In this paper, we focused on characterizing and solving the multiple objective programming problems which have some imprecision of a vague nature in their formulation. The Rough Set Theory is only used in modeling the...
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In this paper, we focused on characterizing and solving the multiple objective programming problems which have some imprecision of a vague nature in their formulation. The Rough Set Theory is only used in modeling the vague data in such problems, and our contribution in data mining process is confined only in the "post-processing stage". These new problems are called rough multiple objective programming (RMOP) problems and classified into three classes according to the place of the roughness in the problem. Also, new concepts and theorems are introduced on the lines of their crisp counterparts;e.g. rough complete solution, rough efficient set, rough weak efficient set, rough Pareto front, weighted sum problem, etc. To avoid the prolongation of this paper, only the 1st-class, where the decision set is a rough set and all the objectives are crisp functions, is investigated and discussed in details. Furthermore, a flowchart for solving the 1st-class RMOP problems is presented. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.
This paper establishes a rough multiple objective programming model for a solid transportation problem. Furthermore, a general model for rough multiple objective programming problem is presented. Properties of the fea...
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This paper establishes a rough multiple objective programming model for a solid transportation problem. Furthermore, a general model for rough multiple objective programming problem is presented. Properties of the feasible and efficient solutions of rough multiple objective programming problems are investigated. In addition, compromise solutions are obtained by using the interactive fuzzy satisfying method. To solve the rough multipleobjective solid transportation problem, the rough simulation-based genetic algorithm is proposed, in which the rough simulation is embedded into the genetic algorithm. Finally, an application of the solid transportation problem at Xiluodu Hydropower Station is provided as an illustration. (C) 2011 Elsevier Inc. All rights reserved.
This paper integrates positive and normative approaches to modelling. The normative approach uses assumptions associated with multiple objective programming. The positive approach uses past observations to estimate th...
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This paper integrates positive and normative approaches to modelling. The normative approach uses assumptions associated with multiple objective programming. The positive approach uses past observations to estimate the weights associated with each objective criteria. The technique encompasses both linear and non-linear objectives such as profit, cost and risk as well as quadratic calibration terms. The proposed methodology minimizes the sum of squared errors about the ideal multipleobjective function, that is one that would reproduce observed results, rather than to minimize errors between fitted and observed activity levels. The technique removes the need to rely upon the use of abstract restraints normally applied to mathematical programming methods and provides a more objective means of testing the appropriateness of a model than previously. The technique has many applications in the field of mathematical modelling such as forecasting and analysing changes in decision-making and behaviour.
An equivalence is demonstrated between solving a linear complementarity problem with general data and finding a certain subset of the efficient points of a multiple objective programming problem. A new multiple object...
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An equivalence is demonstrated between solving a linear complementarity problem with general data and finding a certain subset of the efficient points of a multiple objective programming problem. A new multiple objective programming based approach to solving linear complementarity problems is presented. Results on existence, uniqueness and computational complexity are included.
作者：
Sun, MHUniv Texas
Coll Business Div Management & Mkt San Antonio TX 78249 USA
A multiple objective programming approach is proposed as a new analytical toot to fit a model which is used to project faculty salaries. The projected salaries are used as a basis to allocate the available budget for ...
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A multiple objective programming approach is proposed as a new analytical toot to fit a model which is used to project faculty salaries. The projected salaries are used as a basis to allocate the available budget for faculty salary equity adjustments, The model is also used to classify all faculty members into two categories with one category consisting of those faculty members being underpaid and the other consisting of those being overpaid. The multiple objective programming approach is much more powerful than regression analysis for this purpose because budgetary and policy restrictions can be included in the model as constraints. It is also more flexible than the goal programming approach because it has desirable solution properties. Salary data from a public university are used as an example to demonstrate the use of the approach. In addition, determinants of faculty salaries and variables to be included in the model are briefly discussed. (C) 2002 Elsevier Science B.V. All rights reserved.
Issues in measuring and reporting solution quality are examined when value functions are used in computational experiments of interactive multiple objective programming procedures. They include value functions used, w...
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Issues in measuring and reporting solution quality are examined when value functions are used in computational experiments of interactive multiple objective programming procedures. They include value functions used, weights assigned to the objective functions in the value functions, the size of the efficient set, and the Dumber of objective functions. The feasibility and existence of the ideal and nadir points are also discussed. Detailed examples are presented to demonstrate these issues. Neither the users nor, in fact, the researchers may discern these issues even though they have strong impacts on the reported solution qualities. Common practices in the computational experiments of interactive multiple objective programming procedures are reviewed. (C) 2003 Elsevier B.V. All rights reserved.
In this paper, we propose a new interactive procedure for solving multiple objective programming problems. Based upon feed-forward artificial neural networks (FFANNs), the method is called the Interactive FFANN Proced...
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In this paper, we propose a new interactive procedure for solving multiple objective programming problems. Based upon feed-forward artificial neural networks (FFANNs), the method is called the Interactive FFANN Procedure. In the procedure, the decision maker articulates preference information over representative samples from the nondominated set either by assigning preference ''values'' to the sample solutions or by making pairwise comparisons in a fashion similar to that in the Analytic Hierarchy Process. With this information, a FFANN is trained to represent the decision maker's preference structure. Then, using the FFANN, an optimization problem is solved to search for improved solutions. An example is given to illustrate the Interactive FFANN Procedure. Also, the procedure is compared computationally with the Tchebycheff Method (Steuer and Choo 1983). The computational results indicate that the Interactive FFANN Procedure produces good solutions and is robust with regard to the neural network architecture.
In practical applications of mathematical programming it is frequently observed that the decision maker prefers apparently suboptimal solutions. A natural explanation for this phenomenon is that the applied mathematic...
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In practical applications of mathematical programming it is frequently observed that the decision maker prefers apparently suboptimal solutions. A natural explanation for this phenomenon is that the applied mathematical model was not sufficiently realistic and did not fully represent all the decision makers criteria and constraints. Since multicriteria optimization approaches are specifically designed to incorporate such complex preference structures, they gain more and more importance in application areas as, for example, engineering design and capital budgeting. The aim of this paper is to analyze optimization problems both from a constrained programming and a multicriteria programming perspective. It is shown that both formulations share important properties, and that many classical solution approaches have correspondences in the respective models. The analysis naturally leads to a discussion of the applicability of some recent approximation techniques for multicriteria programming problems for the approximation of optimal solutions and of Lagrange multipliers in convex constrained programming. Convergence results are proven for convex and nonconvex problems.
The literature on portfolio selection mostly concentrates on computational analysis rather than on modelling efforts. In response, this paper provides a comprehensive literature review of multipleobjective determinis...
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The literature on portfolio selection mostly concentrates on computational analysis rather than on modelling efforts. In response, this paper provides a comprehensive literature review of multipleobjective deterministic and stochastic programming models for the portfolio selection problem. First, we summarize different concepts related to portfolio selection theory, including pricing models and portfolio risk measures. Second, we report the mathematical models that are generally used to solve deterministic and stochastic multiple objective programming problems. Finally, we present how these models can be used to solve the portfolio selection problem.
It is a common characteristic of many multiple objective programming problems that the efficient solution set can only be identified in approximation: as this set often contains an infinite number of points, only a di...
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It is a common characteristic of many multiple objective programming problems that the efficient solution set can only be identified in approximation: as this set often contains an infinite number of points, only a discrete representation can be computed, and due to numerical difficulties, each of these points itself might, in general, be only approximate to some efficient point. From among the various approximation concepts, this paper considers the notion of epsilon-efficient solutions and proposes several new methods for their generation. Supporting theoretical results are established and a numerical example is provided.
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