Solving bicriteria 0-1 knapsack problems using a labeling algorithm

Authors:
M. Eugénia Captivo;João Clìmaco;José Figueira;Ernesto Martins;José Luis Santos
Affiliations:
DEIO-CIO, Faculdade de Ciencia, Universidade de Lisboa, Campo Grande, Bloco C2 1749-016 Lisboa, Portugal;Faculdade de Economia, Universidade de Coimbra, Av. Dias da Silva, 165, 3004-512, Coimbra, Portugal and INESC-Coimbra, Rua Antero de Quental, 199, 3000-033, Coimbra, Portugal;Faculdade de Economia, Universidade de Coimbra and INESC-Coimbra, Coimbra, Portugal and LAMSADE, Universitè Paris-Dauphine, Paris, France;Departmento de Matemática, Universidade de Coimbra, Apartado 3008, 3001-454, Coimbra, Portugal;Departmento de Matemática, Universidade de Coimbra, Apartado 3008, 3001-454, Coimbra, Portugal and CISUC, Departamento de Matemática, Universidade de Coimbra, Coimbra, Portugal
Venue:
Computers and Operations Research
Year:
2003

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Abstract

This paper examines the performances of a new labeling algorithm to find all the efficient paths (or non-dominated evaluation vectors) of the bicriteria 0-1 knapsack problem. To our knowledge this is the first time a bicriteria 0-1 knapsack is solved taking advantage of its previous conversion into a bicriteria shortest path problem over an acyclic network. Computational experiments and results are also presented regarding bicriteria instances of up to 900 items. The algorithm is very efficient for the hard bicriteria 0-1 knapsack instances considered in the paper.