# Why does PuLP call copy for addition and how can I avoid it?

Using a for loop to append terms to an expression seems to be much faster than summing a group of terms all at once. Constructing the expression using a for loop uses __iadd__, which does not include a call to copy. The other methods of building the expression result in many calls to __add__ which does call copy and is quite slow.

Of the six methods below, "using_loop" is arguably the most difficult to read, but is by far the fastest.

Is there a best practice method of building large constraints which is both readable and avoids the call to __add__ (and copy) in pulp? If I edit the __add__ function in pulp to remove the copy, are there side effects I should anticipate?

import pulp
import numpy as np

def using_np_mat_mul(X, coef):
x2d = np.atleast_2d(np.array(X))
coef2d = np.atleast_2d(np.array(coef)).T
expr = np.matmul(x2d, coef2d)
return expr

def using_loop(X, coef):
expr = 0
for i in range(len(X)):
expr += X[i]*coef[i]
return expr

def using_sum_of_list(X, coef):
expr = sum([X[i]*coef[i] for i in range(len(X))])
return expr

def using_sum_mult(X, coef):
expr = sum(np.array(X)*np.array(coef))
return expr

def using_lpsum(X, coef):
expr = pulp.lpSum(X[i]*coef[i] for i in range(len(X)))
return expr

def using_dict_and_lpsum(X_dict, coef):
expr = pulp.lpSum(X_dict[i]*coef[i] for i in X_dict.keys())
return expr

if __name__ == "__main__":
nx = 5000

X = [pulp.LpVariable(str(i)) for i in range(nx)]

coef = np.random.rand(nx)

e1 = using_np_mat_mul(X, coef)
e2 = using_loop(X, coef)
e3 = using_sum_of_list(X, coef)
e4 = using_sum_mult(X, coef)
e5 = using_lpsum(X, coef)

# create an expression = X * coef
X_dict = pulp.LpVariable.dicts('', range(nx))
e6 = using_dict_and_lpsum(X_dict, coef)


• Is this a PuLP question or a numpy question? (Would the same issue arise if X were not derived from PuLP variables?) If it's general numpy, you should ask on Stack Overflow instead. If it's specific to PuLP, then it's welcome here. Dec 23, 2019 at 13:49
• Since you're timing, I suggest to test another version: expr = pulp.lpSum(X[i]*coef[i] for i in range(len(X))). Also, check to see the effect if you create your variable X using pulp.LpVariable.dicts() method.
– EhsanK
Dec 24, 2019 at 3:07
• @EhsanK, thank you! Added. It has similar performance to the loop, but is much easier to read. Dec 24, 2019 at 5:38