MILP optimization constraint formulation I'm trying to find a sensible way to add constraint for my optimization problem.
Lets assume we have binary decision variables $x_i\in\{0,1\}$ and two constraints \begin{align*} \sum\limits_{i=1}^n x_i&\geq Y_1\\ \sum\limits_{i=1}^n x_i &\leq Y_2\end{align*}
How could I add constraints to my problems in such way that all decision variables that are $1$ have to be "grouped" together and there is no "holes" (zeroes) inside them. So if $n=5,Y_1=2,Y_2=3$ feasible solutions would be
\begin{align*}&\overbrace{\{1,1,0,0,0\}}^{Y_1\,\text{solutions}}\;\text{OR}\\
&\{0,1,1,0,0\}\;\text{OR}\\
&\vdots\\
&\{0,0,0,1,1\}
&\\
&\overbrace{\{1,1,1,0,0\}}^{Y_2\, \text{solutions}}\;\text{OR}\\
&\vdots\\
&\{0,0,1,1,1\}\end{align*}
And unfeasible solution would be for example
$$\{1,0,1,0,1\}$$
How could this kind of constraint be implemented?
 A: We see such a condition sometimes in power generation modeling: we want to limit the number of start-ups (switch from 0 to 1) of a generator. There is a smart formulation for this:
$$\begin{array}{l}
      z_i \ge x_i - x_{i-1} \\
      \sum_i z_i \le 1 \\
      z_i \in \{0,1\} 
   \end{array}
$$
Notes: 


*

*We only model the implication 'if $x_{i-1}=0$ and $x_i=1$ then $z_i=1$'. Otherwise we leave $z_i$ just floating. This actually works in this case: we don't need to add an implication to force $z_i$ to become zero. The bound on $\sum z_i$ takes care of that if needed. This may not be immediately obvious.   

*Actually we can even relax $z_i$ to be continuous between zero and one.

*The start period $x_1$ always needs some attention. (Does $x_1=1$ count or not?) It looks like you want to forbid $[1,0,1,1,1]$ so the first 1 needs to be counted as a start-up. I.e. we can assume $x_0=0$. In other words we have: 
$$
  \begin{array}{ll}
  z_i \ge x_i - x_{i-1} \> \forall i>1 \\
  z_1 \ge x_1 \\ 
  \sum_i z_i \le 1 \\
   z_i \in \{0,1\} 
 \end{array}
$$

*In practical models we often look up the last historic state $x_0$ in the database (this is not a variable but a fixed parameter). This will give us enough information to deal with $x_1$ correctly. 
