Fuzzy linear programming problems : models and solutions

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, alpha-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately

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

Improved genetic algorithms by means of fuzzy crossover operators for revenue management in airlines

Abstract: Revenue Management is an economic policy that increases the earned profit by adjusting the service demand and inventory. Revenue Management in airlines correlates with inventory control and price levels in different fare classes. We focus on pricing and seat allocation problems in airlines by introducing a constrained optimization problem in Binary Integer Programming (BIP) formulation. Two BIP problems are represented. Moreover, some improved Genetic Algorithms (GAs) approaches are used to solve these problems. We introduce new crossover operators that assign a Fuzzy Membership Function to each parent in GAs. We achieve better outputs with new methods that take lower calculation times and earn higher profits. Three different test problems in different scales are selected to evaluate the effectiveness of each algorithm. This paper defines new crossover operators that help to reach better solutions that take lower calculation times and more earned profits

Solving the four index fully fuzzy transportation problem

In this paper, we will solve the four index fully fuzzy transportation problem (textit{FFTP$_{4}$}) with some adapted classical methods. All problem\u27s data will be presented as fuzzy numbers. In order to defuzificate these data, we will use the ranking function procedure. Our method to solve the textit{FFTP$_{4}$} composed of two phases; in the first one, we will use an adaptation of well-known algorithms to find an initial feasible solution, which are the least cost, Russell\u27s approximation and Vogel\u27s approximation methods. In the second phase, we will test the optimality of the initial solution, if it is not optimal, we will improve it. A numerical analysis of the proposed methods is performed by solving different examples of different sizes; it is determined that they are stable, robust, and efficient. A proper comparative study between the adapted methods identifies the suitable method for solving textit{FFTP$_{4}$}

A reliability-and-cost-based fuzzy approach to optimize preventive maintenance scheduling for offshore wind farms

We study the preventive maintenance scheduling problem of wind farms in the offshore wind energy sector which operates under uncertainty due to the state of the ocean and market demand. We formulate a fuzzy multi-objective non-linear chance-constrained programming model with newly-defined reliability and cost criteria and constraints to obtain satisfying schedules for wind turbine maintenance. To solve the optimization model, a 2-phase solution framework integrating the operational law for fuzzy arithmetic and the non-dominated sorting genetic algorithm II for multi-objective programming is developed. Pareto-optimal solutions of the schedules are obtained to form the trade-offs between the reliability maximization and cost minimization objectives. A numerical example is illustrated to validate the model

Decision support model for the selection of asphalt wearing courses in highly trafficked roads

The suitable choice of the materials forming the wearing course of highly trafficked roads is a delicate task because of their direct interaction with vehicles. Furthermore, modern roads must be planned according to sustainable development goals, which is complex because some of these might be in conflict. Under this premise, this paper develops a multi-criteria decision support model based on the analytic hierarchy process and the technique for order of preference by similarity to ideal solution to facilitate the selection of wearing courses in European countries. Variables were modelled using either fuzzy logic or Monte Carlo methods, depending on their nature. The views of a panel of experts on the problem were collected and processed using the generalized reduced gradient algorithm and a distance-based aggregation approach. The results showed a clear preponderance by stone mastic asphalt over the remaining alternatives in different scenarios evaluated through sensitivity analysis. The research leading to these results was framed in the European FP7 Project DURABROADS (No. 605404).The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007–2013) under Grant Agreement No. 605404