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<p style="margin:0in;font-family:calibri;font-size:11pt">Hi, </p>

<p style="margin:0in;font-family:calibri;font-size:11pt"> </p>

<p style="margin:0in;font-family:calibri;font-size:11pt">I am trying to build
a MILP. </p>

<p style="margin:0in;font-family:calibri;font-size:11pt"> </p>

<p style="margin:0in;font-family:calibri;font-size:11pt">I need to set the
number of linear constraints in the model as a decision variable.</p>

<p style="margin:0in;font-family:calibri;font-size:11pt"> </p>

<p style="margin:0in;font-family:calibri;font-size:11pt">For example: </p>

<p style="margin:0in;font-family:calibri;font-size:11pt"> </p>

<p style="margin:0in;font-family:calibri;font-size:11pt">max 8* x1 + 6 *
x2  - x3</p>

<p style="margin:0in;font-family:calibri;font-size:11pt">s.t. </p>

<p style="margin:0in;font-family:calibri;font-size:11pt">     
constraint 1 : x1 + x2 <= 29</p>

<p style="margin:0in;font-family:calibri;font-size:11pt">     
constraint 2 : x1 - x2 <= 5</p>

<p style="margin:0in;font-family:calibri;font-size:11pt">     
constraint 3 : x2 + x3 <= 56</p>

<p style="margin:0in;font-family:calibri;font-size:11pt"> </p>

<p style="margin:0in;font-family:calibri;font-size:11pt">I would like to make
the all three constraints as candidates such that </p>

<p style="margin:0in;font-family:calibri;font-size:11pt"> </p>

<p style="margin:0in;font-family:calibri;font-size:11pt">1. the objective
maximized. </p>

<p style="margin:0in;font-family:calibri;font-size:11pt">2. At least one
constraint must be active</p>

<p style="margin:0in;font-family:calibri;font-size:11pt">3. How many of
candidate constraints are active depends on the objective optimization value.</p>

<p style="margin:0in;font-family:calibri;font-size:11pt"> </p>

<p style="margin:0in;font-family:calibri;font-size:11pt">I know this may have
exponential complexity because for 3 candidates, I can have 2^3 = 8
combinations of constraints.</p>

<p style="margin:0in;font-family:calibri;font-size:11pt"> </p>

<p style="margin:0in;font-family:calibri;font-size:11pt">Are there some ways
to out all candidate in the model and solve it for one run to get the optimal
solution and let the model decide which candidates should be active  /</p>

<p style="margin:0in;font-family:calibri;font-size:11pt"> </p>

<p style="margin:0in;font-family:calibri;font-size:11pt">thanks</p>

<p style="margin:0in;font-family:calibri;font-size:11pt"> </p>

<p style="margin:0in;font-family:calibri;font-size:11pt">David</p>

<p style="margin:0in;font-family:calibri;font-size:11pt"> </p>

<p style="margin:0in;font-family:calibri;font-size:11pt"> </p>

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