Multi-Objective GPP with General Negative Degree of Difficulty: New Insights

The methods for solving nonlinear multi-objective optimization are divided into three major categories: methods with apriori articulation of preferences, methods with a posteriori articulation of preferences, and methods with no articulation of preferences. Really there is no single approach is superior. In this paper, a combination between two well known approaches has been used to solve multi-objective GP problems having negative degree of difficulty. First, we use an alternative procedure for converting GP problem having negative degree of difficulty to positive degree of difficulty; second we proposed to discuss all available cases for any number of multi-objective in GP problems using Lexicographic method. This avoids the difficulty of non-differentiability of the dual objective function in the classical methods.