The biobjective undirected two-commodity minimum cost flow problem |
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| Institution: | 1. Graduate Program in Electrical Engineering, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, 31270-901 Belo Horizonte, MG, Brazil;2. Department of Information Systems and Computing, Universidade Federal de Ouro Preto, St. Diogo de Vasconcelos 328, 35400-000 Ouro Preto, MG, Brazil;3. Department of Computing, Universidade Federal de Ouro Preto, St. Diogo de Vasconcelos 328, 35400-000 Ouro Preto, MG, Brazil;4. Department of Electrical Engineering, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, 31270-901 Belo Horizonte, MG, Brazil;1. Center for Innovation in Transport (CENIT), C/Jordi Girona 1-3, C3 S120, 08034 Barcelona, Spain;2. Barcelona Tech-UPC, Department of Statistics and Operations Research, C/Jordi Girona 1-3, C5, 08034 Barcelona, Spain;3. Barcelona Tech-UPC, Department of Transport and Regional Planning, C/Jordi Girona 1-3, B1, 08034 Barcelona, Spain;1. Departamento de Análisis Matemático, Universidad de La Laguna, 38200-La Laguna, Spain;2. Computational Science Laboratory, Department of Computer Science, Virginia Tech, Blacksburg, VA 24060, United States of America |
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| Abstract: | We address the two-commodity minimum cost flow problem considering two objectives. We show that the biobjective undirected two-commodity minimum cost flow problem can be split into two standard biobjective minimum cost flow problems using the change of variables approach. This technique allows us to develop a method that finds all the efficient extreme points in the objective space for the two-commodity problem solving two biobjective minimum cost flow problems. In other words, we generalize the Hu's theorem for the biobjective undirected two-commodity minimum cost flow problem. In addition, we develop a parametric network simplex method to solve the biobjective problem. |
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