*3.1. Inequality Based Metrics*

Inequality based metrics comprise metrics that favor the best off individual with the purpose of securing at least one objective in the society to be as good off as possible. This could happen at the expense of all other individuals in the society.

## Elitist Social Welfare

The elitist social welfare metric strives to ensure that one individual is favored to the extent possible. The elitist social welfare metric is defined in Equation (2).

$$f\_{EL}(\mathbb{C}) = \min \{ q\_{t\_i|\mathbb{C}}' \mid i \in n \} \tag{2}$$

Equation (2) shows how the elitist social welfare metric ranks solutions based on the normalized cost of the best off objective. Hence, this metric prefers solution *C* over solution *C* if and only if ↑ *q <sup>t</sup>*1,*<sup>C</sup>* < ↑ *q <sup>t</sup>*1,*C* , where ↑ *q <sup>C</sup>* represents the reordering of the normalized cost value vector *q <sup>C</sup>* = {*q <sup>t</sup>*1,*C*, *q <sup>t</sup>*2,*C*,..., *q tn*,*C*} in ascending order.
