Two-phases Method and Branch and Bound Procedures to Solve the Bi–objective Knapsack Problem

Authors:
M. Visée;J. Teghem;M. Pirlot;E. L. Ulungu
Affiliations:
Laboratory of Mathematics and Operational Research, Faculté Polytechnique de Mons, 9, rue de Houdain B-7000 Mons, Belgium;Laboratory of Mathematics and Operational Research, Faculté Polytechnique de Mons, 9, rue de Houdain B-7000 Mons, Belgium;Laboratory of Mathematics and Operational Research, Faculté Polytechnique de Mons, 9, rue de Houdain B-7000 Mons, Belgium;Laboratory of Mathematics and Operational Research, Faculté Polytechnique de Mons, 9, rue de Houdain B-7000 Mons, Belgium
Venue:
Journal of Global Optimization
Year:
1998

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Abstract

The classical 0–1 knapsack problem is considered with twoobjectives. Two methods of the “two–phases” type aredeveloped to generate the set of efficient solutions. In the first phase,the set of supported efficient solutions is determined by optimizing aparameterized single-objective knapsack problem. Two versions are proposedfor a second phase, determining the non-supported efficient solutions: bothversions are Branch and Bound approaches, but one is “breadthfirst”, while the other is “depth first”. Extensivenumerical experiments have been realized to compare the results of bothmethods.