Multiparametric linear programming involves the solution of linear programming problems with parametric uncertainty. The optimal exact decisions and cost values are defined, in each region, as affine functions of the ...
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We propose a vector linear programming formulation for a non-stationary, finite-horizon Markov decision process with vector-valued rewards. Pareto efficient policies are shown to correspond to efficient solutions of t...
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A new linear programming method with an option for topographical factors is developed for estimating missing precipitation. It is simply assumed that missing precipitation depth at a base station is expressed as a lin...
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A new linear programming method with an option for topographical factors is developed for estimating missing precipitation. It is simply assumed that missing precipitation depth at a base station is expressed as a linear combination of precipitation depths at neighboring index stations in the same period using weighting factors. Also, the topographical factor, which is proportional to the weighting factor, is introduced into the method. The topographical factor is associated with distance and difference in elevation between the base station and the index station. In this research two case studies show an introduction of the topographical factors into the existing linear programming method for estimating missing precipitation and makes weighting factors in the method change into those reflecting the topography of precipitation points. The developed method with an option is useful in estimating the missing precipitation values in the case of hilly regions only when the option is taken after applying four options. DOI: 10.1061/(ASCE)HE.1943-5584.0000602. (C) 2013 American Society of Civil Engineers.
We examine linear program (LP) approaches to boosting and demonstrate their efficient solution using LPBoost, a column generation based simplex method. We formulate the problem as if all possible weak hypotheses had a...
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We examine linear program (LP) approaches to boosting and demonstrate their efficient solution using LPBoost, a column generation based simplex method. We formulate the problem as if all possible weak hypotheses had already been generated. The labels produced by the weak hypotheses become the new feature space of the problem. The boosting task becomes to construct a learning function in the label space that minimizes misclassification error and maximizes the soft margin. We prove that for classification, minimizing the 1-norm soft margin error function directly optimizes a generalization error bound. The equivalent linear program can be efficiently solved using column generation techniques developed for large-scale optimization problems. The resulting LPBoost algorithm can be used to solve any LP boosting formulation by iteratively optimizing the dual misclassification costs in a restricted LP and dynamically generating weak hypotheses to make new LP columns. We provide algorithms for soft margin classification, confidence-rated, and regression boosting problems. Unlike gradient boosting algorithms, which may converge in the limit only, LPBoost converges in a finite number of iterations to a global solution satisfying mathematically well-defined optimality conditions. The optimal solutions of LPBoost are very sparse in contrast with gradient based methods. Computationally, LPBoost is competitive in quality and computational cost to AdaBoost.
We propose an adaptation of the Feasible Direction Interior Points Algorithm (FDIPA) of J. Herskovits, for solving large-scale linear programs. At each step, the solution of two linear systems with the same coefficien...
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We propose an adaptation of the Feasible Direction Interior Points Algorithm (FDIPA) of J. Herskovits, for solving large-scale linear programs. At each step, the solution of two linear systems with the same coefficient matrix is determined. This step involves a significant computational effort. Reducing the solution time of linear systems is, therefore, a way to improve the performance of the method. The linear systems to be solved are associated with definite positive symmetric matrices. Therefore, we use Split Preconditioned Conjugate Gradient (SPCG) method to solve them, together with an Incomplete Cholesky preconditioner using Matlab's ICHOL function. We also propose to use the first iteration of the conjugate gradient, and to presolve before applying the algorithm, in order to reduce the computational cost. Following, we then provide mathematica proof that show that the iterations approach Karush-Kuhn-Tucker points of the problem under reasonable assumptions. Finally, numerical evidence show that the method not only works in theory but is also competitive with more advanced methods.
While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds are not optimized to quantify the performance of quantum codes under the...
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While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds are not optimized to quantify the performance of quantum codes under the effect of arbitrary quantum channels that describe bespoke noise models. Herein, for any Kraus decomposition of any given quantum channel, we introduce corresponding quantum weight enumerators that naturally generalize the Shor-Laflamme quantum weight enumerators. We establish an indirect linear relationship between these generalized quantum weight enumerators by introducing an auxiliary exact weight enumerator that completely quantifies the quantum code's projector, and is independent of the underlying noise process. By additionally working within the framework of approximate quantum error correction, we establish a general framework for constructing a linear program that is infeasible whenever approximate quantum error correcting codes with corresponding parameters do not exist. Our linear programming framework allows us to establish the non-existence of certain quantum codes that approximately correct amplitude damping errors, and obtain non-trivial upper bounds on the maximum dimension of a broad family of permutation-invariant quantum codes.
This article aims to propose and implement an aggregated production planning model to provide optimal strategies in the medium term fora textile company, for which a linear programming model is proposed to minimise to...
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This article aims to propose and implement an aggregated production planning model to provide optimal strategies in the medium term fora textile company, for which a linear programming model is proposed to minimise total costs associated with labour and inventory levels. The model proposed takes into account characteristics associated with fabric contraction, wastes in the process, the efficiency of new employees, and training requirements. The model is implemented and solved in GAMS, supported on an AISExcel interface, to find the optimal solution, which is to apply a hybrid strategy to the production plan, and also some strategies for improving the production process are generated.
作者：
TRIANTAPHYLLOU, EAssistant Professor
Department of Industrial and Manufacturing Systems Engineering Louisiana State University Baton Rouge Louisiana
One of the most difficult issues in many real-life decision-making problems is how to estimate the pertinent data. An approach which uses pairwise comparisons was proposed by Saaty and is widely accepted as an effecti...
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One of the most difficult issues in many real-life decision-making problems is how to estimate the pertinent data. An approach which uses pairwise comparisons was proposed by Saaty and is widely accepted as an effective way of determining these data. Suppose that two matrices with pairwise comparisons are available. Furthermore, suppose that there is an overlapping of the elements compared in these two matrices. The problem examined in this paper is how to combine the comparisons of the two matrices in order to derive the priorities of the elements considered in both matrices. A simple approach and a linear programming approach are formulated and analyzed in solving this problem. Computational results suggest that the LP approach, under certain conditions, is an effective way for dealing with this problem. The proposed approach is of critical importance because it can also result in a reduction of the total required number of comparisons.
This paper analyzes the pipe network system of oil-gas collection and transportation for offshore oilfield development. A '0-1' integer linear programming model is constructed to optimize the investment of sea...
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This paper analyzes the pipe network system of oil-gas collection and transportation for offshore oilfield development. A '0-1' integer linear programming model is constructed to optimize the investment of seabed pipe network. The mathematical model is solved by the spanning tree method of graph theory and network analysis. All spanning trees of a network graph compose all the feasible solutions of the mathematical model. The optimal solution of the model is the spanning tree with the minimum cost among all spanning trees. This method can be used to optimize the seabed pipe network system and give a minimum cost plan for the development of offshore marginal oilfield groups.
The authors present a linearized error analysis and a gross error identification procedure for a power system linear programming state estimator. This type of estimator uses the weighted sum of the estimation residual...
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The authors present a linearized error analysis and a gross error identification procedure for a power system linear programming state estimator. This type of estimator uses the weighted sum of the estimation residuals as its performance criterion and has the property of automatic gross error rejection in most situations likely to occur in practice. Numerical results which illustrate the practical application of the proposed technique to some power systems are presented.< >
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