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A simplex algorithm for network flow problems with piecewise linear fractional objective function

OPSEARCH 2009年第4期46卷 359-389页

作者： Pandey, Pooja Punnen, Abraham P. Univ New Brunswick Dept Math Sci St John NB E2L 4L5 Canada Simon Fraser Univ Dept Math Surrey BC V3T 0A3 Canada

The simplex algorithm for network flow problems has been proposed for linear, piecewise linear, and linear fractional objective functions. Piecewise linear fractional network flow problems can be transformed into equivalent linear or linear fractional programs, but the resulting problems do not possess pure network flow structure and increase the number of variables significantly. We develop a simplex algorithm to solve network flow problems with piecewise linear fractional objective function, unifying and generalizing the network simplex algorithm, network simplex algorithm for piece-wise linear programs, and network simplex algorithm for linear fractional programs. Computational results using the proposed algorithm are also discussed.

关键词： Fractional programming Piecewise linear fractional programming simplex algorithm Network flows

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A Novel Interpolation Method Based on Differential Evolution-simplex algorithm Optimized Parameters for Support Vector Regression

A Novel Interpolation Method Based on Differential Evolution...

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5th International Symposium on Intelligence Computation and Applications

作者： Zhang, Dongmei Liu, Wei Xu, Xue Deng, Qiao China Univ Geosci Dept Comp Sci Wuhan 430074 Peoples R China

ISBN: (纸本)9783642164927

Support Vector Machine (SVM) is a machine learning method based on Structual Risk Minimization (SRM). In traditional SVM, different selections of hyper-parameters have a significant effect on the forecast performance. Differential evolution algorithm (DE) is a rapid evolutionary algorithm based on the real-code, which can avoid the local optimization by the differential mutation operation between individuals. simplex searching algorithm is a direct searching algorithm which solves nonconstraint nonlinear programming problems. This paper introduces the application of SVM in the spatial interpolation in geosciences field. It proposes a new method of optimizing parameters of SVM based on DE algorithm and simplex algorithm. Firstly, DE algorithm is used to obtain the initial value of simplex algorithm, then the simplex local searching strategy is applied to optimize SVR parameters for the second time. Moreover, the spatial interpolation simulation is conducted on the standard dataset of SIC2004. The case study illustrates that the proposed algorithm has higher forecast accuracy and proves the validity of the method.

关键词： spatial interpolation Support Vector Machine parameter optimization differential evolution algorithm (DE) simplex algorithm

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Soft-sensing of Oxygen-content in Flue Gases of Power Plant Based on LS-SVM and simplex algorithm

Soft-sensing of Oxygen-content in Flue Gases of Power Plant ...

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World Congress on Software Engineering

作者： Liu, Changliang Li, Shuna N China Elect Power Univ Sch Control Theory & Control Engn Baoding Hebei Province Peoples R China

ISBN: (纸本)9780769535708

Oxygen-content in flue gases is an important factor for the economical burning in the power plant Because of influence from many different factors, it has some difficulties in testing of oxygen-content in flue gases In this paper the author chooses indirect variables and then the soft sensor model based on least square support vector machine for oxygen-content in flue gases of power plant is put forward. simplex algorithm is applied on searching for the two necessary parameters of LS-SVM, and practical data is handed together to test the model Simulation result shows that the method has more evident advantages than both the traditional oxygen-content instrument and the Radial Basis Function-based soft sensor In this paper, we take RBF as the acronym of Radial Basis Function It also has a better capability index and of important significance for economical burning in the power plant.

关键词： Least squares support vector machines (LS-SVM) simplex algorithm oxygen-content in flue gases soft-sensing

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GA-simplex algorithm and its application: a case study of gas emission estimation

GA-simplex algorithm and its application: a case study of ga...

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IEEE International Conference on Service Operations and Logistics, and Informatics (SOLI)

作者： Li, Hui Lin, Qingqi Lv, Hongqiang Zhang, Jianwen Beijing Univ Chem Technol Informat Sci & Technol Coll Beijing Peoples R China Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing Peoples R China Beijing Univ Chem Technol Fluid Mech & Heat Transfer Lab Beijing Peoples R China

ISBN: (纸本)9781509029273

Among the mathematical optimization algorithms, simplex algorithm is a popular and practical algorithm which was listed as one of the top 10 algorithms of the twentieth century by the journal Computing in Science and Engineering. Although simplex algorithm is efficient in the linear programming, the quality of convergence is unacceptable in practice as a numerical breakdown of the algorithm, even for smooth and well-behaved functions. On the other hand, full convergence might be seen in genetic algorithms (GA) using only crossover. So in this paper we combine the GA and simplex algorithm by initializing simplex from the final individual in GA and getting the converged result through simplex algorithm thereafter. A case study in estimating gas emission shows noteworthy improvement of efficiency and stability, compared with GA or simplex algorithm.

关键词： Multidimensional optimization genetic algorithm simplex algorithm Nelder-Mead algorithm Linear programming

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An Improved Version of the Random-Facet Pivoting Rule for the simplex algorithm 15

An Improved Version of the Random-Facet Pivoting Rule for th...

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47th Annual ACM Symposium on Theory of Computing (STOC) held as part of the Federated Computing Research Conference

作者： Hansen, Thomas Dueholm Zwick, Uri Aarhus Univ Aarhus Denmark Tel Aviv Univ Tel Aviv Israel

ISBN: (纸本)9781450335362

The RANDOM-FACET pivoting rule of Kalai and of Matotgek, Sharir and Welzl is an elegant randomized pivoting rule for the simplex algorithm, the classical combinatorial algorithm for solving linear programs (LPs). The expected number of pivoting steps performed by the simplex algorithm when using this rule, on any linear program involving n inequalities in d variables, is 2 Y(n-d) log (d/ Vn d)) where log n = max{1, log n}. A dual version of the algorithm performs an (1)(\ d log ((n d)/-\/R)) dual expected number of at most 2 pivoting steps. This dual version is currently the fastest known combinatorial algorithm for solving general linear programs. Kalai also obtained a primal pivoting rule which performs an expected number of at most 2c)(-\/.3 log n) pivoting steps. We present an improved version of Kalai's pivoting rule for which the expected number of primal pivoting steps is at most min {2 Oy(n d) log (d/(n d))) 20(Vd log ((n d)/d))}. This seemingly modest improvement is interesting for at least two reasons. First, the improved bound for the number of primal pivoting steps is better than the previous bounds for both the primal and dual pivoting steps. There is no longer any need to consider a dual version of the algorithm. Second, in the important case in which n = 0(d), i.e., the number of linear inequalities is linear in the number of variables, the expected running time becomes 20(A/3) rather than 20Wd log d) Our results, which extend previous results of Gartner, apply not only to LP problems, but also to LP-type problems, supplying in particular slightly improved algorithms for solving 2-player turn-based stochastic games and related problems.

关键词： Linear programming simplex algorithm randomized pivoting rules

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A counterexample to a 'simplex algorithm' for convex bodies

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Geometriae Dedicata 1981年第4期11卷 475-488页

作者： Gallivan, S. Gardner, R.J. Department of Mathematics University College London WC1E 6BT Gower Street United Kingdom Department of Mathematical Sciences University of Petroleum and Minerals Dhahran Saudi Arabia

A counterexample, in E3, is given to the following conjecture. Suppose f* is a linear functional, and e an exposed point of a convex body K such that f* does not attain its maximum on K at e;then there is an f*-strict... 详细信息

A counterexample, in E³, is given to the following conjecture. Suppose f^* is a linear functional, and e an exposed point of a convex body K such that f^* does not attain its maximum on K at e;then there is an f^*-strictly increasing path in the one-skeleton of K emanating from e. The counterexample shows that a certain generalized 'simplex algorithm' fails. Furthermore for a different linear functional f, there are no three disjoint f-strictly increasing paths in the one-skeleton of K leading to e. © 1981 D. Reidel Publishing Co.

关键词： Convex Body simplex algorithm Exposed Point

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Subexponential Lower Bounds for Randomized Pivoting Rules for the simplex algorithm 11

Subexponential Lower Bounds for Randomized Pivoting Rules fo...

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43rd ACM Symposium on Theory of Computing

作者： Friedmann, Oliver Hansen, Thomas Dueholm Zwick, Uri Univ Munich D-80539 Munich Germany

ISBN: (纸本)9781450306911

The simplex algorithm is among the most widely used algorithms for solving linear programs in practice. With essentially all deterministic pivoting rules it is known, however, to require an exponential number of steps to solve some linear programs. No non-polynomial lower bounds were known, prior to this work, for randomized pivoting rules. We provide the first subexponential (i.e., of the form 2(Omega(n alpha)), for some alpha > 0) lower bounds for the two most natural, and most studied, randomized pivoting rules suggested to date. The first randomized pivoting rule considered is RANDOM-EDGE, which among all improving pivoting steps (or edges) from the current basic feasible solution (or vertex) chooses one uniformly at random. The second randomized pivoting rule considered is RANDOM-FACET, a more complicated randomized pivoting rule suggested by Kalai and by Matousek, Sharir and Welzl. Our lower bound for the RANDOM-FACET pivoting rule essentially matches the subexponential upper bounds given by Kalai and by Matousek et al. Lower bounds for RANDOM-EDGE and RANDOM-FACET were known before only in abstract settings, and not for concrete linear programs. Our lower bounds are obtained by utilizing connections between pivoting steps performed by simplex-based algorithms and improving switches performed by policy iteration algorithms for solving Markov Decision Processes (MDPs).

关键词： Linear programming simplex algorithm randomized pivoting rules Markov Decision Processes

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GILP: An Interactive Tool for Visualizing the simplex algorithm 2023

GILP: An Interactive Tool for Visualizing the Simplex Algori...

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54th Annual ACM SIGCSE Technical Symposium on Computer Science Education (SIGCSE TS)

作者： Robbins, Henry W. Gutekunst, Samuel C. Shmoys, David B. Williamson, David P. Cornell Univ Ithaca NY 14850 USA Bucknell Univ Lewisburg PA 17837 USA

ISBN: (纸本)9781450394314

The simplex algorithm for solving linear programs-one of Computing in Science & Engineering's top 10 most influential algorithms of the 20th century-is an important topic in many algorithms courses. While the algorithm relies on intuitive geometric ideas, the computationally-involved mechanics of the algorithm can obfuscate a geometric understanding. In this paper, we present gilp, an easy-to-use simplex algorithm visualization tool designed to connect the mechanical steps of the algorithm with their geometric interpretation. We provide an extensive library of example visualizations, and our tool allows instructors to quickly produce custom interactive HTML files for students to experiment with the algorithm (without requiring students to install anything!). The tool can also be used for interactive assignments in Jupyter notebooks, and has been incorporated into a forthcoming Data Science and Decision Making interactive textbook. In this paper, we first describe how the tool fits into the existing algorithm visualization literature: how it was designed to facilitate student engagement and instructor adoption, and how it substantially extends existing algorithm visualization tools for simplex. We then describe the development and usage of the tool, and report feedback from its use in a course with roughly 100 students. Student feedback was overwhelmingly positive, with students finding the tool easy to use: it effectively helped them link the algebraic and geometrical views of the simplex algorithm and understand its nuances. Finally, gilp is open-source, includes an extension to visualizing linear programming-based branch and bound, and is readily amenable to further extensions.

关键词： simplex algorithm algorithm Visualization Branch and Bound Interactive algorithm Experimentation Understanding Optimization algorithms Linking Geometric and Algebraic Viewpoints

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Fresh views on some recent developments in the simplex algorithm

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Journal of Southeast University(English Edition) 2008年第1期24卷 124-126页

作者：胡剑峰潘平奇东南大学数学系南京210096

First, the main procedures and the distinctive features of the most-obtuse-angle（MOA）row or column pivot rules are introduced for achieving primal or dual feasibility in linear programming. Then, two special auxiliary problems are constructed to prove that each of the rules can be actually considered as a simplex approach for solving the corresponding auxiliary problem. In addition, the nested pricing rule is also reviewed and its geometric interpretation is offered based on the heuristic characterization of an optimal solution.

关键词： linear programming simplex algorithm pivot mostobtuse-angle nested pricing large-scale problem

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Experimental optimization during epoxidation of a high-oleic palm oil using a simplex algorithm

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INDUSTRIAL CROPS AND PRODUCTS 2022年第PartA期187卷

作者： Bohorquez, Wilson F. Orjuela, Alvaro Narvaez Rincon, Paulo Cesar Guillermo Cadavid, Juan Garcia-Nunez, Jesus A. Univ Nacl Colombia Dept Chem & Environm Engn Bogota 111321 DC Colombia Ctr Empresarial Pontevedra CENIPALMA Calle 98 70-91 Bogota 111121 DC Colombia

This work explored the epoxidation of high oleic palm oil (HOPO) extracted from recently developed palm tree hybrids. The process was carried out by reaction with 50 % wt.H2O2 using peracetic acid generated in-situ as oxygen carrier, and H2SO4 as catalyst. The study focused on the optimization of the operating conditions to maximize the productivity of oxirane groups in the epoxidized oil, considering the conversion of unsaturated groups and the selectivity to oxirane ring. The optimization was done by experimental application of a simplex algorithm varying reaction temperature (55-70 degrees C), catalyst loading (1-5 % wt.), mol ratio of H2O2 to HOPO unsaturations (1-10), acetic acid loading with respect to HOPO (2-10 % wt.), and reaction time (1-6 h). Optimal conditions were obtained after eight experimental steps, reaching a conversion of oil's unsaturations of nearly 90 %, with a selectivity towards oxirane groups of 88.6 %. The obtained oil had an oxygen oxirane content of 3.48 % wt., which corresponded to similar to 80 % of theoretical yield. The optimal conditions were tested in a subsequent kinetic experiment, and the results were reproduced obtaining an epoxy number of 3.5 and a yield of 79.7 %. This methodology can also be used to assess novel epoxidation catalysts.

关键词： Epoxidation High oleic palm oil Optimization simplex algorithm Peracetic acid Prileschajew reaction

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