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An interactive reference point approach for multiobjective mixed-integer programming using branch-and-bound
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DOI：10.1016/S0377-2217(99)00183-6.png)
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Abstract
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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 serving 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 tatter 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. (C) 2000 Elsevier Science B.V. All rights reserved.
Keywords:
multi criteria analysis
mixed-integer linear programming
reference points
Tchebycheff metric
branch-and-bound
sensitivity analysis
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