Mathematical Optimization Model Technique for Network Congestion Control in Global System for Mobile Communications

The introduction of Global System for Mobile Communication (GSM) in Nigeria is responsible for significant tremendous teledensity ratio increment, which results in network congestion in most busy areas. In this paper, we applied a Second Order Necessary Condition (a Mathematical Optimization Technique) as a tool in solving the problem of network congestion. One of the GSM providers; Mobile Telecommunication of Nigeria (MTN), was used to demonstrate the usefulness of Second Order Necessary Condition to the control of network congestion at Michael Okpara University of Agriculture, Umudike (MOUAU). Free flow of connection between mobile phone users at different locations within the area of investigation was established, hence congestion controlled.

Efficient force method for tetrahedron finite element analysis using mathematical optimization technique

Purpose The efficiency of the finite element analysis via force method depends on the overall flexibility matrix of the structure, while this matrix is directly affected from null bases vectors. As the null bases for an indeterminate structure are not unique, for an optimal analysis, the selected null bases should be sparse and banded corresponding to sparse, banded and well-conditioned flexibility matrix. This paper aims to present an efficient method for the formation of optimal flexibility matrix of finite element models comprising tetrahedron elements via mathematical optimization technique. Design/methodology/approach For this purpose, a linear mixed integer programming model is presented for finding sparse solution of underdetermined linear system, which is correspond to sparse null vector. The charged system search algorithm is improved and used to find the best generator for formation of null bases. Findings The efficiency of the present method is illustrated through some examples. The proposed method leads to highly sparse, banded and accurate null basis matrices. It makes an efficient force method feasible for the analysis of finite element model comprising tetrahedron elements. Originality/value The force method, in which the member forces are used as unknowns, can be appealing to engineers. The main problem in the application of the force method is the formation of a self-stress matrix corresponding to a sparse flexibility matrix. In this paper, the highly sparse, banded and accurate null basis matrices gains by using mathematical optimization technique.

Fuzzy Systems for Multicriteria Decision Making

One of the techniques used to support decisions in uncertain environments is the Fuzzy TOPSIS method. However, from crisp data, this method considers only one fuzzy set in their analysis, besides being a strictly mathematical optimization technique. This article proposes extensions to the original Fuzzy TOPSIS, exploring two distinct versions: to increase the method with the necessary resources for the mathematics process to consider the membership values of the input data in more than one fuzzy set and to aggregate to method the empiric knowledge of an expert represented through fuzzy rules. In such case, the method, named by Fuzzy F-TOPSIS (Fuzzy Flexible TOPSIS), is proposed with the objective of improving the Fuzzy TOPSIS ability to deal with uncertainty through the combination of the mathematical process involved in the original Fuzzy TOPSIS with the expert empirical knowledge. A case study is presented to validate the proposal.

Calibration of an Activated Sludge Model Based on Human Expertise and on a Mathematical Optimization Technique – a Comparison

Two alternative methods, which both can be used to estimate some of the kinetic parameters of the IAWPRC Activated Sludge Model Nr. 1, are compared. By one method, which is based on professional experience and expertise, the unknown parameter values are determined one after the other by a sequential procedure. By the other method, the parameter values are determined simultaneously by use of a mathematical optimization technique. Both methods allow a good fit of a set of 25 experimental oxygen respiration rate time-series and yield accurate estimates of the model parameters. The sequential procedure can readily be employed for the evaluation of single experiments. The optimization technique is more suitable for the evaluation of larger data sets and allows for additional analysis of the data.