*3.3. Evaluation of Multi-Objective Optimization Pareto Fronts*

We will compare the Pareto fronts obtained by each MOO algorithm using normalized hypervolume and relative coverage. These methods are popular for evaluating the quality of a Pareto front. The Pareto front normalized hypervolume is computed as follows:

$$\text{Normalized Hypervolume} = \frac{\sum\_{j=1}^{N\_p} \prod\_{i=1}^{M} f\_{ji}}{N\_p} \tag{10}$$

where *M* is the number of objectives, *fji* is the value of the *i*-th objective function of the *j*-th Pareto point, and *Np* is the number of Pareto points.

Another way to compare Pareto sets is to compute the coverage of one Pareto set relative to a second Pareto set. This metric is determined by the number of solutions in the first Pareto set that are weakly dominated by at least one solution in the second Pareto set [21]. A smaller number for normalized hypervolume and relative coverage indicates better performance.
