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Applying the approximation method PAINT and the interactive method NIMBUS to the multiobjective optimization of operating a wastewater treatment plant

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ENGINEERING OPTIMIZATION 2015年第3期47卷 328-346页

作者： Hartikainen, Markus E. Ojalehto, Vesa Sahlstedt, Kristian Univ Jyvaskyla Dept Math Informat Technol FI-40014 Jyvaskyla Finland Poyry Finland Ltd FI-01621 Vantaa Finland

Using an interactive multiobjective optimization method called NIMBUS and an approximation method called PAINT, preferable solutions to a five-objective problem of operating a wastewater treatment plant are found. The decision maker giving preference information is an expert in wastewater treatment plant design at the engineering company Poyry Finland Ltd. The wastewater treatment problem is computationally expensive and requires running a simulator to evaluate the values of the objective functions. This often leads to problems with interactive methods as the decision maker may get frustrated while waiting for new solutions to be computed. Thus, a newly developed PAINT method is used to speed up the iterations of the NIMBUS method. The PAINT method interpolates between a given set of Pareto optimal outcomes and constructs a computationally inexpensive mixed integer linear surrogate problem for the original wastewater treatment problem. With the mixed integer surrogate problem, the time required from the decision maker is comparatively short. In addition, a new IND-NIMBUS (R) PAINT module is developed to allow the smooth interoperability of the NIMBUS method and the PAINT method.

关键词： OR in natural resources simulation productivity and competitiveness multiple objective programming

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On the use of the distance in reference point-based approaches for multiobjective optimization

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ANNALS OF OPERATIONS RESEARCH 2015年第1期235卷 559-579页

作者： Luque, Mariano Ruiz, Ana B. Saborido, Ruben Marcenaro-Gutierrez, Oscar D. Univ Malaga Dept Appl Econ Math E-29071 Malaga Spain Ecole Polytech Polytech Montreal Researchers Software Engn Montreal PQ H3C 3A7 Canada Univ Malaga Dept Appl Econ Stat & Econometr E-29071 Malaga Spain

Reference point-based methods are very useful techniques for solving multiobjective optimization problems. In these methods, the most commonly used achievement scalarizing functions are based on the Tchebychev distance (minmax approach), which generates every Pareto optimal solution in any multiobjective optimization problem, but does not allow compensation among the deviations to the reference values given that it minimizes the value of the highest deviation. At the same time, for any , compromise programming minimizes the distance to the ideal objective vector from the feasible objective region. Although the ideal objective vector can be replaced by a reference point, achievable reference points are not supported by this approach, and special care must be taken in the unachievable case. In this paper, for , we propose a new scheme based on the distance, in which different single-objective optimization problems are designed and solved depending on the achievability of the reference point. The formulation proposed allows different compensation degrees among the deviations to the reference values. It is proven that, in the achievable case, any optimal solution obtained is efficient, and, in the unachievable one, it is at least weakly efficient, although it is assured to be efficient if an augmentation term is added to the new formulation. Besides, we suggest an interactive algorithm where the new formulation is embedded. Finally, we show the empirical advantages of the new formulation by its application to both numerical problems and a real multiobjective optimization problem, for achievable and unachievable reference points.

关键词： Reference point multiple objective programming Compromise programming Distance-based multiobjective optimization approaches

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The maximal descriptor index set for a face of a convex polyhedral set and some applications

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2015年第1期429卷 395-414页

作者： Ta Van Tu Corvinus Univ Budapest Dept Operat Res H-1093 Budapest Hungary

A face of a convex polyhedral set can be investigated on the basis of only the maximal descriptor index set for it. This helps us reduce difficulties and computational efforts in solving many problems. In this paper, we consider a multiple objective linear programming (MOLP) problem in which the constraint polyhedron may have no extreme points and the variables may be negative. First we deal with determining the maximal descriptor index set for an arbitrary face of the constraint polyhedron, then we apply the maximal descriptor index sets for faces to compare descriptor sets for the faces and find all maximal efficient faces for the MOLP problem. The methods known so far compare descriptor sets at large computational cost (in terms of computing times and storage) because they require finding all extreme points and directions of them. Known top-down search methods have been devised to find the efficient set of the MOLP problem but they may fail to find all maximal efficient faces and the computational cost is considerable. We propose a new method to compare descriptor sets and a new top-down search method which finds all maximal efficient faces and requires less computational cost. A numerical example is given to illustrate how the method works. (C) 2015 Elsevier Inc. All rights reserved.

关键词： multiple objective programming Faces of a polyhedron Maximal efficient faces The maximal descriptor index set for a face

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Interactive bicriterion decision support for a large scale industrial scheduling system

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ANNALS OF OPERATIONS RESEARCH 2015年第1期227卷 45-61页

作者： Makarouni, Ioanna Psarras, John Siskos, Eleftherios Natl Tech Univ Athens Sch Elect & Comp Engn Decis Support Syst Lab Athens Greece

In this paper we develop an interactive decision analysis approach to treat a large scale bicriterion integer programming problem, addressing a real world assembly line scheduling problem of a manufacturing company. This company receives periodically a set of orders for the production of specific items (jobs) through a number of specialised production (assembly) lines. The paper presents a non compensatory approach based on an interactive implementation of the epsilon-constraint method that enables the decision maker to achieve a satisfactory goal for each objective separately. In fact, the method generates and evaluates a large number of non dominated solutions that constitute a representative sample of the criteria ranges. The experience with a specific numerical example shows the efficiency and usefulness of the proposed model in solving large scale bicriterion industrial integer programming problems, highlighting at the same time the modelling limitations.

关键词： multiple objective programming Interactive decision analysis Job scheduling Pareto optimality Mixed-model assembly line

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Some Transportation Problems Under Uncertain Environments

Some Transportation Problems Under Uncertain Environments

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7th International Symposium on Advances in Artificial Intelligence and Applications / Federated Conference on Computer Science and Information Systems

作者： Kundu, Pradip Natl Inst Technol Durgapur Dept Math Durgapur 713209 India

ISBN: (纸本)9783662478158;9783662478141

Transportation problem (TP) is a very important area in operations research and management science. TPs not only involve with cost minimization, but also involve with many other goals such as profit maximization, time minimization, minimization of total deterioration of goods, etc. Also the available data of a transportation system such as transportation costs, resources, demands, conveyance capacities are not always crisp or precise but are uncertain. In this dissertation some transportation problems have been formulated and solved in different uncertain environments, e.g., fuzzy, type-2 fuzzy, rough and linguistic. Section 1 is introductory. Some basic concepts and definitions of fuzzy set, type-2 fuzzy set, rough set and variable are introduced in Sect. 2. In Sect. 3, we have formulated and solved two solid transportation problems (STPs) with fuzzy parameters namely a multi-objective STP with budget constraints and a multi-objective multi-item STP. Section 4 presents some theoretical developments related to type-2 fuzzy variables (T2 FVs) - a defuzzification method of T2 FVs and an interval approximation method of continuous T2 FVs. In this section, three transportation models with type-2 fuzzy parameters have been formulated and solved. In Sect. 5, we have presented two transportation mode selection problems with linguistic evaluations represented by fuzzy variables and interval type-2 fuzzy variables respectively. Here we have developed two fuzzy multi-criteria group decision making methods and these methods are applied to solve the respective mode selection problems. Section 6 presents a practical solid transportation model considering per trip capacity for each type of conveyances. Also in this problem fluctuating cost parameters are represented by rough variables. Rough chance constrained programming model, rough expected value model and rough dependent-chance programming model are used to solve the problem with rough cost parameters.

关键词： Transportation problem Solid transportation problem Fuzzy set theory Rough set theory multiple objective programming Fuzzy programming

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Biobjective optimization over the efficient set methodology for pareto set reduction in multiobjective decision making: Theory and application

Biobjective optimization over the efficient set methodology ...

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作者： Homrich da Jornada, Daniel Texas A&M University

学位级别：Ph.D.

A large number of available solutions to choose from poses a significant challenge for multiple criteria decision making. This research develops a methodology that reduces the set of efficient solutions under consideration. This dissertation is composed of three major parts: (i) the formalization of a theoretical framework; (ii) the development of a solution approach; and (iii) a case study application of the methodology. In the first part, the problem is posed as a multiobjective optimization over the efficient set and considers secondary robustness criteria when the exact values of decision variables are subjected to uncertainties during implementation. The contributions are centered at the modeling of uncertainty directly affecting decision variables, the use of robustness to provide additional trade-off analysis, the study of theoretical bounds on the measures of robustness, and properties to ensure that fewer solutions are identified. In the second part, the problem is reformulated as a biobjective mixed binary program and the secondary criteria are generalized to any convenient linear functions. A solution approach is devised in which an auxiliary mixed binary program searches for unsupported Pareto outcomes and a novel linear programming filtering excludes any dominated solutions in the space of the secondary criteria. Experiments show that the algorithm tends to run faster than existing approaches for mixed binary programs. The algorithm enables dealing with continuous Pareto sets, avoiding discretization procedures common to the related literature. In the last part, the methodology is applied in a case study regarding the electricity generation capacity expansion problem in Texas. While water and energy are interconnected issues, to the best of our knowledge, this is the first study to consider both water and cost objectives. Experiments illustrate how the methodology can facilitate decision making and be used to answer strategic questions pertaining to the

关键词： multiple criteria decision making multiple objective programming Robustness andsensitivity analysis Optimization over the efficient set Pareto set reduction Multiobjective mixed binary programming Water-energy nexus Thesis

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Explicit Location Covering Problems An alternative formulation and solution approach 5

Explicit Location Covering Problems An alternative formulati...

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2015 International Conference on Industrial Engineering and Operations Management (IEOM)

作者： Kellerman, H. J. Yadavalli, V. S. S. Univ Pretoria Dept Ind & Syst Engn Pretoria South Africa

ISBN: (纸本)9781479960651

Location covering problems is a widely researched field due to the fact that it is useful for siting of facilities in real-life situations. This article discusses the history of location covering problems and provides an alternative formulation for both the Location Set Covering Problem-Explicit and the Maximal Covering Location Problem-Explicit. The article further demonstrates how these models can be used to site reaction vehicles of the Private Security Industry in South Africa.

关键词： Facility location linear programming location problems multiple objective programming queuing theory

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Multi-objective Integer programming: An Improved Recursive Algorithm

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2014年第2期160卷 470-482页

作者： Ozlen, Melih Burton, Benjamin A. MacRae, Cameron A. G. RMIT Univ Sch Math & Geospatial Sci Melbourne Vic 3000 Australia Univ Queensland Sch Math & Phys Brisbane Qld 4072 Australia

This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-objective Integer programming (MOIP) problem. We significantly improve the earlier recursive algorithm of A-zlen and Azizoglu by using the set of already solved subproblems and their solutions to avoid solving a large number of IPs. A numerical example is presented to explain the workings of the algorithm, and we conduct a series of computational experiments to show the savings that can be obtained. As our experiments show, the improvement becomes more significant as the problems grow larger in terms of the number of objectives.

关键词： multiple objective programming Integer programming

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A LINEAR multiple objective programming FOR ASSORTMENT AND PACKING PROBLEMS

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JOURNAL OF INDUSTRIAL AND PRODUCTION ENGINEERING 2009年第2期26卷 77-86页

作者： Yu, Jing-Rung Chang, Jui-Mei Yu, Shiuh-Sheng Sheu, Her-Jiun Natl Chi Nan Univ Dept Informat Management 470 Univ Rd Nantou 470 Taiwan Natl Chiao Tung Univ Dept Management Sci Hsinchu 30050 Taiwan

This study proposed a multiple objective programming method to solve assortment and packing problems. Instead of using a two-stage method, as proposed by Li & Tsai [7], this study integrated the two stages into a multiple objective program to address assortment problems in one application. Moreover, this method could be extended to solve packing problems containing fewer 0-1 variables, thus, compared with Li et al. [8] the performance time of the proposed method could be decreased. The numerical examples showed that the proposed method is more efficient than Li & Tsai's [7], and Li et al.' s approaches [8].

关键词： multiple objective programming assortment issues packing issues

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Supplier Selection Mode of Aerospace Batch Production Based on multiple objective programming

Supplier Selection Mode of Aerospace Batch Production Based ...

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1st International Conference on Multimedia Information Networking and Security (MINES 2009)

作者： Zhao Shengbin Shi Chunsheng Harbin Inst Technol Sch Management Harbin 150006 Peoples R China

ISBN: (纸本)9780769538433

One of the essential problems of aerospace batch production management is to ensure that production material is supplied in time, and to strengthen the control management of suppliers. A Supplier selection mode of aerospace batch production is presented based on multiple objective programming theories. The principle, absolutely, restrictive condition and objectively restrictive condition are analyzed, according to the real demand in development suppliers' selection. Results showed that the method is valid to improve the performance of supplier selection by an existence.

关键词： Supplier Selection multiple objective programming Aerospace Batch Production Mode

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