I have implemented a column generation algorithm in Gurobi in Python. The most computationally expensive aspect of this algorithm is the reconstruction of the master problem when a column is added (or sometimes removed). For example, a sample constraint set for my master problem is as follows:
mdl_master.addConstrs((gp.quicksum((A[s][i] - B[s][i]) * chi[s] for s in s_set) >= E[i] for i in i_set), name='cst')
E represent parameters of the master problem,
chi is a continuous decision variable, and
s is the index of columns.
Given that new columns can be added to the master problem or some unused columns can be eliminated, how do you suggest I reduce the computational cost of building such constraints in an iterative algorithm like column generation? Would it be possible and beneficial to partially modify the LHS of such a constraint set instead of building it from scratch? If so, how?