A zero-sum nonlinear quadratic differential games with closed-loop feedback solution by homotopy analysis method

In this paper, we consider zero-sum nonlinear quadratic differential games which the coefficients of the quadratic form are quadratic matrix, function of the state variable. Dynamic constraints are represented bilinear differential systems of the for

A new DEA approach to rank alternatives in MCDA

One of the principal subjects in multiple criteria decision analysis is ranking alternatives. Here, we present a new method to rank alternatives by using data envelopment analysis. In this paper, one ranking method is proposed based on applying an artificial alternative called aggregate alternative. The method is based on the fact that one efficient alternative with a better performance has stronger effects on the group of other alternatives. That means its deletion forces the remaining alternatives to get smaller efficiency. The described idea in this paper is inspired of Lotfi and et al. (2011). One feature of the proposed method is that it does not need to determine the weight of the prior. Two examples are used to illustrate how the proposed method works in actual practices, and the results are compared with those obtained from the TOPSIS method

An optimal control approach for solving an inverse heat source problem applying shifted Legendre polynomials

This study addresses the inverse issue of identifying the space-dependent heat source of the heat equation, which is stated using the optimal con-trol framework. For the numerical solution of this class of problems, an approach based on shifted Legendre polynomials and the associated oper-ational matrix is presented. The approach turns the primary problem into the solution of a system of nonlinear algebraic equations. To do this, the temperature and heat source variables are enlarged in terms of the shifted Legendre polynomials with unknown coefficients employed in the objectivefunction, inverse problem, and initial and Neumann boundary conditions. When paired with their operational matrix, these basis functions provide a quadratic optimization problem with linear constraints, which is then solved using the Lagrange multipliers approach. To assess the method’s efficacy and precision, two examples are provided

Supply chain management problem modelling in hesitant fuzzy environment

Complex nature of the current market is often caused by uncertainties, data uncertainties, their manner of use, and differences in managers' viewpoints. To overcome these problems, Hesitant Fuzzy Sets (HFSs) can be useful as the extension of fuzzy set theory, in which the degree of membership of an element can be a set of possible values and provide greater flexibility in design and, thus, model performance. The power of this application becomes clear when different decision-makers tend to independently record their views. In most real-world situations, there are several goals for managers to achieve the desired performance. Therefore, in this study, a description of the solution of the Hesitant Fuzzy Linear Programming (HFLP)  problem for solving hesitant fuzzy multi-objective problems is considered. In the following, the multi-objective and three-level supply chain management problem is modeled with the hesitant fuzzy approach. Then, with an example, the flexibility of the model responses is evaluated by the proposed method. The hesitant fuzzy model presented in this study can be extended to other supply chain management problems

An artificial neural network-based method for the optimal control problem governed by the fractional parabolic equation

In this paper, we propose an artificial neural network model (ANN) to solve a partial differential equation (PDE) constrained optimization problem. Here, the discretize then optimize approach is used. At first, the Legendre polynomials are used to discretize the optimization problem and transform it into a quadratic optimization problem with linear constraint. Then an ANN model is proposed to solve the obtained quadratic optimization problem. Finally, several examples are presented to illustrate the abilities and efficiency of the proposed approach