We can force the vegetarian pizza and the histamine-free pizza to be different with:

V_{j} + Y_{j} = 1 \forall j

We can force that one pizza is histamine free with:

\sum_{j}V_{j} = 1

\sum_{i} h_{i}*X_{i,j} \leq 6 - 6V_{j} \forall j

We can force that two pizzas do not share more than 2 ingredients with:

new variable W_{i,j,k} if two pizzas j and k share an ingredient i (0,1)

X_{i,j} + X_{i,k} \leq 1 + W_{i,j,k}

\sum_{i} W_{i,j,k} \leq 2 \forall j, k>j

We can force that any ingredient is not on two or more pizzas with:

\sum_{i} X_{i,j} \leq 2 \forall j

We can for that at least half of the ingredients are vegetarian with:

\sum_{i} (1-v_{i})X_{i,j} \leq 0.5 \sum_{i} X_{i,j}

We can force that two pizzas do not share more than 2 ingredients with:

X_{i,j} + X_{i,k} \geq W_{i,j,k}

\sum_{i} W_{i,j,k} \leq 2 \forall j, k>j