The purpose of this article is to review the literature on the topic of deterministic vehicle routing problem (VRP) and to give a review on the exact and approximate solution techniques. More specifically the approximate (meta-heuristic) solution techniques are classified into: tabu search, simulated annealing, genetic algorithm, evolutionary algorithm, hybrid algorithm, and Ant Colony Opti...

1 Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor, 81310 Johor Bahru, Malaysia 2 Department of Mathematics, Faculty of Science, University of Kordofan, North Kordofan State, Elobeid 51111, Sudan 3 Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia, Johor, 81310 Johor Bahru, Malaysia 4 Department of Computer Science an...

The present paper proposes an approximation method to solve the problem of approximate nonlinear output regulation. In this approach, the solution of the regulator equations, consists of partial differential equations and an algebraic equation, is analytically approximated by Galerkin approximation method. The proposed method is general and can be applied on a wide class of nonlinear systems th...

The nonlinear dynamical system modeling the immobilized enzyme kinetics with Michaelis-Menten mechanism for an irreversible reaction without external mass transfer resistance is considered. Laplace transform homotopy perturbation method is used to obtain the approximate solution of the governing nonlinear differential equation, which consists in determining the series solution convergent to the...

‎In this paper we propose a method for computing approximations of solution of fuzzy fractional differential equations using fuzzy variational iteration method. Defining a fuzzy fractional derivative, we verify the utility of the method through two illustrative ‎examples.‎

Using a help system to make easier the CAS-user connection, we propose the problem of solving the equation of diffusion with variable coefficients. We transform the problem at the Laplace domain and we use the Bromwich integral and the residue theorem in order to do the inverse Laplace transform and then explicit solution is obtained.

Aims. We look for a simple analytic model to distinguish between stellar clusters undergoing a bimodal hydrodynamic solution from those able to drive only a stationary wind. Clusters in the bimodal regime undergo strong radiative cooling within their densest inner regions, which results in the accumulation of the matter injected by supernovae and stellar winds and eventually in the formation of...

We consider linear least squares problems, or linear systems that can be formulated into least squares problems, of very large dimension, such as those arising for example in dynamic programming (DP) and inverse problems. We introduce an associated approximate problem, within a subspace spanned by a relatively small number of basis functions, and solution methods that use simulation, importance...

Many numerical integration methods have been developed for predicting the evolution of the response of dynamical systems. Standard algorithms approach approximate the solution at a future time by introducing using a truncated power series representation that attempts to recover an n-th order Taylor series approximation, while only numerically sampling a single derivative model. An exact fifthor...

For strongly monotone variational inequality problems (VIP) convergence of an algorithm is investigated which, at each iteration k, adds a quadratic cut through an approximate analytic center xk of the subsequently shrinking convex body. First it is shown that the sequence of xk converges to the unique solution x ∗ of the VIP at O(1/ √ k). As an interesting detail note that — for increasingly a...