Tratamento da Imprecisão e da Incerteza em Programação Linear Multiobjectivo

Ref.: PRAXIS/2/2.1/MAT/465/94


Prof. Carlos Alberto Henggeler C. Antunes

Grupo de investigação (INESC):

Ana Rosa Borges

João Clímaco

Luís Dias

Maria João Alves

Solange Lucas

António Martins

José Craveirinha

Breve descrição

In the 1st year of this project studies regarding sensitivity analysis in multiobjective linear programming have been carried out. An interactive approach has been developed which enables to evaluate the robustness of nondominated solution with respect to uncertainty, stemming from distinct sources, underlying the decision process. This approach is based on the weight space and the developed techniques enable to study changes in the objective function coefficient matrix, in the right-hand side of the constraints, introduction of new constraints and introduction of new variables.
Other research directions have also been followed concerning extensions to deal with:

- partial information associated with the cost coefficients in shortest path problems; instead of selecting a "central" value for each parameter, this approach studies the sets of all the results compatible with a given set of consistent parameter combinations.
- multiobjective integer linear programming; an approach based on reference points and cutting planes has been developed, which enables to identify intervals of the reference point components which lead to the same nondominated solution.

In the 2nd year of the project special attention has been paid to the use of interval programming and fuzzy sets analysis to cope with uncertainty and imprecision in multiple objective mathematical programming decision models. A new interactive approach to multiobjective linear programming based on fuzzy sets has been developed, which enables to evaluate the stability of (fuzzy) nondominated solutions according to the values of the membership functions. As the sensitivity analyses techniques developed in the 1st year, this approach is also based on the decomposition of the weight space (which is now analytically dependent on the membership functions). The integration of these two approaches will be exploited. As far as interval programming is concerned, a study has been initiated to evaluate the stability of nondominated solutions when the models parameters are given in the form of intervals.
Moreover, promising research directions have also been pursued concerning extensions to deal with (besides those referred to above):

- multiobjective integer linear programming based on branch-and-bound tehniques;
- study of ELECTRE (Elimination and Choice Translating Reality) method's credibility indices under partial information.