An exact method for a discrete multiobjective linear fractional optimization

Integer linear fractional programming problem with multiple objective MOILFP is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions, then generate an integer feasible solution. Using the reduced gradients of the objective functions, an efficient cut is built and a part of the feasible domain not containing efficient solutions is truncated by adding this cut. A sample problem is solved using this algorithm, and the main practical advantages of the algorithm are indicated.multiobjective programming, integer programming, linear fractional programming, branch and cut

An exact method for a discrete multiobjective linear fractional optimization

Integer linear fractional programming problem with multiple objective MOILFP is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions, then generate an integer feasible solution. Using the reduced gradients of the objective functions, an efficient cut is built and a part of the feasible domain not containing efficient solutions is truncated by adding this cut. A sample problem is solved using this algorithm, and the main practical advantages of the algorithm are indicated

FLIP - Multiobjective Fuzzy Linear Programming Package

FLIP (Fuzzy LInear Programming) is a package designed to help in analysis of multiobjective linear programming (MOLP) problems in an uncertain environment. The uncertainty of data is modeled by L-R type fuzzy numbers. They can appear in the objective functions as well as on the both sides of the constraints. The input data to the FLIP package include the characteristics of the analyzed fuzzy MOLP problem, i.e., the number of criteria, constraints and decision variables, fuzzy cost coefficients for every objective and fuzzy coefficients of LHS and RHS for all constraints. The data loading is supported by a graphical presentation of fuzzy coefficients. The calculation is preceded by a transformation of the fuzzy MOLP problem into a multiobjective linear fractional program. It is then solved with an interactive method using a linear programming procedure as the only optimiser. In every iteration, one gets a series of solutions that are presented very clearly in a graphical and numerical form. In FLIP, interaction with the user takes place at two levels: first, when safety parameters have to be defined in the transformation phase, and second, when the associate deterministic problem is solved. The package is written in TURBO-Pascal and can be used on microcomputers compatible with IBM-PC XT/AT with hard disc and a graphic card

Integrated FANP-f-MIGP model for supplier selection in the renewable energy sector

The available integrated models for choosing efficient suppliers developed so far are mostly specific to companies with mass production capabilities. However, in some sectors involved in project-type manufacturing, the same decision-making criteria cannot be applied and, plus, there is no point in determining the quantity of orders. For instance, in wind power plant projects, a single turbine supplier needs to be selected for each project. This study proposes an integrated FANP-f-MIGP model that ensures the selection of the optimal supplier for each project by applying the model to an energy firm. The criteria specific to the selection of wind power plant turbine suppliers are established, and the criteria weights are obtained by fuzzy analytic network process (FANP). As a result of the analysis, the most important criterion of all is cost. These weights constitute the coefficients of the f-MIGP model’s objective function. Under the defined constraints, by minimizing cost and risk and maximizing quality and services of the firm, the selection of an optimal wind turbine supplier from three suppliers for each of three projects is ensured. This study contributes to the literature both by the specific criteria it establishes and its proposed integrated model which allows for the selection of the best supplier in wind turbine and similar project-based productions

Land use optimization using the fuzzy mathematical-spatial approach: a case study of Chelgerd watershed, Iran

In recent years, inappropriate land use, urban and industrial development along with different pollutions emanating from it gives rise to loss of natural resources and further leads to destructive floods, soil erosion, sedimentation and other various environmental, economic and social damages. Thus, management and planning are essential for the proper utilization, protection and revival of these resources. This study aimed to develop a mathematical-spatial optimum utilization model using FGP – MOLA in watershed including environmental and economic objectives while considering social issues. The results showed that the proposed model can lead to economic growth to 37% and decreasing the environmental damages to 2.4%. Under optimized condition, the area allocated to dry farming lands will decrease about 12% and gardens will increase about 423% and the other land uses remain unchanged too. In addition to, the results demonstrated the usefulness and efficiency of the proposed fuzzy model due to its flexibility and capability to simultaneously provide both optimum values and location of production resources

A rule-based method for scalable and traceable evaluation of system architectures

Despite the development of a variety of decision-aid tools for assessing the value of a conceptual design, humans continue to play a dominant role in this process. Researchers have identified two major challenges to automation, namely the subjectivity of value and the existence of multiple and conflicting customer needs. A third challenge is however arising as the amount of data (e.g., expert judgment, requirements, and engineering models) required to assess value increases. This brings two challenges. First, it becomes harder to modify existing knowledge or add new knowledge into the knowledge base. Second, it becomes harder to trace the results provided by the tool back to the design variables and model parameters. Current tools lack the scalability and traceability required to tackle these knowledge-intensive design evaluation problems. This work proposes a traceable and scalable rule-based architecture evaluation tool called VASSAR that is especially tailored to tackle knowledge-intensive problems that can be formulated as configuration design problems, which is demonstrated using the conceptual design task for a laptop. The methodology has three main steps. First, facts containing the capabilities and performance of different architectures are computed using rules containing physical and logical models. Second, capabilities are compared with requirements to assess satisfaction of each requirement. Third, requirement satisfaction is aggregated to yield a manageable number of metrics. An explanation facility keeps track of the value chain all along this process. This paper describes the methodology in detail and discusses in particular different implementations of preference functions as logical rules. A full-scale example around the design of Earth observing satellites is presented

Quadratic and nonlinear programming problems solving and analysis in fully fuzzy environment

AbstractThis paper presents a comprehensive methodology for solving and analyzing quadratic and nonlinear programming problems in fully fuzzy environment. The solution approach is based on the Arithmetic Fuzzy Logic-based Representations, previously founded on normalized fuzzy matrices. The suggested approach is generalized for the fully fuzzy case of the general forms of quadratic and nonlinear modeling and optimization problems of both the unconstrained and constrained fuzzy optimization problems. The constrained problems are extended by incorporating the suggested fuzzy logic-based representations assuming complete fuzziness of all the optimization formulation parameters. The robustness of the optimal fuzzy solutions is then analyzed using the recently newly developed system consolidity index. Four examples of quadratic and nonlinear programming optimization problems are investigated to illustrate the efficacy of the developed formulations. Moreover, consolidity patterns for the illustrative examples are sketched to show the ability of the optimal solution to withstand any system and input parameters changes effects. It is demonstrated that the geometric analysis of the consolidity charts of each region can be carried out based on specifying the type of consolidity region shape (such as elliptical or circular), slope or angle in degrees of the centerline of the geometric, the location of the centroid of the geometric shape, area of the geometric shape, lengths of principals diagonals of the shape, and the diversity ratio of consolidity points. The overall results demonstrate the consistency and effectiveness of the developed approach for incorporation and implementation for fuzzy quadratic and nonlinear optimization problems. Finally, it is concluded that the presented concept could provide a comprehensive methodology for various quadratic and nonlinear systems’ modeling and optimization in fully fuzzy environments

Fuzzy Linear Programming with Interval Type-2 fuzzy constraints

Doctorad

Decomposition's Dantzig-Wolfe applied to fuzzy multicommodity flow problems

We present, in this paper, a method for solving linear programming problems with fuzzy costs based on the classical method of decomposition's Dantzig-Wolfe. Methods using decomposition techniques address problems that have a special structure in the set of constraints. An example of such a problem that has this structure is the fuzzy multicommodity flow problem. This problem can be modeled by a graph whose nodes represent points of supply, demand and passage of commodities, which travel on the arcs of the network. the objective is to determine the flow of each commodity on the arcs, in order to meet demand at minimal cost while respecting the capacity constraints of the arcs and the flow conservation constraints of the nodes. Using the theory of fuzzy sets, the proposed method aims to find the optimal solution, working with the problem in the fuzzy form during the resolution procedure. (c) 2012 Elsevier B.V. All rights reserved.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Univ Campinas UNICAMP, Sch Elect & Comp Engn, BR-13083852 Campinas, SP, BrazilUNIFESP, ICT, BR-12231280 Sao Jose Dos Campos, SP, BrazilUNIFESP, ICT, BR-12231280 Sao Jose Dos Campos, SP, BrazilWeb of Scienc