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Interactive fuzzy programming for two-level linear and linear fractional production and assignment problems: A case study

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2001年第1期135卷 142-157页

作者： Sakawa, M Nishizaki, I Uemura, Y Hiroshima Univ Fac Engn Dept Ind & Syst Engn Higashihiroshima 7398527 Japan Juken Sangyou Co Ltd Prod Projects Dev Dept Hiroshima 7388502 Japan

In this paper, we deal with actual problems on production and work force assignment in a housing material manufacturer and a subcontract firm. We formulate two kinds of two-level programming problems;one is a profit maximization problem of both the housing material manufacturer and the subcontract firm, and the other is a profitability maximization problem of them. Applying the interactive fuzzy programming for two-level linear and linear fractional programming problems, we derive satisfactory solutions to the problems. After comparing the two problems, we discuss the results of the applications and examine actual planning of the production and the work force assignment of the two firms to be implemented. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： optimization production and work force assignment problems two-level linear and linear fractional programming problem interactive fuzzy programming satisfactory solution

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Characterization of solution sets of quasiconvex programs

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2003年第3期117卷 627-636页

作者： Penot, JP Univ Pau & Pays Adour Fac Sci Lab Appl Math Pau France

We examine to what extent one can provide characterizations of the sets of solutions to quasiconvex programs using adapted subdifferentials which generalize known characterizations in the convex case.

关键词： generalized convexity invexity optimality conditions programming problem quasiconvex function solutions subdifferentials

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OPTIMAL IDENTIFICATION OF PARAMETERS IN AN INHOMOGENEOUS-MEDIUM WITH QUADRATIC programming

SOCIETY OF PETROLEUM ENGINEERS JOURNAL

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SOCIETY OF PETROLEUM ENGINEERS JOURNAL 1975年第5期15卷 371-375页

作者： YEH, WWG UNIV CALIF LOS ANGELESCA 90024

Abstract. The paper develops a new algorithm for parameter identification in a partial differential equation associated with an inhomogeneous aquifer system. The parameters chosen for identification are the storage coefficient, a constant, and transmissivities, functions of the space variable. An implicit finite-difference scheme is used to approximate the solutions of the governing equation. A least-squares criterion is then established. Using distributed observations on the dependent variable within the system, parameters are identified directly by solving a sequence of quadratic programming problems such that the final solution converges to the original problem. The advantages of this new algorithm problem. The advantages of this new algorithm include rapid rate of convergence, ability to handle any inequality constraints, and easy computer implementation. The numerical example presented demonstrates the simultaneous identification of 12 parameters in only seconds of computer time. parameters in only seconds of computer timeIntroduction. Simulation and mathematical models are often used in analyzing aquifer systems. Physically based mathematical models are implemented by high-speed computers. Most models are of a parametric type, in which parameters used in parametric type, in which parameters used in deriving the governing equation are not measurable directly from the physical point of view and, therefore, must be determined from historical records. The literature dealing with parameter identification in partial differential equations has become available only within the last decade. The approaches include gradient searching procedures, the balanced error-weighted gradient method, the classical Gauss-Newton least-squares procedure, optimal control and gradient optimization, quasi linearization, influence coefficient algorithm, linear programming, maximum principle, and regression analysis allied with the steepest-descent algorithm. Yeh analyzed a typical paramet

关键词： reservoir simulation programming problem inhomogeneous medium optimization problem constraint quasilinearization increment Upstream Oil & Gas objective function identification Information Management and Systems Reservoir Simulation

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Diversely polarised sparse array design with minimum interelement spacing constraint for polarised pattern synthesis

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ELECTRONICS LETTERS 2020年第5期56卷 221-+页

作者： Shi, Shuli Xu, Yougen Zhao, Kang Huang, Yunlin Liu, Zhiwen Beijing Inst Technol Sch Informat & Elect Beijing 100081 Peoples R China

The problem of optimised design of diversely polarised sparse array for joint synthesis of spatial and polarisation beampattern is addressed in this Letter. Two kinds of polarised array configurations, cocentred and non-cocentred crossed-dipole arrays, are considered. Minimum interelement spacing constraint along with non-cocentred constraint are involved in the design methods by using two discrete linear operators. The optimisation process can be formulated as a mixed-integer quadratically constrained programming problem which guarantees the optimal solution of the sparse array configuration. Comparison examples with state-of-the-art method validate the advantages of the proposed method in terms of the reduction of required element number and the enlargement of adjacent element spacing.

关键词： optimisation dipole antenna arrays electromagnetic wave polarisation antenna radiation patterns polarised pattern synthesis spatial polarisation beampattern polarised array configurations noncocentred crossed-dipole arrays noncocentred constraint optimisation process programming problem sparse array configuration adjacent element spacing interelement spacing constraint polarisation beampattern discrete linear operators mixed-integer quadratic constrained programming problem polarised sparse array

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Kinetic mechanism reduction based on an integer programming approach

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AICHE JOURNAL 2000年第2期46卷 361-371页

作者： Androulakis, IP Exxon Res & Engn Co Corp Res Sci Labs Annandale NJ 08801 USA

An approach toward kinetic mechanism reduction both in terms of reactions and species, is discussed. The driving force of the approach is to derive reduced kinetic models while maintaining the structural integrity of the detailed mechanisms. The mechanism reduction problem is defined as an integer optimization problem with binary variables denoting the existence/nonexistence of reactions or species. A Branch & Bound framework is implemented for the solution of the resulting mathematical programming problem. Several examples, utilizing a variety of kinetic networks, are presented and the results are analyzed.

关键词： .Mechanism Reduction structural integrity reduction problem integer optimization programming problem reacting species detailed network Nr reactions

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Estimation of an optimal solution of a LP problem with unknown objective function - A stochastic approximation approach based on the simplex method

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MATHEMATICAL programming 2004年第3期101卷 463-478页

作者： Prieto-Rumeau, T Univ Nacl Educ Distancia Dept Econ Aplicada Cuantitat 2 Madrid Spain

We consider a linear programming problem with unknown objective function. Random observations related to the unknown objective function are sequentially available. We define a stochastic algorithm, based on the simplex method, that estimates an optimal solution of the linear programming problem. It is shown that this algorithm converges with probability one to the set of optimal solutions and that its failure probability is of order inversely proportional to the sample size. We also introduce stopping criteria for the algorithm. The asymptotic normality of some suitably defined residuals is also analyzed. The proposed estimation algorithm is motivated by the stochastic approximation algorithms but it introduces a generalization of these techniques when the linear programming problem has several optimal solutions. The proposed algorithm is also close to the stochastic quasi-gradient procedures, though their usual assumptions are weakened.

关键词： Objective Function Mathematical Method Approximation Algorithm programming problem Failure Probability

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An Approach to Nonlinear programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1973年第3期11卷 219-227页

作者： Luenberger, D. G. Stanford Univ Dept Engn Econ Syst Stanford CA 94305 USA

A nonlinear programming problem with inequality constraints and with unknown vector x is converted to an unconstrained minimization problem in unknowns x and lambda, where lambda is a vector of Lagrange multipliers. It is shown that, if the original problem possesses standard convexity properties, then local minima of the associated unconstrained problem are in fact global minima of that problem and, consequently, Kuhn-Tucker points for the original problem. A computational procedure based on the conjugate residual scheme is applied in the x lambda-space to solve the associated unconstrained problem. The resulting algorithm requires only first-order derivative information on the functions involved and will solve a quadratic programming problem in a finite number of steps.

关键词： Lagrange Multiplier programming problem Minimization problem Global Minimum Original problem

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GENERALIZED HESSIAN MATRIX AND 2ND-ORDER OPTIMALITY CONDITIONS FOR problemS WITH C1,1 DATA

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APPLIED MATHEMATICS AND OPTIMIZATION 1984年第1期11卷 43-56页

作者： HIRIARTURRUTY, JB STRODIOT, JJ NGUYEN, VH FAC UNIV NAMUR DEPT MATHB-5000 NAMURBELGIUM

In this paper, we present a generalization of the Hessian matrix toC1,1 functions, i.e., to functions whose gradient mapping is locally Lipschitz. This type of function arises quite naturally in nonlinear analysis and optimization. First the properties of the generalized Hessian matrix are investigated and then some calculus rules are given. In particular, a second-order Taylor expansion of aC1,1 function is derived. This allows us to get second-order optimality conditions for nonlinearly constrained mathematical programming problems withC1,1 data.

关键词： Optimality Condition System Theory Mathematical Method programming problem Mathematical programming

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Multi-objective non-linear solid transportation problem with fixed charge, budget constraints under uncertain environments

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SYSTEMS SCIENCE & CONTROL ENGINEERING 2022年第1期10卷 899-909页

作者： Haque, S. Bhurjee, A. K. Kumar, P. Prince Sultan Univ Dept Math Riyadh Saudi Arabia VIT Bhopal Univ Dept Math Sehore Madhya Pradesh India SRM Inst Sci & Technol Dept Math Chennai Tamil Nadu India

Transportation-based models are widely used to solve real-life problems such as supply chain problems, inventory level problems, business models, management problems, etc. The parameters of these problems have been conventionally measured as deterministic. However, these parameters have vagueness due to the uncertainty in the data sets. Such uncertainty of the parameters is generally measured using randomness (probability theory) or fuzziness (fuzzy theory), with certain assumptions and limitations. Closed intervals interpretation is another concept to deal with the uncertainties of real-world issues in recent decades, avoiding the limitations in probability theory and fuzzy set theory. This study formulates a fixed-charged multi-objective non-linear solid transportation with parameters such as availability of items, conveyance capacity, transportation cost, requirement, and budget for destinations in the form of closed intervals, where objectives are minimization of total transportation cost and action of time under the restriction over budget. An efficient solution procedure is developed with the help of interval analysis based on the parametric perception of intervals. Initially, the objective functions are converted into a crisp function using multiple integrations, and as a result, the problem is converted into a deterministic multi-objective non-linear programming problem. In addition, a real-world numerical problem is considered for testing the developed solution process for greater comprehension and clarity.

关键词： Interval analysis solid transportation problem multi-objective programming problem partial ordering

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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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