Computational study of the relationships between feasible and efficient sets and an approximation

The computational difficulty of obtaining the efficient set in multi-objective programming, specially in nonlinear problems, suggests the need of considering an approximation approach to this problem. In this paper, we provide the computational results of the relationships between an approximation to the efficient set and the feasible and efficient sets. Random problem generation is considered for different sizes of the feasible set and we study the implications with respect to the number of objective functions and various kinds of objective functions. Computational experience with this approximation suggests that we obtain a substantial improvement when it increases the number of objective functions.