An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.

Measures in Sectorization Problems

Sectorization means dividing a whole into parts (sectors), a procedure that occurs in many contexts and applications, usually to achieve some goal or to facilitate an activity. The objective may be a better organization or simplification of a large problem into smaller sub-problems. Examples of applications are political districting and sales territory division. When designing/comparing sectors some characteristics such as contiguity, equilibrium and compactness are usually considered. This paper presents and describes new generic measures and proposes a new measure, desirability, connected with the idea of preference.

Sectorization: measures and an electromagnetism based approach

Sectorization means dividing a set of basic units into sectors or parts, a procedure that occurs in several contexts, such as political, health and school districting, social networks and sales territory or airspace assignment, to achieve some goal or to facilitate an activity. This presentation will focus on three main issues: Measures, a new approach to sectorization problems and an application in waste collection. When designing or comparing sectors different characteristics are usually taken into account. Some are commonly used, and they are related to the concepts of contiguity, equilibrium and compactness. These fundamental characteristics will be addressed, by defining new generic measures and by proposing a new measure, desirability, connected with the idea of preference. A new approach to sectorization inspired in Coulomb’s Law, which establishes a relation of force between electrically charged points, will be proposed. A charged point represents a small region with specific characteristics/values creating relations of attraction/repulsion with the others (two by two), proportional to the charges and inversely proportional to their distance. Finally, a real case about sectorization and vehicle routing in solid waste collection will be mentioned.

Viver mais... Pensar o passado, viver o presente e sonhar o futuro Projeto de Investigação e Intervenção em Educação Social

Este relatório é o resultado descritivo e reflexivo de um Projeto de Educação e Intervenção Social, "Viver mais... Pensar o passado, viver o presente e sonhar o futuro", desenvolvido com um grupo de idosos do Centro de Caridade Nossa Senhora do Perpetuo Socorro. O projeto de investigação e de intervenção social seguiu as linhas metodológicas da Investigação Ação Participativa, em que os sujeitos são atores participativos e interventivos. Para o desenvolvimento deste projeto foi necessário recorrer a algumas técnicas de investigação, como a observação participante, conversas intencionais e análise documental, que facilitaram a recolha de informações, a análise da realidade e a intervenção desenvolvida. A partir da análise da realidade emergiram alguns problemas e necessidades que foram priorizados pelos sujeitos, daí surgiu o projeto de intervenção que aqui se apresenta com a finalidade de “Melhorar a qualidade de vida dos idosos do Centro de Dia do Centro de Caridade Nossa Senhora do Perpetuo Socorro, através da valorização das suas histórias de vida e melhoria das relações interpessoais”. Este projeto teve três grandes focos importantes que foi a recolha e construção das narrativas de vida de alguns participantes, a realização de vários encontros intergeracionais entre os idosos do Centro de Dia e as crianças do Jardim de Infância e o processo de consciencialização por parte dos idosos sobre a importância do grupo para o bem-estar pessoal, a gestão de conflitos e a melhoria das dinâmicas relacionais. Os resultados do projeto foram relevantes porque foram o produto de um processo reflexivo e de partilha entre os indivíduos, que favoreceu o desenvolvimento de um sentimento de utilidade e de valorização pessoal nos sujeitos, melhorando e fortalecendo assim as relações interpessoais entre eles.

A filter inexact-restoration method for nonlinear programming

A new iterative algorithm based on the inexact-restoration (IR) approach combined with the filter strategy to solve nonlinear constrained optimization problems is presented. The high level algorithm is suggested by Gonzaga et al. (SIAM J. Optim. 14:646–669, 2003) but not yet implement—the internal algorithms are not proposed. The filter, a new concept introduced by Fletcher and Leyffer (Math. Program. Ser. A 91:239–269, 2002), replaces the merit function avoiding the penalty parameter estimation and the difficulties related to the nondifferentiability. In the IR approach two independent phases are performed in each iteration, the feasibility and the optimality phases. The line search filter is combined with the first one phase to generate a “more feasible” point, and then it is used in the optimality phase to reach an “optimal” point. Numerical experiences with a collection of AMPL problems and a performance comparison with IPOPT are provided.