An interactive reference point approach for multiobjective mixed-integer programming using 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 ecient (nondominated) solution. In the latter case, a directional search is performed adjusting automatically the reference point used at each stage. Tchebyche€ mixed-integer scalarizing programs are successively solved by branch-and-bound. Postoptimality techniques have been developed enabling the algorithm to pro®t from previous computations to solve the next scalarizing programs. The previous branch-and-bound tree is used as a starting point and operations of simpli®cation and branching are then performed to obtain a new ecient solution. Computational results have shown that this approach is e€ective for carrying out directional or local searches for ecient solutions. Ó 2000 Elsevier Science B.V. All rights reserved.