The maintenance of a proper diversity is an important issue for the correct behavior of Evolutionary Algorithms (EAs). The loss of diversity might lead to stagnation in suboptimal regions, producing the effect known as "premature convergence". Several methods to avoid premature convergence have been previously proposed. Among them, the use of Multi-objective Evolutionary Algorithms (MOEAs) is a promising approach. Several ways of using MOEAs for single-objective optimization problems have been devised. The use of an additional objective based on calculating the diversity that each individual introduces in the population has been successfully applied by several researchers. Several ways of measuring the diversity have also been tested. In this work, the main weaknesses of some of the previously presented approaches are analyzed. Considering such drawbacks, a new scheme whose aim is to maintain a better diversity than previous approaches is proposed. The proposed approach is empirically validated using a set of well-known single-objective benchmark problems. Our preliminary results indicate that the proposed approach provides several advantages in terms of premature convergence avoidance. An analysis of the convergence in the average-case is also carried out. Such an analysis reveals that the better ability of our proposed approach to deal with premature convergence produces a reduction in the convergence speed in the average-case for several of the benchmark problems adopted.