Article ID: | iaor20011536 |
Country: | Netherlands |
Volume: | 124 |
Issue: | 3 |
Start Page Number: | 478 |
End Page Number: | 494 |
Publication Date: | Aug 2000 |
Journal: | European Journal of Operational Research |
Authors: | Clmaco Joo, Alves Maria Joo |
Keywords: | programming: linear, programming: branch and bound |
We propose an interactive reference point approach for multiple objective (mixed) integer linear programming problems that exploits the use of branch-and-bound techniques for solving the scalarizing programs. At each dialogue phase, the decision maker must specify a criterion reference point or just choose an objective function he/she wants to improve in respect to the previous efficient (nondominated) solution. In the latter case, a directional search is performed adjusting automatically the reference point used at each stage. Tchebycheff mixed-integer scalarizing programs are successively solved by branch-and-bound. Postoptimality techniques have been developed enabling the algorithm to profit from previous computations to solve the next scalarizing programs. The previous branch-and-bound tree is used as a starting point and operations of simplification and branching are then performed to obtain a new efficient solution. Computational results have shown that this approach is effective for carrying out directional or local searches for efficient solutions.