Multiple Roots of Systems of Equations by Repulsion Merit Functions

In this paper we address the problem of computing multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function. The search procedure for a global minimizer of the merit function is carried out by a metaheuristic, known as harmony search, which does not require any derivative information. The multiple roots of the system are sequentially determined along several iterations of a single run, where the merit function is accordingly modified by penalty terms that aim to create repulsion areas around previously computed minimizers. A repulsion algorithm based on a multiplicative kind penalty function is proposed. Preliminary numerical experiments with a benchmark set of problems show the effectiveness of the proposed method.

Finding a school technological partner: a multicriteria method for school information system producer selection

The choice of an information systems is a critical factor of success in an organization's performance, since, by involving multiple decision-makers, with often conflicting objectives, several alternatives with aggressive marketing, makes it particularly complex by the scope of a consensus. The main objective of this work is to make the analysis and selection of a information system to support the school management, pedagogical and administrative components, using a multicriteria decision aid system – MMASSITI – Multicriteria Method- ology to Support the Selection of Information Systems/Information Technologies – integrates a multicriteria model that seeks to provide a systematic approach in the process of choice of Information Systems, able to produce sustained recommendations concerning the decision scope. Its application to a case study has identi- fied the relevant factors in the selection process of school educational and management information system and get a solution that allows the decision maker’ to compare the quality of the various alternatives.

Testing Nelder-Mead Based Repulsion Algorithms for Multiple Roots of Nonlinear Systems via a Two-Level Factorial Design of Experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.