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APPROXIMATING THE NONINFERIOR SET IN LINEAR BIOBJECTIVE PROGRAMS USING MULTIparametric DECOMPOSITION

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1989年第3期41卷 355-366页

作者： SOLANKI, RS COHON, JL JOHNS HOPKINS UNIV DEPT GEOG & ENVIRONM ENGNBALTIMOREMD 21218

An algorithm is developed to generate an approximate representation of the noninferior set in the objective space for linear biobjective programs. A sharp measure of geometrical error based on multiparametric decomposition is used to obtain a subset of the noninferior objective vectors distributed over the entire noninferior set. The deviation of the approximate representation from the exact noninferior set in the objective space can be controlled by specifying the maximum possible deviation. The algorithm attempts to select each additional noninferior objective vector to be included in the approximation to reduce the deviation as quickly as possible. [ABSTRACT FROM AUTHOR]

关键词： Multiple criteria programming parametric programming

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W-efficient partitions and the solution of the sequential clustering problem

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ANNALS OF OPERATIONS RESEARCH 1997年第s期74卷 305-319页

作者： Joseph, A Bryson, N UNIV MIAMI SCH BUSINESS ADMCORAL GABLESFL 33124 HOWARD UNIV SCH BUSINESSWASHINGTONDC 20059 HOWARD UNIV HU FASTWASHINGTONDC 20059

Clustering involves partitioning a set of related objects into a set of mutually exclusive and completely exhaustive clusters. The objective is to form clusters which reflect minimum difference among objects as measured by the relevant clustering criterion. Most statements of clustering problems assume that the number of clusters, g, in the partition is known. In reality, a value for g may not be immediately obvious. It is known that as g increases, there is an improvement in the value of the clustering criterion function. However, for some values of g, this rate of improvement may be less than expected. Because there may be a cost factor involved, there is also interest in identifying those values of g that offer attractive rates of improvement. Partitions that are optimal for a given g, and for which the given g offer an attractive rate of improvement, are referred to as being w-efficient;other partitions, even if optimal for a given g, are referred to as being w-inefficient. We present a linear programming approach for generating the w-efficient partitions of the sequential clustering problem, and demonstrate the importance of w-efficient partitions to the efficient solution of the sequential clustering problem.

关键词： clustering w-efficiency parametric programming biobjective programming

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Virtual Prototyping and parametric Design of 3D-Printed Tablets Based on the Solution of Inverse Problem

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AAPS PHARMSCITECH 2018年第8期19卷 3414-3424页

作者： Novak, Matej Boleslavska, Tereza Grof, Zdenek Wanek, Adam Zadrazil, Ales Beranek, Josef Kovacik, Pavel Stepanek, Frantisek Univ Chem & Technol Dept Chem Engn Tech 5 Prague 16628 6 Czech Republic Zentiva Ks U Kabelovny 130 Prague 10200 10 Czech Republic

The problem of designing tablet geometry and its internal structure that results into a specified release profile of the drug during dissolution was considered. A solution method based on parametric programming, inspired by CAD (computer-aided design) approaches currently used in other fields of engineering, was proposed and demonstrated. The solution of the forward problem using a parametric series of structural motifs was first carried out in order to generate a library of drug release profiles associated with each structural motif. The inverse problem was then solved in three steps: first, the combination of basic structural motifs whose superposition provides the closest approximation of the required drug release profile was found by a linear combination of pre-calculated release profiles. In the next step, the final tablet design was constructed and its dissolution curve found computationally. Finally, the proposed design was 3D printed and its dissolution profile was confirmed experimentally. The computational method was based on the numerical solution of drug diffusion in a boundary layer surrounding the tablet, coupled with erosion of the tablet structure encoded by the phase volume function. The tablets were 3D printed by fused deposition modelling (FDM) from filaments produced by hot-melt extrusion. It was found that the drug release profile could be effectively controlled by modifying the tablet porosity. Custom release profiles were obtained by combining multiple porosity regions in the same tablet. The computational method yielded accurate predictions of the drug release rate for both single- and multi-porosity tablets.

关键词： 3D printing hot-melt extrusion parametric programming dissolution mathematical modelling

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AN O(N) ALGORITHM FOR QUADRATIC KNAPSACK-PROBLEMS

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OPERATIONS RESEARCH LETTERS 1984年第3期3卷 163-166页

作者： BRUCKER, P Fachbereich Mathematik Universität Osnabrück Postfach 4469 4500 Osnabrück Federal Republic of Germany

An algorithm is presented which solves bounded quadratic optimization problems with n variables and one linear constraint in at most O( n ) steps. The algorithm is based on a parametric approach combined with well-known ideas for constructing efficient algorithms. It improves an O( n log n ) algorithm which has been developed for a more restricted case of the problem.

关键词： nonlinear programming convex programming quadratic programming knapsack problem parametric programming

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Computing multiple-output regression quantile regions from projection quantiles

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COMPUTATIONAL STATISTICS 2012年第1期27卷 29-49页

作者： Paindaveine, Davy Siman, Miroslav Univ Libre Brussels ECARES B-1050 Brussels Belgium ASCR Inst Informat Theory & Automat Prague 18208 8 Czech Republic

In the multiple-output regression context, Hallin et al. (Ann Statist 38:635-669, 2010) introduced a powerful data-analytical tool based on regression quantile regions. However, the computation of these regions, that are obtained by considering in all directions an original concept of directional regression quantiles, is a very challenging problem. Paindaveine and iman (Comput Stat Data Anal 2011b) described a first elegant solution relying on linear programming techniques. The present paper provides another solution based on the fact that the quantile regions can also be computed from a competing concept of projection regression quantiles, elaborated in Kong and Mizera (Quantile tomography: using quantiles with multivariate data 2008) and Paindaveine and iman (J Multivar Anal 2011a). As a by-product, this alternative solution further provides various characteristics useful for statistical inference. We describe in detail the algorithm solving the parametric programming problem involved, and illustrate the resulting procedure on simulated data. We show through simulations that the Matlab implementation of the algorithm proposed in this paper is faster than that from Paindaveine and iman (Comput Stat Data Anal 2011b) in various cases.

关键词： Directional quantile Halfspace depth Multiple-output regression parametric programming Quantile regression

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Plausibility in Early Stages of Architectural Design: A New Tool for High-Rise Residential Buildings

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Tsinghua Science and Technology 2009年第3期14卷 327-332页

作者： Dirk Donath Danny Lobos Chair of Computer Science in Architecture Faculty of Architecture Bauhaus-UniversityWeimar 99423 Germany

This paper analyzes the problem of the design of envelopes for high-rise isolated residential buildings. The phenomenon of envelope creation appears in the early stages of the architectural design. Variables that influence the final shape and size of such envelopes are then identified. This paper presents the state-of-the-art tools for the current solutions at the commercial and academic/scientific level. The variables identified in this research are the client＇s needs, the urban code and architectural practice, and their specific components for the final creation of a new decision support system tool based on the building information modeling （BIM） software platform, to facilitate the work in the project development and drawing production stages. This tool generates several options for building envelopes according to the parameters required by the city Zoning Planning Commission. These options then lead to deliver reliable data and a geometry that can be analyzed in a timely fashion by the engineers, builders, architects, government, and clients in the early stages of the building＇s design. The results show that use of specific information and communication technologies （ICT） tools in the early stages of a building design helps reduce the working time, increases confidence in the generated solution, and contributes to the exploration of alternatives in a short period of time.

关键词： constraint based design parametric programming urban modeling optimization architectural design

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Structural approach to parametric analysis of an IP - On the case of the right-hand side

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1996年第1期92卷 148-156页

作者： Wang, HF Horng, JS NATL TSING HUA UNIV INST IND ENGNHSINCHUTAIWAN

In this paper, we define a stepsize to parametrize the right-hand side of an integer programming problem. Based on the properties of the defined stepsize, we derive an algorithm for solving families of integer linear programming problems with the right-hand side in the form of b + theta b', where b and b' are vectors and the single parameter theta is a scalar. The proposed algorithm is applicable to the cases when the vector b' consists of positive and/or negative components. A complexity analysis of solving the entire problem is done with numerical examples.

关键词： parametric programming right-hand side integer programming complexity

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A parametric approach to solve neutrosophic linear programming models

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JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES 2021年第3期42卷 631-654页

作者： Abdelfattah, Walid Northern Border Univ Coll Arts & Sci Dept Math Raffia 3282 Saudi Arabia Fac Econ & Management Modeling Optimizat & Decis Making Ind & Logist Sy Sfax 3018 Tunisia

When solving a linear programming model, the coefficients should be fixed at specific values in advance. In practice, however, data overwhelmingly lack precision and this affects the model's optimal solution. Among other theories including fuzzy set and intuitionistic fuzzy set theories, the neutrosophic set theory is considered a generalization of the two theories mentioned and is shown to be very powerful in assimilating inaccurate, vague, and maladjusted data. In this study, we deal with neutrosophic linear programming models where all coefficients are represented by triangular neutrosophic numbers. Maximization, minimization, and all types of constraints are considered. A novel parametric-based approach is introduced to solve this type of model and a few numerical examples are provided. Results show that the presented approach yields more realistic solutions. Finally, we conclude that the proposed approach is efficient, flexible, and capable of solving neutrosophic linear programming models.

关键词： Linear programming Neutrosophic set Triangular neutrosophic number parametric programming Interval linear programming

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PROPER EFFICIENCY IN NONCONVEX VECTOR-MAXIMIZATION-PROBLEMS

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1991年第1期54卷 74-80页

作者： BELKEZIZ, K PIRLOT, M UNIV LIBRE BRUXELLES CP 210BLD TRIOMPHEB-1050 BRUSSELSBELGIUM

Vector-maximization-problems arise when more than one objective function are to be simultaneously maximized over a feasibility region. The concept of proper efficiency has been introduced by Geoffrion in order to eliminate points of a certain anomalous type. In this paper, a generalization is provided for the characterization of the properly efficient solutions, as solutions of some parametric programming problems. A specific characterization is given in the case of bicriterion programs.

关键词： VECTOR-MAXIMIZATION-PROBLEMS parametric programming BICRITERION programming PROPER EFFICIENCY

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A modified standard embedding with jumps in nonlinear optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2006年第3期169卷 1185-1206页

作者： Guddat, J Vázquez, G Nowack, D Rückmann, JJ Univ Americas Puebla Escuela Ciencias Cholula 72820 Mexico Humboldt Univ Inst Math D-10099 Berlin Germany

The paper deals with a combination of pathfollowing methods (embedding approach) and feasible descent direction methods (so-called jumps) for solving a nonlinear optimization problem with equality and inequality constraints. Since the method that we propose here uses jumps from one connected component to another one, more than one connected component of the solution set of the corresponding one-parametric problem can be followed numerically. It is assumed that the problem under consideration belongs to a generic subset which was introduced by Jongen, Jonker and Twilt. There already exist methods of this type for which each starting point of a jump has to be an endpoint of a branch of local minimizers. In this paper the authors propose a new method by allowing a larger set of starting points for the jumps which can be constructed at bifurcation and turning points of the solution set. The topological properties of those cases where the method is not successful are analyzed and the role of constraint qualifications in this context is discussed. Furthermore, this new method is applied to a so-called modified standard embedding which is a particular construction without equality constraints. Finally, an algorithmic version of this new method as well as computational results are presented. (c) 2005 Published by Elsevier B.V.

关键词： parametric programming pathfollowing methods with jumps genericity Jongen-Jonker-Twilt regularity modified standard embedding

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