Journal of Mathematical Modeling
Volume:10 Issue: 3, Summer 2022

A multi-agent single machine scheduling problem with transportation constraints is studied. We assume that there are several independent agents placed in different geographical locations, each of them has several orders and each order includes different types of products. We use a simple and effective model to obtain maximum profit of the products. To have desired on-time deliveries, the minimization of the transportation costs and total tardiness costs are considered as objective functions. The main idea of this research is to develop a simple and integrated scheduling and transportation model which can be applied in many factories, chain stores, and so on. In order to solve this problem, a mixed integer linear programming (MILP) model is presented. Moreover, since solving large instances of the proposed MILP model is very time-consuming, a heuristic algorithm is presented. Implementing of two approaches on a variety of datasets show that the heuristic algorithm can provide good-quality solutions in very short time.

In this paper, we use the rational radial basis function (RRBF) method for solving the one dimensional Sine-Gordon (SG) equation, especially the case with steep front or sharp gradient solutions. The time and spatial derivatives are approximated by the finite difference and RRBF method, respectively. Some numerical experiments are given in both perturbed and unperturbed cases, and are compared with some other numerical methods to confirm the good accuracy of the presented method. The conservation law of energy is also investigated.

In this work, we study a data visualization problem which is classified in the field of shape-preserving interpolation. When   function  is known to be bounded, then it is  natural to expect its interpolant to adhere boundedness. Two spline-based techniques are proposed to handle this kind of problem. The proposed methods   use quadratic splines as basis and involve solving a linear programming or a mixed integer linear  programming problem which gives $C^1$ interpolants. An energy minimization technique is employed to gain the optimal smooth solution. The reliability  and  applicability of  the proposed techniques  have been illustrated through examples.

In this paper, new upper bounds for the ultraspherical coefficients of differentiable functions are presented. Using partial sums of ultraspherical polynomials, error approximations are presented to estimate differentiable functions. Also, an error estimate of the Gauss-Jacobi quadrature is obtained and we state an upper bound for Legendre coefficients which is sharper than upper bounds proposed so far. Numerical examples are given to assess the efficiency of the presented theoretical results.

In a linear optimization problem, objective function, coefficients matrix, and the right-hand side might be perturbed with distinct parameters independently. For such a problem, we are interested in finding the region that contains the origin, and the optimal partition remains invariant. A computational methodology is presented here for detecting the boundary of this region. The cases where perturbation occurs only in the coefficients matrix and right-hand side vector or the objective function are specified as special cases. The findings are illustrated with some simple examples.

In this paper, we introduce and investigate a new definition for the density function of fuzzy random variables. Then, based on this definition, we give a new viewpoint on aging properties. To do this end, the concepts of the hazard rate function and mean residual function are investigated for the Exponential fuzzy random variable. Also, we obtain  the aging properties of  new Exponential fuzzy random variables based on existing methods.  Finally, using a practical example, we illustrate the proposed approach and show that  the performance of proposed  approach is better than two other existing  methods.

Classical image deconvolution seeks an estimate of the true image when the blur kernel or the point spread function (PSF) of the blurring system is known a priori. However, blind image deconvolution addresses the much more complicated, but realistic problem where the PSF is unknown. Bayesian inference approach with appropriate priors on the image and the blur has been used successfully to solve this blind problem, in particular with a Gaussian prior and a joint maximum a posteriori (JMAP) estimation. However, this technique is unstable and suffers from significant ringing artifacts in various applications. To overcome these limitations, we propose a regularized version using $H^1$ regularization terms on both the sharp image and the blur kernel. We present also useful techniques for estimating the smoothing parameters.  We were able to derive an efficient algorithm that produces high quality deblurred results compared to some well-known methods in the literature.

In this paper, we present a new hybrid conjugate gradient method for unconstrained optimization that possesses sufficient descent property independent of any line search. In our method, a convex combination of the Hestenes-Stiefel (HS) and the Fletcher-Reeves (FR) methods, is used as the conjugate parameter and the hybridization parameter is determined by minimizing the distance between the hybrid conjugate gradient direction and direction of the three-term HS method proposed by M. Li (emph{A family of three-term nonlinear conjugate gradient methods close to the memoryless BFGS method,} Optim. Lett. textbf{12} (8) (2018) 1911--1927). Under some standard assumptions, the global convergence property on general functions is established. Numerical results on some test problems in the CUTEst library illustrate the efficiency and robustness of our proposed method in practice.

This paper is concerned with the stochastic linear quadratic regulator (LQR) optimal control problem in which dynamical systems have control-dependent diffusion coefficients. In fact, providing the solution to this problem leads to solving a matrix Riccati differential equation as well as a vector differential equation with boundary conditions. The present work mainly  proposes not only a novel method but also an efficient fixed-point scheme based on the spline interpolation for the numerical solution to the stochastic LQR problem. Via implementing the proposed method to the corresponding differential equation of the stochastic LQR optimal control problem, not only is the numerical solution gained, but also a suboptimal control law is obtained. Furthermore, the method application is illustrated by means of an optimal control example with the financial market problems, including two investment options.

In this article, a first-order iterative Lasota-Wazewska model with a  nonlinear delayed harvesting term is discussed. Some sufficient conditions  are derived for proving the existence, uniqueness and continuous dependence  on parameters of positive periodic solutions with the help of  Krasnoselskii's and Banach fixed point theorems along with the Green's  functions method. Besides, at the end of this work, three examples are  provided to show the accuracy of the conditions of our theoretical findings which are completely innovative and complementary to some earlier  publications in the literature.

Orthogonal neural networks (ONNs) are some  powerful types of the neural networks in the modeling of non-linearity. They are constructed by the usage  of orthogonal functions sets. Piecewise continuous orthogonal functions (PCOFs) are some important classes of orthogonal functions. In this work, based on a set of hyperbolic PCOFs, we propose the hyperbolic ONNs  to identify the nonlinear dynamic systems. We train the proposed neural models with the stochastic gradient descent learning algorithm. Then, we prove the stability of this algorithm. Simulation results show the efficiencies of proposed model.

This paper aims to advance the radial basis function method for solving space-time variable-order fractional partial differential equations. The fractional derivatives for time and space are considered in the Coimbra and the Riemann-Liouville sense, respectively. First, the time-variable fractional derivative is discretized through a finite difference approach. Then, the space-variable fractional derivative is approximated by radial basis functions. Also, we advance the Rippa algorithm to obtain a good value for the shape parameter of the radial basis functions. Results obtained from numerical experiments have been compared to the analytical solutions, which indicate high accuracy and efficiency for the proposed scheme.