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

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

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

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

A critical review of the approaches to optimization problems under uncertainty

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Science of Bilkent University, 2001.Thesis (Master's) -- Bilkent University, 2001.Includes bibliographical references leaves 58-72.In this study, the issue of uncertainty in optimization problems is studied. First of all, the meaning and sources of uncertainty are explained and then possible ways of its representation are analyzed. About the modelling process, different approaches as sensitivity analysis, parametric programming, robust optimization, stochastic programming, fuzzy programming, multiobjective programming and imprecise optimization are presented with advantages and disadvantages from different perspectives. Some extensions of the concepts of imprecise optimization are also presented.Gürtuna, FilizM.S

Field D* pathfinding in weighted simplicial complexes

Includes abstract.Includes bibliographical references.The development of algorithms to efficiently determine an optimal path through a complex environment is a continuing area of research within Computer Science. When such environments can be represented as a graph, established graph search algorithms, such as Dijkstra’s shortest path and A*, can be used. However, many environments are constructed from a set of regions that do not conform to a discrete graph. The Weighted Region Problem was proposed to address the problem of finding the shortest path through a set of such regions, weighted with values representing the cost of traversing the region. Robust solutions to this problem are computationally expensive since finding shortest paths across a region requires expensive minimisation. Sampling approaches construct graphs by introducing extra points on region edges and connecting them with edges criss-crossing the region. Dijkstra or A* are then applied to compute shortest paths. The connectivity of these graphs is high and such techniques are thus not particularly well suited to environments where the weights and representation frequently change. The Field D* algorithm, by contrast, computes the shortest path across a grid of weighted square cells and has replanning capabilites that cater for environmental changes. However, representing an environment as a weighted grid (an image) is not space-efficient since high resolution is required to produce accurate paths through areas containing features sensitive to noise. In this work, we extend Field D* to weighted simplicial complexes – specifically – triangulations in 2D and tetrahedral meshes in 3D