WSE optimizer

Let $W$, $S$, $E$ be the collection of all permissible weapon, secondary, and emblem configurations, respectively. Then
$\Omega := W \times S \times E$
is the collection of all possible combinations of weapons, secondaries, and emblems. Let
$\varphi: \Omega \to \Gamma$
be the final damage function which depends on a user's given base stats. Finally, let $\sigma$ be the map which sends singletons to their corresponding preimages under $\varphi$. Identifying $\gamma \in \Gamma$ with $\{\gamma\}$ gives the map
$\sigma: \Gamma \to \mathcal{P}(\Omega)$.
Then the output of the WSE optimizer consists of the tuples
$\varphi(\omega) \times \sigma(\varphi(\omega))$.