Modified NSGA-II Based Interactive Algorithm for Linear Multiobjective Bilevel Programs

An interactive algorithm based on a modified NSGA-II is presented for linear multiobjective bilevel programs (LMOBLPs). The LMOBLP is converted into a linear multi-objective single-level implicit programming, when the lower-level multiobjective optimization problem (MOP) becomes a single-objective linear programming (LP) through an adaptive weighted sum approach. In the interactive algorithm, every individual in the population is updated according to the modified NSGA-II, while the related lower-level decision variable is obtained afterwards through the resolution of the lower-level linear scalarization problem for every given individual in the population. Some illustrative numerical instances are constructed to show that the interactive algorithm can reach a good convergence towards the entire Pareto front (PF).