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In this paper, we consider a Fuzzy Linear Fractional Programming (FLFP) problem under the condition that the objective function and the values of the right-hand side are represented by symmetric trapezoidal fuzzy numbers while the left-hand side constraints are represented by real numbers. Decision variables are characterized by trapezoidal fuzzy numbers and non-negative numbers. Utilizing the ranking function and computation of trapezoidal fuzzy numbers, the FLFP problem is transformed into a Crisp Linear Fractional Programming (CLFP) problem. This paper outfits another idea for diminishing the computational complexity, in any case without losing its viability crisp LFP problem. A modified possibility programming problem, Swarup is utilized to solve this program. Lead from real-life problems, a couple of mathematical models is considered to survey the legitimacy, usefulness and applicability of our method. Finally, some mathematical analysis along with one case study is given to show the novel strategies are superior to the current techniques.

In this paper, we consider a Fuzzy Linear Fractional Programming (FLFP) problem under the condition that the objective function and the values of the right-hand side are represented by symmetric trapezoidal fuzzy numbers while the left-hand side constraints are represented by real numbers. Decision variables are characterized by trapezoidal fuzzy numbers and non-negative numbers. Utilizing the ranking function and computation of trapezoidal fuzzy numbers, the FLFP problem is transformed into a Crisp Linear Fractional Programming (CLFP) problem. This paper outfits another idea for diminishing the computational complexity, in any case without losing its viability crisp LFP problem. A modified possibility programming problem, Swarup is utilized to solve this program. Lead from real-life problems, a couple of mathematical models is considered to survey the legitimacy, usefulness and applicability of our method. Finally, some mathematical analysis along with one case study is given to show the novel strategies are superior to the current techniques.

In this paper, we consider a Fuzzy Linear Fractional Programming (FLFP) problem under the condition that the objective function and the values of the right-hand side are represented by symmetric trapezoidal fuzzy numbers while the left-hand side constraints are represented by real numbers. Decision variables are characterized by trapezoidal fuzzy numbers and non-negative numbers. Utilizing the ranking function and computation of trapezoidal fuzzy numbers, the FLFP problem is transformed into a Crisp Linear Fractional Programming (CLFP) problem. This paper outfits another idea for diminishing the computational complexity, in any case without losing its viability crisp LFP problem. A modified possibility programming problem, Swarup is utilized to solve this program. Lead from real-life problems, a couple of mathematical models is considered to survey the legitimacy, usefulness and applicability of our method. Finally, some mathematical analysis along with one case study is given to show the novel strategies are superior to the current techniques.

In this paper, we consider a Fuzzy Linear Fractional Programming (FLFP) problem under the condition that the objective function and the values of the right-hand side are represented by symmetric trapezoidal fuzzy numbers while the left-hand side constraints are represented by real numbers. Decision variables are characterized by trapezoidal fuzzy numbers and non-negative numbers. Utilizing the ranking function and computation of trapezoidal fuzzy numbers, the FLFP problem is transformed into a Crisp Linear Fractional Programming (CLFP) problem. This paper outfits another idea for diminishing the computational complexity, in any case without losing its viability crisp LFP problem. A modified possibility programming problem, Swarup is utilized to solve this program. Lead from real-life problems, a couple of mathematical models is considered to survey the legitimacy, usefulness and applicability of our method. Finally, some mathematical analysis along with one case study is given to show the novel strategies are superior to the current techniques.

This article is from BMC Systems Biology , volume 6 . Abstract Background: Acupuncture has been practiced in China for thousands of years as part of the Traditional Chinese Medicine (TCM) and has gradually accepted in western countries as an alternative or complementary treatment. However, the underlying mechanism of acupuncture, especially whether there exists any difference between varies acupoints, remains largely unknown, which hinders its widespread use. Results: In this study, we develop a novel Linear Programming based Feature Selection method (LPFS) to understand the mechanism of acupuncture effect, at molecular level, by revealing the metabolite biomarkers for acupuncture treatment. Specifically, we generate and investigate the high-throughput metabolic profiles of acupuncture treatment at several acupoints in human. To select the subsets of metabolites that best characterize the acupuncture effect for each meridian point, an optimization model is proposed to identify biomarkers from high-dimensional metabolic data from case and control samples. Importantly, we use nearest centroid as the prototype to simultaneously minimize the number of selected features and the leave-one-out cross validation error of classifier. We compared the performance of LPFS to several state-of-the-art methods, such as SVM recursive feature elimination (SVM-RFE) and sparse multinomial logistic regression approach (SMLR). We find that our LPFS method tends to reveal a small set of metabolites with small standard deviation and large shifts, which exactly serves our requirement for good biomarker. Biologically, several metabolite biomarkers for acupuncture treatment are revealed and serve as the candidates for further mechanism investigation. Also biomakers derived from five meridian points, Zusanli (ST36), Liangmen (ST21), Juliao (ST3), Yanglingquan (GB34), and Weizhong (BL40), are compared for their similarity and difference, which provide evidence for the specificity of acupoints. Conclusions: Our result demonstrates that metabolic profiling might be a promising method to investigate the molecular mechanism of acupuncture. Comparing with other existing methods, LPFS shows better performance to select a small set of key molecules. In addition, LPFS is a general methodology and can be applied to other high-dimensional data analysis, for example cancer genomics.

This article is from BMC Systems Biology , volume 6 . Abstract Background: Acupuncture has been practiced in China for thousands of years as part of the Traditional Chinese Medicine (TCM) and has gradually accepted in western countries as an alternative or complementary treatment. However, the underlying mechanism of acupuncture, especially whether there exists any difference between varies acupoints, remains largely unknown, which hinders its widespread use. Results: In this study, we develop a novel Linear Programming based Feature Selection method (LPFS) to understand the mechanism of acupuncture effect, at molecular level, by revealing the metabolite biomarkers for acupuncture treatment. Specifically, we generate and investigate the high-throughput metabolic profiles of acupuncture treatment at several acupoints in human. To select the subsets of metabolites that best characterize the acupuncture effect for each meridian point, an optimization model is proposed to identify biomarkers from high-dimensional metabolic data from case and control samples. Importantly, we use nearest centroid as the prototype to simultaneously minimize the number of selected features and the leave-one-out cross validation error of classifier. We compared the performance of LPFS to several state-of-the-art methods, such as SVM recursive feature elimination (SVM-RFE) and sparse multinomial logistic regression approach (SMLR). We find that our LPFS method tends to reveal a small set of metabolites with small standard deviation and large shifts, which exactly serves our requirement for good biomarker. Biologically, several metabolite biomarkers for acupuncture treatment are revealed and serve as the candidates for further mechanism investigation. Also biomakers derived from five meridian points, Zusanli (ST36), Liangmen (ST21), Juliao (ST3), Yanglingquan (GB34), and Weizhong (BL40), are compared for their similarity and difference, which provide evidence for the specificity of acupoints. Conclusions: Our result demonstrates that metabolic profiling might be a promising method to investigate the molecular mechanism of acupuncture. Comparing with other existing methods, LPFS shows better performance to select a small set of key molecules. In addition, LPFS is a general methodology and can be applied to other high-dimensional data analysis, for example cancer genomics.

This volume was digitized and made accessible online due to deterioration of the original print copy.

This volume was digitized and made accessible online due to deterioration of the original print copy.

This volume was digitized and made accessible online due to deterioration of the original print copy.

This volume was digitized and made accessible online due to deterioration of the original print copy.

Igor Ferst https://www.pyohio.org/2019/presentations/86 How do airlines choose which planes service which routes? How does a hospital optimize the shift schedule for hundreds of doctors and nurses? How do you choose the optimal location for a group of fulfillment centers, or oil derricks, or cell towers? These kinds of problems (and many others!) can be solved with integer linear programming (ILP), a powerful and decades-old framework for solving optimization problems. In this talk we will give a brief introduction to ILP and describe it's uses, strengths, and weaknesses. We will also show how to solve a real-world vehicle routing problem using Google's open-source python library for ILP. Trigger warning: this talk will contain high-school level math. Integer linear programming (ILP) is a powerful framework for solving optimization problems related to scheduling, resource allocation, vehicle routing, and many other areas. This talk will give a brief introduction to ILP and show how to solve a real-world vehicle routing problem using Google's open-source python library for ILP. === https://pyohio.org A FREE annual conference for anyone interested in Python in and around Ohio, the entire Midwest, maybe even the whole world. Produced by NDV: https://youtube.com/channel/UCQ7dFBzZGlBvtU2hCecsBBg?sub_confirmation=1 Sun Jul 28 14:30:00 2019 at Hays Cape

The methodology of Johnson, Baner, Moore, and Grant can be applied to large scale linear programming models. A methodology for optimality analysis of linear programs was developed to create metamodels using response surface methodology techniques such as experimental design and least squares regression. A metamodel consists of a simple equation which is able to predict the optimal objective function value of a linear program. What is needed is some large scale application of the techniques to verify how accurate they are. In the research, I plan to use the large scale LP model, STORM. I use the "Hot Start" idea for the efficiency of STORM program calculation. The developed metamodels of the large scale LP can provide some useful information about the relationships between the objective function value and the right-hand-side vector and coefficients of the objective function (unit cost vector) by varying the right-hand-side vector and unit cost vector.

Learning and retention may be influenced by subtle instructional stimulus characteristics and certain visual memory aptitudes. Ten stimulus characteristics were chosen for study; 50 sequences of programed instructional material were specially written to conform to sampled values of each stimulus characteristic. Seventy-three freshman subjects received the 50 sequences and then took an immediate and a delayed (one-week) posttest to assess learning. Measures on four visual memory and cognition aptitude factors were available for 43 of the subjects. By means of tear-down regression algorithms, the 10 stimulus characteristics were used to predict to the learning criteria. The ratio of examples within a sequence to the number of frames in the sequence had a correlation of about -.70 with both the immediate and delayed posttest. The inclusion of other variables did not increase the prediction significantly. Together, total frames and number of responses per frame predicted item difficulty on the posttest (multiple R to the second power=.90). Of the aptitude variables, Vocabulary aptitude and Short Term Object Memory tended to increase prediction to the delayed posttest criterion, while Serial Integration aptitude and short Term Color Memory did not. (LS)

How much should a person with a given set of qualifications be paid so that his salary is consistent with other salaries in an organization. The purpose of this document is to explore the possible utilization of linear programming techniques for answering the above question in job-salary evaluation. Specifically, a linear programming model is used to analyze a hierarchical salary structure in a school district. The model is used to determine the relative importance of each of the compensable elements of each function (position) in a school district. In addition, monetary equivalents to these elements are derived from the model in order to develop a consistent scale of compensation within a school district. The proposed type of job-salary evaluation scheme might have wide application in the Air Force as well as civilian sector, since it could be of important use in determining discrepancies or in determining those positions in the Air Force which seem 'out of line' in terms of salary or grade classification. The development of utility objective functions, so factors of a job which are considered crucial, receive higher relative weights would tend to increase the flexibility of the salary schedule in responding to the changing needs and demands of the organization.

Certain new approaches to linear programming have recently received considerable publicity because of the promise of substantial improvements in efficiency compared to the simplex method. This note briefly discusses several research directions in methods for solving linear programs using nonlinear problem transformations. In particular, we describe application of a barrier transformation to the dual, and the development of sparse least-squares methods based on the LU factorization of the least-squares matrix of its transpose. (Author)

During this contract period DSA has concentrated on achieving a geometrical rather than an algebraic understanding of Karmarkar's algorithm, and on the formulation of alternative approaches that retain the main advantages of Karmarkar's approach while avoiding the undesireable computational aspects of his specific algorithm. From a geometric perspective, we have asked why does the algorithm work, when it works? How can one understand the convergence process, which occurs in the shifting coordinates of Karmarkar's simplex, in terms of an orderly convergence process in the original space? This has led to a number of non-obvious insights concerning the essence of the Karmarkar algorithm. The findings of this part of the study are contained in a separate report that has been distributed, and is being prepared for publication. Keywords: Optimization; non-linear programming; quadratic programming; numerical stability.

This report documents a FORTRAN routine LINOPT for solving linear programming problems. Upper and lower bounds on all variables are permitted, and the dual problem includes as a special case linearly-constrained minimum l1-norm problems. Basic theory, the algorithm used, input-output procedures and examples of use are included. (Author)

This research investigates a special class of stochastic linear programs known as two-stage stochastic linear programming with relatively complete and fixed recourse. These models characterize a two-phase process where the first- stage decision (itself subject to a separate set of first-stage linear constraints) allocates a set of resources to the second-stage linear program prior to the realization of random variables affecting second-stage resource availability. Since the second-stage decision deterministically follows both first-stage allocation and random variable realization, the first-stage variables constitute the only true decision. The expected cost of the two-stage recourse problem is also a piecewise convex function of the first-stage decision variables, thus allowing a global optimal solution that minimizes the total expected cost.

The main purpose of this work is to give explicit sparsity-preserving SOR(Successive Overrelaxation) algorithms for the solution of separable quadratic and linear programming problems. The principal and computationally distinguishing feature of the present SOR algorithms is that they preserve the sparsity structure of the problem and do not require the computation of the product of the constraint matrix by its transpose as is the case in earlier SOR algorithms for linear and quadratic programming. (Author)

The project explored the theoretical properties and computational performance of algorithms for solving constrained optimization problems (linear and nonlinear programs). Particular emphasis was placed on algorithms for solving large problems. The practical applications of optimization are innumerable. For example, mathematical models of the economy (to analyze the optimal use of natural resources) are typically large linear or nonlinear programs. Areas in which we have been actively involved include optimal generation and transmission of electricity, optimization of aircraft and spacecraft trajectories, optimal structural design, and financial modeling such as portfolio optimization. Progress on solution algorithms and software for such applications is ultimately reflected in improved techniques in many other areas of science and industry.

Electrical Engineering 127, 001 - Spring 2014 Creative Commons 3.0: Attribution-NonCommercial-NoDerivs

Electrical Engineering 127, 001 - Spring 2014 Creative Commons 3.0: Attribution-NonCommercial-NoDerivs

Electrical Engineering 127, 001 - Spring 2014 Creative Commons 3.0: Attribution-NonCommercial-NoDerivs

Electrical Engineering 127, 001 - Spring 2014 Creative Commons 3.0: Attribution-NonCommercial-NoDerivs

This volume was digitized and made accessible online due to deterioration of the original print copy.

This volume was digitized and made accessible online due to deterioration of the original print copy.

This volume was digitized and made accessible online due to deterioration of the original print copy.

This volume was digitized and made accessible online due to deterioration of the original print copy.

This volume was digitized and made accessible online due to deterioration of the original print copy.

From the bitsavers.org collection, a scanned-in computer-related document. ibm :: generalInfo :: E20-0127-0 Linear Programming - Aluminum Alloy Blending

From the bitsavers.org collection, a scanned-in computer-related document. ibm :: generalInfo :: E20-0127-0 Linear Programming - Aluminum Alloy Blending

From the bitsavers.org collection, a scanned-in computer-related document. ibm :: 1620 :: general program library :: 10.1.007 Linear Programming I

Bell System Technical Journal, 38: 6 November 1959 pp 1485-1512. Error-Correcting Codes--A Linear Programming Approach (McCluskey, E.J., Jr.)

Zlatar Ski Center has an extremely high potential as a ski resort that could be among the most visited ones in Serbia. What characterizes this center is the proximity of Kokin Brod Lake, the Tara River and the like. Therefore, Zlatar should be considered both as a ski center and in terms of other diversities. The aim of this paper is to analyze the possibility of expanding the capacity of ski resorts by increasing the possible flow of skiers on new ski lifts and ski slopes. The methods used in this paper belong to operational research, specifically, the geometric interpretation of linear programming. It is also shown how to optimize the extended capacities. If the capacities of ski slopes are to be increased, it would initiate greater investment in accommodation capacities in the area of the municipality of Nova Varoš, which would affect its improvement in terms of tourism.

To assess the degree of practical implementation of the optimization principle when comparing options for plans compiled in different ways, this paper proposes a comprehensive indicator of the effectiveness of planned calculations. The advantage of the indicator is that its value is proportional to the magnitude of potential losses from incomplete and incomplete use of available resources, that is, those factors that symbolize the loss of resources in the economic planning process, but have not yet served as criteria for the quality of planning decisions. Therefore, the fact that the optimization method makes it possible to improve (reduce) the value of these indicators with the same volumes of available production resources allows us to conclude that the structural optimization method is very effective and promising in solving production problems of linear programming and in the process of economic planning.

To assess the degree of practical implementation of the optimization principle when comparing options for plans compiled in different ways, this paper proposes a comprehensive indicator of the effectiveness of planned calculations. The advantage of the indicator is that its value is proportional to the magnitude of potential losses from incomplete and incomplete use of available resources, that is, those factors that symbolize the loss of resources in the economic planning process, but have not yet served as criteria for the quality of planning decisions. Therefore, the fact that the optimization method makes it possible to improve (reduce) the value of these indicators with the same volumes of available production resources allows us to conclude that the structural optimization method is very effective and promising in solving production problems of linear programming and in the process of economic planning.

The increase in the size of the problems facing humans, their overlap, the division of labor, the multiplicity of departments, as well as the diversity of products and commodities, led to the complexity of business and the emergence of many administrative and production problems. It was necessary to search for appropriate methods to confront these problems. The science of operations research, with its diverse methods, provided the optimal solutions. It addresses many problems and helps in making scientific and thoughtful decisions to carry out the work in the best way within the available capabilities. Operations research is one of the modern applied sciences that uses the scientific method as a basis and method in research and study, and its basic essence is to build a model that helps management in making decisions related to difficult administrative problems. For example, the military field, financial aspects, industry, in construction for building bridges and huge projects to evaluate the time taken for each project and reduce this time, financial markets and stocks and forecasting economic conditions, in hospital management and controlling the process of nutrition and medicines within the available capabilities, in agriculture Agricultural marketing and many other problems that have been addressed using classical operations research methods. We know that the agricultural sector is one of the important sectors in every country, and the agricultural production process is regulated by those responsible for securing the needs of citizens. Also, those responsible for the agricultural sector are responsible for rationalizing the agricultural process so that the surplus is saved. Due to the difficult circumstances that the country may be going through, in this research, we will reformulate the general model for the optimal distribution of agricultural lands using the concepts of neutrosophic science.

The increase in the size of the problems facing humans, their overlap, the division of labor, the multiplicity of departments, as well as the diversity of products and commodities, led to the complexity of business and the emergence of many administrative and production problems. It was necessary to search for appropriate methods to confront these problems. The science of operations research, with its diverse methods, provided the optimal solutions. It addresses many problems and helps in making scientific and thoughtful decisions to carry out the work in the best way within the available capabilities. Operations research is one of the modern applied sciences that uses the scientific method as a basis and method in research and study, and its basic essence is to build a model that helps management in making decisions related to difficult administrative problems. For example, the military field, financial aspects, industry, in construction for building bridges and huge projects to evaluate the time taken for each project and reduce this time, financial markets and stocks and forecasting economic conditions, in hospital management and controlling the process of nutrition and medicines within the available capabilities, in agriculture Agricultural marketing and many other problems that have been addressed using classical operations research methods. We know that the agricultural sector is one of the important sectors in every country, and the agricultural production process is regulated by those responsible for securing the needs of citizens. Also, those responsible for the agricultural sector are responsible for rationalizing the agricultural process so that the surplus is saved. Due to the difficult circumstances that the country may be going through, in this research, we will reformulate the general model for the optimal distribution of agricultural lands using the concepts of neutrosophic science.

Method and Validation for Optimal Lineup Creation for Daily Fantasy Football Using Machine Learning and Linear Programming

Linear and Semidefinite programs provide the best approximation algorithms for many NP-hard combinatorial optimization problems. This talk will introduce recent techniques to give unconditional lower bounds for algorithms based on Linear and Semidefinite programs (LPs and SDPs, respectively). In particular, I will define and give background about LP and SDP hierarchies, which include a large class of SDPs and LPs including the most famous SDP algorithms (which occur very low in the hierarchy). I will then sketch two lower bounds for these hierarchies. The first result shows that a large class of linear programs (generated by the Lovasz-Schrijver hierarchy) requires exponential time to approximate Vertex Cover to better than a factor of 2-epsilon. The second result shows that a large class of semidefinite programs (generated by the Lasserre hierarchy) requires exponential time to refute a random 3-XOR instance (even though such an instance is very far from satisfiable). As a corollary, the same class requires exponential time to approximate Vertex Cover to better than a factor of 7/6-epsilon. This result is the first construction of a Lasserre integrality gap, and simplifies, strengthens, and helps to explain several previous results.

Method and Validation for Optimal Lineup Creation for Daily Fantasy Football Using Machine Learning and Linear Programming

Method and Validation for Optimal Lineup Creation for Daily Fantasy Football Using Machine Learning and Linear Programming

xiv, 242 pages 25 cm

ix, 174 p. : 24 cm

ix, 174 p. : 24 cm

ix, 174 p. : 24 cm

ix, 174 p. : 24 cm

Current force planning methodology for determining the proper level, mix, and balance of U.S. Army Engineer Forces required to support theater level military operations is examined and a linear programming model is described for use in the planning process. The structure of the linear programming model and feasible ways to derive required parameter values are explained in detail. A test problem and results obtained using the linear programming model are presented to amplify the explanations and to provide a basis for further evaluation and analysis. Alternate model formulation for solving minimum force, minimum cost, or maximum productivity theater force objectives, and extensions for applications of the model in force development and analysis activities are described.

Current force planning methodology for determining the proper level, mix, and balance of U.S. Army Engineer Forces required to support theater level military operations is examined and a linear programming model is described for use in the planning process. The structure of the linear programming model and feasible ways to derive required parameter values are explained in detail. A test problem and results obtained using the linear programming model are presented to amplify the explanations and to provide a basis for further evaluation and analysis. Alternate model formulation for solving minimum force, minimum cost, or maximum productivity theater force objectives, and extensions for applications of the model in force development and analysis activities are described.

Theorem 21 and Corollary 22 are in error; The modeling needs 9-dimensional variables instead of the 8-dimensional variables defined in notations 6.9. Examples of the correct model (with 9-index variables) are: (1) Diaby, M., "Linear Programming Formulation of the Set Partitioning Problem," International Journal of Operational Research 8:4 (August 2010) pp. 399-427; (2) Diaby, M., "Linear Programming Formulation of the Vertex Coloring Problem," International Journal of Mathematics in Operational Research 2:3 (May 2010) pp. 259-289; (3) Diaby, M., "The Traveling Salesman Problem: A Linear Programming Formulation," WSEAS Transactions on Mathematics, 6:6 (June 2007) pp. 745-754.