如何节省计算时间以在python中添加约束和求和函数

Question

I am trying to use quicksum function in added constraints when building model in Python and using Gurobi to solve it. When I use a large-scale case, it will take a long time. Any way to improve it? (V[(i,t)] is the inputs and Q[(i,j,t)] is the variable in my model):

for i in range(I):
    for t in range(T):
        m.addConstr(quicksum(Q[(i,j,t)] for j in range(J))<=V[(i,t)])

Answer 1

The Gurobi Documentation says this:

Note that while quicksum is much faster than sum, it isn't the fastest approach for building a large expression. Use addTerms or the LinExpr() constructor if you want the quickest possible expression construction.

Based on that comment, you could try one of the options below and compare the performance:

for i in range(I):
    for t in range(T):
        m.addConstr(LinExpr((1.0, Q[(i,j,t)]) for j in range(J))<=V[(i,t)])

for i in range(I):
    for t in range(T):
        expr = LinExpr()
        m.addConstr(expr.addTerms([1.0]*J, Q[(i,j,t)] for j in range(J))<=V[(i,t)])

In a comment you asked how to expand this to handle nested quicksums:

obj=quicksum(quicksum(Q[(i,j,t)]*g[i,j,t] for i in range(I)) for j in range(J)) for t in range(T))

You can build up your objective function using nested for loops instead of nested quicksums. Each call to addTerms does just what it says, it adds additional terms to the existing expression. Just make sure you pull the expression declaration out of the loops:

obj= LinExpr()
for i in range(I):
    for t in range(T):
        obj.addTerms(g[(i,j,t)] for j in range(J), 
                     Q[(i,j,t)] for j in range(J))
m.setObjective(obj)