Dear community.
I have a multi objective Mixed Quadratic binary non-linear problem.
Following a scalarization approach, the objective function includes the sum of some binary variables (say Z_j) minus lambda times the sum of the products of some other binary variables (say x_i * y_k) .
Furthermore, a set of constraints include the product of these optimization variables (x_i * y_k)..
I derived a MILP formulation by linearizing each product of two binary variables, through 0-1 indicator variables I_d (and the necessary constraints). Hence, I replaced the sum of x_i * y_k with the sum of the indicators in the objective function.
To reach an approximate solution in reasonable time, I am working on a costructive iterative algorithm based on succesive linear relaxation of the original problem.
While I can easily understand the rationale and fix the values of Z_j according to a rounding procedure, I am not confident enough that relaxing the indicator variables still allows to reasonably apply the rounding technique to x_i , and y_k.
According to your knowledge and expertise, should I still leave indicator variables in the continuous relaxation of the MILP formualtion, or should I try another path to solve my problem?
Any suggestion or reference to documentation I should study is highly appreciated.
Thanks in advance.
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