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 has introduced. This approach combines with the Reference Direction (RD) introduced by Narula et al. [10] and the Attainable Reference Point (ARP) method introduced by Wang et al. [17]. In the interactive approach, we still start 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 Programming (LWTP) problem; hence we modify the reference point in the case of an unsatisfactory solution for the Decision Maker (DM) he (she) wishes. The cooperative continuous static game is introduced as an application and hence the stability set of the first kind is determined corresponding to its solution through the interactive approach. Finally, a numerical example has given to the utility of our interactive approach.