Making constraints non-binding
Ongoing
Hi. I have a set of constraints that I want to active them dynamically, i.e., when a certain binary variable is for example 0, activates constraints which changes the values of variables, otherwise, don't change them by deactivating the constraint (or making it non-binding). This problem gets even more complex, if in some of these constraints we are trying to obtain another binary variable with big M method. I specifically mentioned this as we cannot easily use big M method for making the constraint non-binding, since we have already another binary variable to be determined in the constraint, which cancels the non-binding binary variable. to understand the problem better, take a look a the constraints written below. We have a binary variable 'BETA' for considering activation of the constraint; if 'BETA == 0', the constraint is binding, otherwise is non-binding. Further, the constraint written has binary variable 'gamma' to be determined. How we can manage this? Consider that there are a lot of these constraints that have the same issue. I have also tried indicator constraints but Gurobi cannot support for loops within the indicator constraint which brings more complexity in the case of constraint arrangement since some constraints require a combination of different for loops for indices and some other wouldn't.
self.model.addConstr(self.Q_prime[t, d, m, k] >= 1 - big_M * (1 - self.BETA[t, d, m, k]))
self.model.addConstr(self.Y[d, n, k] <= t + big_M * (1 - self.gama[t, d, n, k]))
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The constraints
self.model.addConstr(self.Q_prime[t, d, m, k] >= 1 - big_M * (1 - self.BETA[t, d, m, k]))
self.model.addConstr(self.Y[d, n, k] <= t + big_M * (1 - self.gama[t, d, n, k]))will be "active" if the BETA and gama variables take the value 1, respectively.
These can be modelled by adding two indicator constraints:
self.model.addConstr( (self.BETA[t, d, m, k]==1) >> (self.Q_prime[t, d, m, k] >= 1) )
self.model.addConstr( (self.gama[t, d, n, k]==1) >> (self.Y[d, n, k] <= t) )Would this not work for your model?
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Thank you for your response. I'm using Gurobi 13.0.0, and doesn't support this way. Eventually, I linearized the combination of these binary variables, and put the combination as the condition of indicator constraint instead of writing them in chain. Now I have another question. I want to make a new matrix of variables of matrix divided by the sum of all variables of that matrix. Since this not a linear operation, how can I linearize it?
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