دانلود مقاله ISI انگلیسی شماره 25186
عنوان فارسی مقاله

# یک کلاس از مدل برنامه ریزی خطی چند هدفه با ضرایب ناهموار تصادفی

کد مقاله سال انتشار مقاله انگلیسی ترجمه فارسی تعداد کلمات
25186 2009 18 صفحه PDF سفارش دهید 10761 کلمه
خرید مقاله
پس از پرداخت، فوراً می توانید مقاله را دانلود فرمایید.
عنوان انگلیسی
A class of multiobjective linear programming models with random rough coefficients
منبع

Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)

Journal : Mathematical and Computer Modelling, Volume 49, Issues 1–2, January 2009, Pages 189–206

کلمات کلیدی
متغیر راف - متغیر ناهموار تصادفی - اندازه گیری اعتماد - اندازه گیری احتمال - شبیه سازی خشن تصادفی - الگوریتم ژنتیک - راه حل مصالحه
پیش نمایش مقاله

#### چکیده انگلیسی

In the present paper, we concentrate on dealing with a class of multiobjective programming problems with random rough coefficients. We first discuss how to turn a constrained model with random rough variables into crisp equivalent models. Then an interactive algorithm which is similar to the interactive fuzzy satisfying method is introduced to obtain the decision maker’s satisfying solution. In addition, the technique of random rough simulation is applied to deal with general random rough objective functions and random rough constraints which are usually hard to convert into their crisp equivalents. Furthermore, combined with the techniques of random rough simulation, a genetic algorithm using the compromise approach is designed for solving a random rough multiobjective programming problem. Finally, illustrative examples are given in order to show the application of the proposed models and algorithms.

#### مقدمه انگلیسی

In realistic decision making situations, there are cases in which a decision must be made on the basis of uncertain data. For dealing with such decision making problems including uncertainty, many scholars have introduced models including random or fuzzy or rough variables to formulate the uncertainty, such as Moran [1], Liu [2], Amelia Bilbao Terol [3], Hsien-Chung Wu [4] and Slowinski [5]. They all constructed models for solving the practical and complex problems according to the following mathematical programming problem: View the MathML sourcemaxf(x,ξ)s.t.{gi(x,ξ)≤0,i=1,2,…,px∈X, Turn MathJax on where the set X⊂RNX⊂RN, f(x,ξ)f(x,ξ) is the objective function, View the MathML sourcegi(x,ξ)(i=1,2,…,p) are constraints, and ξξ is the uncertain variable. In [1], Moran introduced a SALSA (Stochastic Approach for Link-Structure Analysis) algorithm to examine random walks on graphs derived from the link structure. In [2], Liu presented a stochastic expected model, stochastic chance constrained programming and stochastic dependent chance programming. In [3], Amelia Bilbao Terol designed flexible decision making models in the distance metric optimization framework for problems including parameters which are represented by fuzzy numbers. In [4], Hsien-Chung Wu made the fuzzy numbers embed into a normed space, then invoked the scalarization techniques to evaluate the multiobjective programming problems with fuzzy coefficients. In [5], Slowinski applied the method of rough sets to solve an uncertain problem in the medical domain. In these models, randomness, fuzziness and roughness are considered as separate aspects. However, in a decision making process, we may face a hybrid uncertain environment. Jun Li, Jiuping Xu and Mitsuo Gen [6] discussed a class of multiobjective programming problems with fuzzy random coefficients. Tadeusz Gerstenkorn and Jacek Manko [7] introduced the notion of bifuzzy probabilistic sets and discussed some properties of these sets. Peng and Liu [8] introduced a novel concept of a birandom variable and exhibited the framework of birandom variables. However, there is a class of uncertain problems with randomness and roughness simultaneously which are still paid less attention. For example, in a supply–demand problem, the demand accords with normal distribution but the expected value is a rough variable, i.e., the minimum mean demand amount varies in an interval and the max mean demand amount also varies in an interval. In [2] and [9], Liu introduced the concept of random rough variable and presented a random rough expected value model and chance constrained programming: View the MathML sourcemax{f1,f2,…,fm}s.t.{Ch{fi(x,ξ)≥fi}(γi)≥δi,i=1,2,…,mCh{gr(x,ξ)≤0}(ηr)≥θr,r=1,2,…,px∈X, Turn MathJax on where ξξ is a random rough variable, γi,δi,ηrγi,δi,ηr and θrθr are predetermined confidence levels, i=1,2,…,m,r=1,2,…,pi=1,2,…,m,r=1,2,…,p. This is a useful tool for dealing with uncertain problems with randomness and roughness simultaneously. In this paper, on the basis of the chance measure of random rough variable [9], the tr–pr constrained multiobjective programming model can be easily given. Then we discuss the consistency with the models when random rough variable View the MathML sourceξ̄̃ degenerates to a rough variable View the MathML sourceξ̄ or a random variable View the MathML sourceξ̃. Thereby, it is proved that the proposed models are reasonable. However, it is difficult to get the optimal solution of many problems with random rough coefficients. Thus, we propose a crisp equivalent model aimed at this kind of multiobjective problem. Then we apply the technique of random rough simulation to deal with general random rough objective functions and random rough constraints. This is an efficient method and the convergence of the random rough simulation can be guaranteed [9]. Finally, combined with the techniques of random rough simulation, a genetic algorithm using the compromise approach is designed for solving a random rough multiobjective programming problem. The rest of this paper is organized as follows. In Section 2 we recall some definitions and properties for random variables, rough variables and random rough variables. Then the tr–pr constrained multiobjective programming model is introduced in Section 3. A crisp equivalent model is proposed for a special type of random rough variable, and an interactive random satisfying method is adopted to obtain the decision maker’s satisfactory solution. In Sections 4 and 5, we respectively represent random rough simulation and a random rough simulation-based genetic algorithm using a compromise approach. In Section 6, two illustrative examples are given in order to show the application of the proposed models and algorithms. Finally, the conclusions are given in Section 7.

#### نتیجه گیری انگلیسی

In this paper, we have developed a crisp equivalent model for tr–pr constrained multiobjective linear programming with random rough coefficients and presented two approaches for solving this kind of problem. One is the interactive satisfying method which is used to solve a special type of random rough multiobjective programming problem, and the other applies a random rough simulation-based genetic algorithm using a compromise approach which is effective for solving the general random rough multiobjective programming problem. They are both more viable and efficient than traditional algorithm methods for handling some complex problems. Although the random rough model constructed in this paper should be helpful for solving some real world problems, detailed analysis and further research are necessary to reveal more properties of a good method for solving other problems.

خرید مقاله
پس از پرداخت، فوراً می توانید مقاله را دانلود فرمایید.