In this paper we consider equilibrium problem and introduce minimization problem such as equilibrium problem. We also investigated minimax inequalitiy of Ky Fan and we proved a minimax inequality of mapping with non-compact domain by using the coincidence theorem, then given a minimax inequality for mappings with noncompact domain. As its direct consequences some minimax inequalities and minimax theorems are obtained.

Economic roles in all areas particularly in the steel industry have been grown dramatically. In this article, a new look to the field of mathematical modeling of distributed systems in terms of fuzzy location model and the theory of fuzzy has been allocated and an integer linear programming is used. The distribution system generally includes three levels so that the first level suppliers of iron ore, mining, steel and so on are placed. The second level involves locating distribution centers consider so that a limited number of distribution centers can serve as stations and the third level of local warehouses or factories in steel production are using the integer programming technique, a fuzzy mathematical model for distributed systems is presented. The second level of distribution center location selection techniques based on Fuzzy Analytical Hierarchy Process (FAHP) is proposed and its output as input in integer programming model is used. It's worth mentioning presented model is analyzed by software of maple 12.

This paper contributes an efficient numerical approach for optimal control of switched system with time delay via Bezier curves. A simple transformation is first used to map the optimal control problem with varying switching times into a new optimal control problem with fixed switching times. Then, the Bezier curves is used to approximate the optimal control problem a NLP. The NLP could be solved by using known algorithms.

The present paper attempts to develop order reduction methods where the suggested reduction model consists of two phases. First, full order system is expanded by Hermite polynomials, then a set of parameters in a fixed structure are determined, whose values define the reduced order system. The values are obtained using Genetic Algorithm (GA) by minimizing the errors between the l first coefficients of Hermite polynomials expansion of full and reduced systems. To satisfy the stability, Routh criterion is used as constraints in optimization problem. To present the ability of the proposed method, three test systems are reduced. The results obtained are compared with other existing techniques. The results obtained show the accuracy and efficiency of the proposed method.

In this paper, by considering distributed optimal control over a PDE, a gradient based iterative Algorithm is proposed for solving is proposed and analyzed. Galerkin finite element method is used for solving underlying PDE, then the adjoint base technique for derivative computation to implementation of the optimal control issue in preconditioned Newton's conjugate gradient method isused. The interface and connection between quadratic programming extracted from discretizing the problem and Newton's type method, as well as the convergence rate of the algorithm in each iteration is established. Updating control values at discretization points in each iteration yields optimal control of the problem, where the corresponding state values at these points approximate the desired function. Numerical experiments are presented for illustrating the theoretical results.

The growing volume of spam emails has resulted in the necessity for more accurate and efficient email classification system. The purpose of this research is presenting an machine learning approach for enhancing the accuracy of automatic spam detecting and filtering and separating them from legitimate messages. In this regard, for reducing the error rate and increasing the efficiency, the hybrid architecture on feature selection has been used. Features used in these systems, are the body of text messages. Proposed system of this research has used the combination of two filtering models, Filter and Wrapper, with Information Gain (IG) filter and Support Vector Machine (SVM) wrapper as feature selectors. In addition, MNB classifier, DMNB classifier, SVM classifier and Random Forest classifier are used for classification. Finally, the output results of this classifiers and feature selection methods are examined and the best design is selected and it is compared with another similar works by considering different parameters. The optimal accuracy of the proposed system is evaluated equal to 99%.

The planning and scheduling activities are viewed profoundly important to generate successful plans and to maximize the utilization of scarce resources. Moreover, real life planning problems often involve several objectives that should be simultaneously optimized and real world environment is usually characterized by uncertain and incontrollable information. Thus, finding feasible and efficient plans is a considerable challenge. In this respect, the Multi-Objective Resource-Constrained Project-Scheduling problem (MRCPSP) tries to schedule activities and allocate resources in order to find an efficient course of actions to help the project manager and to optimize several optimization criteria. In this research, A Potts mean field feedback artificial neural network algorithm is developed and explored for the multi-objective resource constrained project scheduling problem. A convenient encoding of inequality constraints is achieved by means of multi-linear penalty function. An approximate energy minimum is obtained by iterating a set of Potts means field equation, is combination with annealing. Priority rule-based heuristics are the most widely used scheduling methods though their performance depends on the characteristics of the projects. To overcome this deficiency, a Potts mean field feedback artificial neural network is designed and integrated into the scheduling scheme so as to automatically select the suitable activity for each stage of project scheduling. Testing on Paterson’s classic test problems and comparison with other exact method how that the proposed Potts mean field annealing neural network based heuristic is able to improve the performance of project scheduling.

One of discussions in multivariable analysis is defining the factor and main vectors by calculating eigenvalue. In this paper we deal with an unbiased estimator of eigenvector and as a result we define eigenvalues. The purpose was introducing a new statistical method that is different from other numerical methods, which it defines the eigenvalue matrix. On the other hand, the efficiency of this method is up when the mass and dimension of matrix are high. Therefore, this is a low cast and efficient method in calculation. This paper covers some background of data compression and how Markov chain Monte Carlo (MCMC) and principal component analysis (PCA) has been and can be used for calculating eigenvalue.