Experiências computacionais com modelos de fluxo para múltiplos produtos com funções de custo não lineares e não separáveis

 

Luis Ernesto Torres Guardia ^†

João Carlos C. B. Soares de Mello ^†

 

^† Departamento de Engenharia de Produção – Universidade Federal Fluminense, Brasil

tepletg@vm.uff.br

jcsmello@pesquisador.cnpq.br

http://www.uff.br/decisao

 

 

Title: Computational experiments with flow models for multicommmodity using non linear and non separable cost functions.

 

Abstract

In this paper we present the study and the numerical implementation of the primal-dual interior-point method for the solution of the convex nonlinear multicommodity network flow problem. At each iteration of the interior-point method, we solve the corresponding linear system, expressed by the augmented-indefinite system,  using an indefinite preconditioned conjugate gradient algorithm combined with the AINV algorithm. We conduct some numerical experiments for networks of different dimensions and number of products and for some nonlinear costs. The computational results show the effectiveness of the interior-point method for this class of network problem.

Keywords: Nonlinear programming. Interior-point method. Network flow problem

 

 

Resumo

Neste trabalho são apresentados o estudo e a implementação numérica do método de pontos interiores primal-dual para o problema não linear convexo de fluxo em rede com múltiplos produtos. Em cada iteração do método de pontos interiores, resolve-se o correspondente sistema linear, expresso na forma de aumentado indefinido usando o algoritmo do gradiente conjugado com um pré-condicionador indefinido apropriado combinado com o algoritmo AINV. Foram realizados alguns testes numéricos para redes de várias dimensões e vários produtos, com funções de custos não lineares. Os resultados computacionais mostram a eficiência do método de pontos interiores para o caso de fluxo em rede para múltiplos produtos.

 

 

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