Revista de Matemática Aplicada e Computacional

Volume 3, Emitir 4 (2014)

Artigo de Pesquisa

Two-stage Particle Swarm Optimization Algorithm for the Time Dependent Alternative Vehicle Routing Problem

Hsiao-Fan Wang and Yen-Yi Lee

This study considered a Time Dependent Alternative Vehicle Routing Problem (TDAVRP) in a multi-graph network (TDAVRP) and was formulated into a Mixed Integer Programming model. Due to its NP nature, an algorithm based on Particle Swarm Optimization (PSO) with local improvement was developed to speed up the solution procedure. By using different sets of Solomon’s benchmark problems and continuous travel time functions, the accuracy and efficiency of the two-stage PSO were evaluated. The computational results showed that the proposed algorithm is capable of deriving optimal or near optimal solutions in a short period of time when the size of the problems are small and is able to obtain feasible solutions within a reasonable time when solving the large problems which cannot be solved by ILOG CPLEX. In addition, Sensitivity Analysis was conducted to evaluate the performances of the parameters. The results indicated that the number of customers is a sensitive parameter and will influence the required number of vehicles, value of violations and percentage of alternative edges in the solution sets.

Artigo de Pesquisa

The Numerical Solution of Linear FredholmIntegro-Differential Equations via Parametric Iteration Method

Tamamgar M

In this paper a parametric iteration method (PIM) is purposed for solving Linear FredholmIntegro-differential equations (LFIDEs). The solution process is illustrated by some examples. Comparisons are made between PIM and exact solution and CAS wavelet method. The results show the simplicity and efficiency of PIM. Also, the convergence of this method is studied in this work

Artigo de Pesquisa

Second Hankel Determinant for a Subclass of Alpha Convex Functions

Gagandeep Singh and Gurcharanjit Singh

In this paper a sharp upper bound of second Hankel determinant 2 2 4 3 a a − a for the functions belonging to the class M (A, B) α of alpha convex functions is established. The class of alpha convex functions is an extended version of the classes of starlike functions and convex functions. By giving the particular values to alpha, it is easy to obtain the results of starlike and convex functions. The class discussed in this paper is an extended version of the class of alpha convex functions. By giving the particular values to A and B, the result of alpha convex functions can be easily obtained.

Artigo de Pesquisa

Forecasting of Traffic Jams at Disturbed Sections of High-ways

Igor Grabec

Disturbances of driving conditions on high-ways usually lead to evolution of traffic jams. Disturbances are often caused by traffic accidents, installed bottlenecks, adverse weather, etc, and result in a decreased road capacit. By using an estimate of a desired speed in the disturbed section the traffic information providers can forecast quantitatively the evolution of jams and inform the population about them in advance. The article presents a new mathematical method for this purpose. The corresponding intelligent unit first forecasts the traffic flow at a disturbed road section based upon records of traffic flow in the past. Forecast data are next mapped to characteristics of evolving jam by using the desired speed value and a new fundamental diagram of traffic flow. Performance of the method is demonstrated by forecasting the evolution of jam at the point of maximal traffic activity on a high-way in Slovenia.

Artigo de Pesquisa

A Novel Artificial Neural Network and an Improved Particle Swarm Optimization used in Splice Site Prediction

Wei Bin and Zhao Jing

The amount of DNA sequence data produced by several genomic projects had increased dramatically in recent years. One of the main goals of bioinformatics was to identify genes. A crucial part of the gene identification was to precisely detect the exon intron boundaries, i.e. the splice sites. This paper introduced a new type of artificial neural network (called NANN), which was designed specifically to solve the splice sites prediction problem. Moreover, the network connection weights of NANN were determined by an improved particle swarm optimization which was inspired by the wolves' activities circle. In addition, three types of encoding approaches were applied to generate the input for the NANN. Intensive experiments were presented in this paper, and the results showed that our algorithm was better than some current methods, that is, the NANN_IPSO was applicable to splice site prediction problem.

Artigo de Pesquisa

A General System of Regularized Non-convex Variational Inequalities

Lee BS and Salahuddin S

In this communication, we introduced a general system of regularized non-convex variational inequalities (GSRNVI) and established an equivalence between this system and fixed point problems. By using this equivalence we define a projection iterative algorithm for solving GSRNVI, we also proved existence and uniqueness of GSRNVI. The convergence analysis of the suggested iterative algorithm is studied.

Artigo de Pesquisa

A Generlization of the Enestrom-Kakeya Theorem

Pukhta MS

In this paper we obtain a generalization of well-known result of Eneström -Kakeya concerning the bounds for the moduli of the zeros of polynomials with complex coefficients which improve upon some results due to A. Aziz and Q.G Mohammad and others.

Artigo de Pesquisa

The Systematic Formation of High-Order Iterative Methods

Isaac Fried

Fixed point iteration and the Taylor-Lagrange formula are used to derive, some new, efficient, high-order, up to octic, methods to iteratively locate the root, simple or multiple, of a nonlinear equation. These methods are then systematically modified to account for root multiplicities greater than one. Also derived, are super-quadratic methods that converge contrarily, and super-linear and super-cubic methods that converge alteratingly, enabling us, not only to approach the root, but also to actually bound and bracket it.

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