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multiobjective linear programming model on injection oilfield recovery system

COMPUTERS & MATHEMATICS WITH APPLICATIONS 1998年第5期36卷 127-135页

作者： Xiao, W Liu, ZB Jiang, MZ China SW Petr Inst Dept Comp Sci Sichuan 637001 Peoples R China Univ Nebraska Dept Informat Syst & Quantitat Anal Omaha NE 68182 USA

This paper proposes a multiobjective linear programming (MLP) model on injection oilfield recovery system. A modified interior-point algorithm to MLP problems has been constructed by using concepts of Kamarkar's interior point algorithm and the Analytic Hierarchy Process (AHP). This algorithm is shown to likely be more efficient than other MLP's algorithms in the application of decision making on the petroleum industry through the demonstration of a numerical example. The MLP model's optimal solution allows decision makers to optimally design the developing plan of the injection oilfield recovery system. (C) 1998 Elsevier Science Ltd. All rights reserved.

关键词： multiobjective linear programming injection oilfield recovery system analytic hierarchy process on measure interior-point algorithm

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multiobjective linear programming to Determine the Most Suitable Electrical Energy Matrix for Countries: a Case Study at Brazil

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IEEE LATIN AMERICA TRANSACTIONS 2019年第3期17卷 426-433页

作者： de Castro Reis, Juliana dos Santos Constant, Renata Angulo Meza, Lidia Soares de Mello, Joao Carlos Univ Fed Fluminense Engn Prod Pesquisa Operac Niteroi RJ Brazil Ctr Univ Serra dos Orgaos Dept Engn Prod Teresopolis RJ Brazil Univ Fed Fluminense Dept Engn Prod TEP Niteroi RJ Brazil

Long-term planning to meet the growth of electricity demand in a country or region is a decision of strategic importance that should aim at maximizing the benefits provided and at minimizing negative impacts on the environment and society. In this sense, the objective of this study is to develop a methodology to determine the most suitable electric energy matrix of a country, that is, the best combination for the use of electricity generation sources. Thus, a multiobjective linear programming model is proposed to calculate the amount of energy that must be generated by each source available in the country, considering its internal demand and capacity constraints. In addition, this article aims to present the results of a case study in Brazil in the determination of its electric energy matrix, considering the use of several sources of electricity generation. The methodology developed was applied for the years 2015, 2020 and 2030 and generated some important reflections when compared with the actual values and current practices. The proposed model proved to be a useful tool to assist in the analysis and planning of the use, and possible extension, of the generation capacity of each electric power source of a given country.

关键词： linear programming IEEE transactions Planning Reflection Analytical models Tools Capacity planning Electrical Power Matrix Generation Sources multiobjective linear programming

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AN INTERACTIVE FUZZY SATISFICING METHOD FOR LARGE-SCALE multiobjective linear-programming PROBLEMS WITH BLOCK ANGULAR STRUCTURE

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FUZZY SETS AND SYSTEMS 1994年第1期67卷 5-17页

作者： SAKAWA, M SAWADA, K MATSUSHITA ELECT WORKS LTD CTR INFORMAT SYSTOSAKA 571JAPAN

In this paper, we present an interactive fuzzy satisficing method for large-scale multiobjective linear programming problems with the block angular structure. By considering the vague nature of human judgements, we assume that the decision maker (DM) may have a fuzzy goal for each of the objective functions. Having elicited the corresponding linear membership functions, if the DM specifies the reference membership levels for all the membership functions, the corresponding Pareto optimal solution which is, in the minimax sense, nearest to the requirement or better than that if the reference membership levels are attainable can be obtained by solving the minimax problem. Here it is shown that the formulated minimax problem can be reduced to one master problem and a number of linear subproblems and the Pareto optimal solution together with the trade-off rate information between the membership functions can be obtained by applying the Dantzig-Wolfe decomposition method. In this way, the satisficing solution for the DM can be derived from Pareto optimal solutions by updating the current reference membership levels on the basis of the current levels of the membership functions together with the trade-off rates between the membership functions.

关键词： LARGE-SCALE linear programming multiobjective linear programming BLOCK ANGULAR STRUCTURE FUZZY GOALS INTERACTIVE FUZZY SATISFICING METHOD

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Adjacency based method for generating maximal efficient faces in multiobjective linear programming

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APPLIED MATHEMATICAL MODELLING 2012年第12期36卷 6301-6311页

作者： Krichen, S. Masri, H. Guitouni, A. Univ Jendouba Fac Law Econ & Management Jendouba 8189 Tunisia Univ Tunis LARODEC Lab Inst Super Gest Tunis Bardo 2000 Tunisia DRDC Valcartier Command & Control Decis Support Syst Sect Quebec City PQ G3J 1X5 Canada Univ Victoria Fac Business Victoria BC Canada

multiobjective linear optimization problems (MOLPs) arise when several linear objective functions have to be optimized over a convex polyhedron. In this paper, we propose a new method for generating the entire efficient set for MOLPs in the outcome space. This method is based on the concept of adjacencies between efficient extreme points. It uses a local exploration approach to generate simultaneously efficient extreme points and maximal efficient faces. We therefore define an efficient face as the combination of adjacent efficient extreme points that define its border. We propose to use an iterative simplex pivoting algorithm to find adjacent efficient extreme points. Concurrently, maximal efficient faces are generated by testing relative interior points. The proposed method is constructive such that each extreme point, while searching for incident faces, can transmit some local informations to its adjacent efficient extreme points in order to complete the faces' construction. The performance of our method is reported and the computational results based on randomly generated MOLPs are discussed. (C) 2012 Elsevier Inc. All rights reserved.

关键词： multiobjective linear programming Adjacency Efficient set Efficient faces Outcome set

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Fuzzy harmonic mean technique for solving fully fuzzy multilevel multiobjective linear programming problems

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ALEXANDRIA ENGINEERING JOURNAL 2022年第10期61卷 8189-8205页

作者： Fathy, E. Hassanien, A. E. Helwan Univ Fac Sci Dept Math Cairo Egypt Cairo Univ Fac Comp & Artificial Intelligence Cairo Egypt

This paper illustrates how the fuzzy harmonic mean technique can efficiently solve fully fuzzy multilevel multiobjective linear programming (FFMMLP) problems. First, at each level, the FFMMLP problem can be converted into three crisp multiobjective linear programming (CMLP) problems using the crisp linear technique. Then, the fuzzy harmonic mean technique is utilized to aggregate each crisp problem's multiobjective into a single objective. Second, the ensuing final, single-objective problem is constructed using the harmonic mean for each level. Finally, it is solved to obtain a fuzzy compromise solution for the FFMMLP problem in general. Two examples are given to obtain the application of the proposed method. One example is applying the proposed approach to a multilevel multiobjective production planning model for a supply chain under a fully fuzzy environment. (c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY-NC-ND license (http://***/ licenses/by-nc-nd/4.0/).

关键词： Fully Fuzzy linear Pro-gramming Harmonic Mean Technique Multilevel linear Program-ming multiobjective linear programming

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Duality theory and slackness conditions in multiobjective linear programming

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 1999年第4-5期37卷 101-109页

作者： Balbas, A Jimenez, P Heras, A Univ Carlos III Madrid 126 Dept Econ Empresa Madrid 28903 Spain Univ Nacl Educ Distancia Dept Matemat Fundamentales Madrid 28040 Spain Univ Complutense Madrid Dept Econ Financiera & Actuarial Madrid 28223 Spain

The aim of this paper is to develop a duality theory for linear multiobjective programming verifying similar properties as in the scalar case. We use the so-called "strongly proper optima" and we characterize such optima and its associated dual solutions by means of some complementary slackness conditions. Moreover, the dual solutions can measure the sensitivity of the primal optima. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： multiobjective linear programming duality strongly proper optimum slackness conditions

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A Semidefinite programming approach for solving multiobjective linear programming

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JOURNAL OF GLOBAL OPTIMIZATION 2014年第3期58卷 465-480页

作者： Blanco, Victor Puerto, Justo Ben Ali, Safae El Haj Univ Granada Dept Quantitat Methods Econ & Business Granada Spain Univ Seville IMUS Seville Spain

Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions of multiobjective linear Programmes (MOLPs). However, all of them are based on active-set methods (simplex-like approaches). We present a different method, based on a transformation of any MOLP into a unique lifted Semidefinite Program (SDP), the solutions of which encode the entire set of Pareto-optimal extreme point solutions of any MOLP. This SDP problem can be solved, among other algorithms, by interior point methods;thus unlike an active set-method, our method provides a new approach to find the set of Pareto-optimal solutions of MOLP.

关键词： multiobjective linear programming Semidefinite programming Polynomial optimization Moment problem

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A method for solving linear programming problems with fuzzy parameters based on multiobjective linear programming technique

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2007年第4期24卷 557-573页

作者： Zangiabadi, M. Maleki, H. R. Shahid Bahonar Univ Kerman Fac Math & Comp Sci Kerman Iran Shiraz Univ Technol Dept Basic Sci Shiraz Iran

In the real-world optimization problems, coefficients of the objective function are not known precisely and can be interpreted as fuzzy numbers. In this paper we define the concepts of optimality for linear programming problems with fuzzy parameters based on those for multiobjective linear programming problems. Then by using the concept of comparison of fuzzy numbers, we transform a linear programming problem with fuzzy parameters to a multiobjective linear programming problem. To this end, we propose several theorems which are used to obtain optimal solutions of linear programming problems with fuzzy parameters. Finally some examples are given for illustrating the proposed method of solving linear programming problem with fuzzy parameters.

关键词： linear optimization fuzzy number ranking function multiobjective linear programming

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OPTIMIZATION OF RADIOACTIVE-WASTE MANAGEMENT-SYSTEM BY APPLICATION OF multiobjective linear-programming

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JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 1981年第10期18卷 773-784页

作者： SHIMIZU, Y Research Reactor Institute Kyoto University

A mathematical procedure is proposed to make a radioactive waste management plan comprehensively. Since such planning is relevant to some different goals in management, decision making has to be formulated as a multiobjective optimization problem. A mathema-tical programming method was introduced to make a decision through an interactive manner which enables us to assess the preference of decision maker step by step among the con-flicting objectives. The reference system taken as an example is the radioactive waste management system at the Research Reactor Institute of Kyoto University (KUR). Its linear model was built based on the experience in the actual management at KUR. The best-compromise model was then formulated as a multiobjective linear programming by the aid of the computa-tional analysis through a conventional optimization. It was shown from the numerical re-sults that the proposed approach could provide some useful informations to make an actual management plan.

关键词： radioactive waste management multiobjective linear programming best compromise solution decision making man-machine interaction management cost minimizing water consumption minimizing released radioactivity minimiz-ing

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Bifurcation and adaptation in evolutionary interactive multiobjective linear programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1996年第3期93卷 602-610页

作者： Dror, M Shakun, MF NYU LEONARD N STERN SCH BUSINESSNEW YORKNY 10012 UNIV ARIZONA COLL BUSINESSDEPT MISTUCSONAZ 85721

This paper shows how a formal modeling framework, Evolutionary Systems Design (ESD), for evolutionary problem definition and solution, can be used for problem adaptation and restructuring in optimization problems, as developed for multiobjective linear programming (MOLP). Restructuring through a heuristic controls/goals/values referral process and adaptation are discussed for interactive MOLP, and illustrated by a numerical example.

关键词： adaptive processes problem restructuring evolutionary systems design multiobjective linear programming

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