Solving a Mixed Integer Quadratic Program using SCIP
<p>I have a mixed integer quadratic program (MIQP) which I would like to solve using SCIP. The program is in the form such that on fixing the integer variables, the problem turns out to be a linear program. And on fixing the the continuous variables it becomes a Integer Program. A simple example :</p>

<p>max. \Sigma_{i} n_i * f_i(x_i)  </p>

<p>such that.<br>
n_1 * x_1 + n2 * x_2 &lt; t<br>
n_3 * x_1 + n2 * x_2 &lt; m<br>
.<br>
.<br>
many random quadratic constraints in n_i's and x_i's<br>
so on</p>

<p>Here f_i is a concave piecewise linear function.<br>
x_i's are continuous variables ( they take real values )<br>
n_i's are integer variables</p>

<p>I am able to solve the problem using SCIP. But on problems with a large number of variables SCIP takes a lot of time to find the solution. I have particularly noticed that it does not find many primal solutions. Thus the rate at which the upper bound reduces is very slow. However, I could get better results by doing set heuristics emphasis aggressive.<br>
It would be great if anyone can guide me on the following questions :<br>
1) Is there any particular algorithm/ Software package which solves problems that fit perfectly into the model as described above ?<br>
2) Suggestions on how to improve the rate at which primal solutions are found.<br>
3) What type of branching can I use to get better results ?<br>
4) Any guidance on improving performance would be really helpful.</p>

<p>I am okay with relaxing the integer constraints as well. </p>

<p>Thanks</p>