A fuzzy dual decomposition method for large-scale multiobjective nonlinear programming problems

In this paper, the authors propose a fuzzy dual decomposition method for large-scale multiobjective nonlinear programming problems (LS-MONLPs) with the block angular structure. By considering the vague nature of human judgements, they assume that the decision maker (DM) may have a fuzzy goal for each of the objective functions in he LS-MONLP. After eliciting the corresponding membership function for each of the objective functions through the interaction with the DM, an extended primal problem and the corresponding extended dual problem are formulated. Then a two-level optimization algorithm for the extended dual problem is proposed for deriving the compromise solution for the DM to the LS-MONLP. Based on the proposed algorithm, FORTRAN programs are developed and an illustrative numerical example is demonstrated.