如何获得提供的 MIP start 的客观价值？

Question

One can easily provide a MIP start solution, eg

from gurobipy import Model

mdl = Model()

x = mdl.addVar(vtype="I")
y = mdl.addVar(ub = 5, vtype="I")

x.start = 2.0
y.start = 1.0

mdl.setObjective(x*x-y*y)
mdl.addConstr(x <= 2.0*y)

mdl.optimize()

In this example it is easily seen that the MIP start has objective value 3. How can I get the MIP start objective value by Gurobi without calculating it on my own? The mdl.objVal attribute is only available after calling the mdl.optimize() method and returns the optimal objective value then.

Answer 1

Assuming that you want to solve the model anyway, you could use a callback like this:

from gurobipy import Model, GRB

# ... your model

# The callback saves the objective value of the first found incumbent,
# i.e. the mip start in your case
def callback(model, where):
    if where == GRB.Callback.MIPSOL:
        if model.cbGet(GRB.Callback.MIPSOL_SOLCNT) == 0:
            # creates new model attribute '_startobjval'
            model._startobjval = model.cbGet(GRB.Callback.MIPSOL_OBJ)


mdl.optimize(callback)

print(f"MIP Start objVal: {mdl._startobjval}, optimal objVal: {mdl.objVal}")