An interactive approach for solving multi-objective nonlinear programming and its application to cooperative continuous static games

In this paper, an interactive approach for solving multi- objective nonlinear programming (MONLP) problem is introduced. This approach is combined with the Reference Direction (RD) introduced by Narula et al. (1993) and the Attainable Reference Point (ARP) method introduced by Wang et al. (2001). In the interactive approach, we still starting with a weak efficient solution as the first step and use the corresponding objective values to improve the weighting coefficients of the augmented Lexicographic Weighted Tchebycheff problem and hence modify the reference point in the case of an unsatisfactory solution for the decision maker (DM) he (she) wishes. Cooperative continuous static game is introduced as an application and its solution is obtained under the proposed interactive approach. Finally, a numerical example is given to the utility of our proposed method.