  In this paper we consider multi-objective optimization problems over a box.
The problem is very relevant and several computational approaches have been
proposed in the literature. They broadly fall into two main classes:
evolutionary methods, which are usually very good at exploring the feasible
region and retrieving good solutions even in the nonconvex case, and descent
methods, which excel in efficiently approximating good quality solutions. In
this paper, first we confirm, through numerical experiments, the advantages and
disadvantages of these approaches. Then we propose a new method which combines
the good features of both. The resulting algorithm, which we call Non-dominated
Sorting Memetic Algorithm (NSMA), besides enjoying interesting theoretical
properties, excels in all of the numerical tests we performed on several,
widely employed, test functions.
