ANNALS OF OPERATIONS RESEARCH 1998年第0期81卷 51-62页

作者： Mraz, F Univ S Bohemia Dept Math Ceske Budejovice 37115 Czech Republic

The paper deals with computing the exact upper and lower bounds of optimal values for linear programming problems whose coefficients vary in given intervals. The theoretical background for calculating these bounds is described and corresponding algorithms are given. A comparison with other approaches, some applications and a software package are mentioned.

关键词： linear programming problem inexact data interval coefficients

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Global and polynomial-time convergence of an infeasible-interior-point algorithm using inexact computation

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MATHEMATICAL programming 1999年第1期84卷 105-122页

作者： Mizuno, S Jarre, F Inst Stat Math Minato Ku Tokyo 106 Japan Univ Wurzburg Inst Angew Math & Stat D-97074 Wurzburg Germany

In this paper, we propose an infeasible-interior-point algorithm for solving a primal-dual linear programming problem. The algorithm uses inexact computations for solving a linear system of equations at each iteration. Under a very mild assumption on the inexactness we show that the algorithm finds an approximate solution of the linear program whenever the primal-dual linear programming problem is feasible. The assumption on the inexact computation is satisfied ii the approximation to the solution of the linear system is just a little bit "better" than the trivial approximation 0.

关键词： linear programming problem interior-point method primal-dual convergence inexact computation

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Selecting additional tag SNPs for tolerating missing data in genotyping

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BMC BIOINFORMATICS 2005年第1期6卷 1-16页

作者： Huang, YT Zhang, K Chen, T Chao, KM Natl Taiwan Univ Dept Comp Sci & Informat Engn Taipei 10764 Taiwan Natl Taiwan Univ Grad Inst Networking & Multimedia Taipei 10764 Taiwan Univ Alabama Birmingham Dept Biostat Sect Stat Genet Birmingham AL 35294 USA Univ So Calif Dept Biol Sci Los Angeles CA 90089 USA

Background: Recent studies have shown that the patterns of linkage disequilibrium observed in human populations have a block-like structure, and a small subset of SNPs ( called tag SNPs) is sufficient to distinguish each pair of haplotype patterns in the block. In reality, some tag SNPs may be missing, and we may fail to distinguish two distinct haplotypes due to the ambiguity caused by missing data. Results: We show there exists a subset of SNPs ( referred to as robust tag SNPs) which can still distinguish all distinct haplotypes even when some SNPs are missing. The problem of finding minimum robust tag SNPs is shown to be NP-hard. To find robust tag SNPs efficiently, we propose two greedy algorithms and one linear programming relaxation algorithm. The experimental results indicate that ( 1) the solutions found by these algorithms are quite close to the optimal solution;( 2) the genotyping cost saved by using tag SNPs can be as high as 80%;and ( 3) genotyping additional tag SNPs for tolerating missing data is still cost-effective. Conclusion: Genotyping robust tag SNPs is more practical than just genotyping the minimum tag SNPs if we can not avoid the occurrence of missing data. Our theoretical analysis and experimental results show that the performance of our algorithms is not only efficient but the solution found is also close to the optimal solution.

关键词： Greedy Algorithm linear programming problem Haplotype Block Integer Program problem Reasonable Period

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Difference Schemes in the Undetermined Coefficient Space and Dual problems of linear programming

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2018年第6期58卷 827-839页

作者： Lobanov, A. I. Moscow Inst Phys & Technol Dolgoprudnyi 141700 Moscow Oblast Russia

Using properties of the difference schemes approximating a one-dimensional transport equation as an example, it is shown that optimization of the properties of difference schemes based on the analysis in the space of undetermined coefficients and optimization of these properties based on the method of parametric correction are dual problems. Hybrid difference schemes for the linear transport equation are built as solutions to dual linear programming problems. It is shown that Godunov's theorem follows from the linear program optimality criterion as one of the complementary slackness conditions. A family of hybrid difference schemes is considered. It is shown that Fedorenko's hybrid difference scheme is obtained by solving the dual linear programming problem.

关键词： linear transport equation difference scheme Fedorenko's hybrid scheme linear programming problem complementary slackness conditions monotonic schemes Lagrange multipliers Godunov's theorem

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A simple procedure to weight empirical potentials in a fitness function so as to optimize its performance in ab initio protein-folding problem

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BIOPHYSICAL CHEMISTRY 2003年第1期105卷 105-118页

作者： Agostini, L Morosetti, S Univ Roma La Sapienza Dept Chem I-00185 Rome Italy

In an approach to the protein folding problem by a Genetic Algorithm, the fitness function plays a critical role. Empirical potentials are generally used to build the fitness function, and they must be weighted to obtain a valuable one. The weights are generally found by the comparison with a set of misfolded structures (decoys), but a dependence of the obtained fitness generally arises on the used decoys. Here we describe a general procedure to find out, from a given set of potentials, their better linear combination that could either identify the wild structure or prove their powerlessness. We use topological considerations over the hyperspace of the potentials, and a multiple linear inequalities solver. The iterated method flows through the following steps: it determines a direction in the hyperspace of the potentials, which identifies the native structure as a vertex among a set of misfolded decoys. A multiple linear inequalities solver obtains the direction. A Genetic Algorithm, tailored to the specific problem, uses the fitness function defined by this direction and generally reaches a new structure better than the experimental one, which is added to the ensemble. The decoys so generated are not dependent on a deterministic criterion. This iterative procedure can be stopped either by identifying an effective fitness function or by proving the impossibility of its achievement. In order to test the method under the hardest conditions, we choose numerous and heterogeneous quantities as components of the fitness function. This method could be a useful tool for the scientific community in order to test any fitness proposed and to recognize the most important components on which it is built. (C) 2003 Elsevier B.V. All rights reserved.

关键词： genetic algorithm linear programming problem dynamic generation of the decoys principal component analysis (PCA) Haar transform principle of minimal frustration

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Numerical optimization method for packing regular convex polygons

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2016年第8期56卷 1402-1413页

作者： Galiev, Sh. I. Lisafina, M. S. Kazan Natl Res Technol Univ Ul Karla Marksa 10 Kazan 420111 Tatarstan Russia

An algorithm is presented for the approximate solution of the problem of packing regular convex polygons in a given closed bounded domain G so as to maximize the total area of the packed figures. On G a grid is constructed whose nodes generate a finite set W on G, and the centers of the figures to be packed can be placed only at some points of W. The problem of packing these figures with centers in W is reduced to a 0-1 linear programming problem. A two-stage algorithm for solving the resulting problems is proposed. The algorithm finds packings of the indicated figures in an arbitrary closed bounded domain on the plane. Numerical results are presented that demonstrate the effectiveness of the method.

关键词： packing problem polygon packing packing of polygons in a given domain packing of regular convex polygons linear programming problem numerical algorithm

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Lexicographic Multiobjective Integer programming for Optimal and Structurally Minimal Petri Net Supervisors of Automated Manufacturing Systems

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2015年第11期45卷 1459-1470页

作者： Huang, Bo Zhou, MengChu Zhang, GongXuan Ammari, Ahmed Chiheb Alabdulwahab, Ahmed Fayoumi, Ayman G. Nanjing Univ Sci & Technol Sch Comp Sci & Engn Nanjing 210094 Jiangsu Peoples R China New Jersey Inst Technol Dept Elect & Comp Engn Newark NJ 07102 USA King Abdulaziz Univ Renewable Energy Res Grp Jeddah 21589 Saudi Arabia King Abdulaziz Univ Renewable Energy Res Grp Dept Elect & Comp Engn Jeddah 21589 Saudi Arabia Carthage Univ INSAT Inst MMA Lab Tunis 1080 Tunisia King Abdulaziz Univ Dept Informat Syst Jeddah 21589 Saudi Arabia

Based on Petri net (PN) models of automated manufacturing systems, this paper proposes a deadlock prevention method to obtain a maximally permissive (optimal) supervisor while minimizing its structure. The optimal supervisor can be achieved by forbidding all first-met bad markings (FBMs) and permitting all legal markings in a PN model. An FBM obtained via a single transition's firing at a legal marking is a deadlock or marking that inevitably evolves into a deadlock. A lexicographic multiobjective integer programming problem with multiple objectives to be achieved sequentially is formulated to design such an optimal and structurally minimal supervisor. As a nonlinear function, the quantity of its directed arcs is minimized. A conversion method is proposed to convert the nonlinear model into a linear one. With the premise that each place in the supervisor is associated with a nonnegative place invariant, the controlled net holds all legal markings of the net model, and the supervisor has the minimal structure. Finally, some examples are used to illustrate the application of the proposed approach.

关键词： Automated manufacturing system (AMS) deadlock prevention discrete event system linear programming problem Petri net (PN)

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A new approach to fuzzy part-family formation in cellular manufacturing systems

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2001年第8期18卷 591-597页

作者： Ravichandran, KS Rao, KCS Shanmugha Coll Engn Dept Math Thanjavur 613402 Tamil Nadu India Alagappa Univ Dept Math Karaikkudi Tamil Nadu India

Group technology (GT) is one of the major issues in successful implementation of cellular manufacturing systems. The success of GT implementation depends only on an effective formation of part-families. The effective formation of part-families depends mainly on an effective formation of a similarity coefficient measure. Many similarity coefficients have been produced over the past three decades, but better similarity coefficient measures are required. The decision-making process in a manufacturing system often involves uncertainties and ambiguities. Under such circumstances, fuzzy methodologies have proved to be effective tools for taking fuzziness into consideration. In this paper, we use fuzzy cluster analysis to form part-families and assign parts to existing part-families. We have established a new approach to convert a fuzzy clustering matrix into a zero-one incidence matrix. We have also developed a new similarity coefficient measure and this coefficient measure is used to form a part-family. A mathematical model that uses this similarity coefficient for solving optimally, the part-family formation problems in cellular manufacturing is developed. Finally, it is compared with other models by giving an illustration with a numerical example.

关键词： cellular manufacturing conventional clustering fuzzy clustering fuzzy set theory group technology linear programming problem part-family similarity coefficient

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BOTTLENECK linear-programming

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MATHEMATICAL programming 1976年第3期11卷 291-298页

作者： GARFINKEL, RS RAO, M UNIV TENNESSEE KNOXVILLETN 37916 UNIV ROCHESTER ROCHESTERNY 14627

The Bottleneck linear programming problem (BLP) is to maximizex0 = max j c j ,x j > 0 subject toAx = b, x ⩾ 0. A relationship between the BLP and a problem solvable by a “greedy” algorithm is established. Two alg... 详细信息

关键词： Mathematical Method programming problem Computational Experience linear programming problem

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Automated synthesis of fixed structure QFT prefilter using piecewise linear approximation based linear programming optimization techniques

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IFAC-PapersOnLine 2016年第1期49卷 349-354页

作者： Nataraj, P.S.V. Makwana, Dipesh Systems and Control Engineering Group IIT Bombay India

Prefilter synthesis is one of the important design steps of Horowitz's quantitative feedback theory (QFT) to robust feedback system synthesis. The prefilter is designed to achieve tracking specifications. In this paper, a new, computationally efficient approach for automation of the prefilter design step is proposed. A linear programming based algorithm is proposed for the automatic synthesis of fixed structure QFT prefilter. In present work, prefilter synthesis problem is posed as a piecewise linear approximation based linear programming problem and solved with GUROBI optimizer *** proposed method is validated using a benchmark problem and a simple, low order prefilter is obtained in quick time. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Piecewise linear techniques Feedback linear programming Robust control Automatic synthesis Computationally efficient linear programming optimization linear programming problem Order sets Piecewise linear approximations Prefilter designs Quantitative feedback theory

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