sum of array constraints

Answered

Muhammad Ridwan Reza Nugraha

November 19, 2022 11:57 Edited

Hi

I have several array, let say

a1=np.array([1,0,0,0,0])

a2=np.array([0,1,0,0,0])

a3=np.array([0,0,1,0,0])

a4=np.array([0,0,0,0,1])

i have x a binary decision variable (x1,x2,x3,x4)

I want to create a constraint : x1*a1+x2*a2+x3*a3+x4*a4 = [1,1,0,0,0]

I can do it for each array elements (5 times), like these:

m.addConstr( x1*a1[0]+x2*a2[0]+x3*a3[0]+x4*a4[0] == 1 )

m.addConstr( x1*a1[1]+x2*a2[1]+x3*a3[1]+x4*a4[1] = 1 )

m.addConstr( x1*a1[2]+x2*a2[2]+x3*a3[2]+x4*a4[2] = 0 )

m.addConstr( x1*a1[3]+x2*a2[3]+x3*a3[3]+x4*a4[3] = 0 )

m.addConstr( x1*a1[4]+x2*a2[4]+x3*a3[4]+x4*a4[4] = 0 )

are there any other ways?

Thank you

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Official comment
Simranjit Kaur

Gurobi Staff

November 13, 2026 01:52
This post is more than two years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.
Simon Bowly

Gurobi Staff

November 21, 2022 03:59
Hi Muhummad,

What you have here is a standard form matrix constraint, and the ideal way to model this is to use MVars and the matrix-friendly API:
A = np.array([a1, a2, a3, a4]).transpose() # 5 rows by 4 columns
b = np.array([1, 1, 0, 0, 0]) # length 5 vector

model = gp.Model()
x = model.addMVar(4, name="x") # length 4 MVar
model.addConstr(A @ x == b) # 5 constraints

Note though that if your data has a lot of zeros, then it is best to use a scipy.sparse matrix to represent A, instead of the dense numpy format.
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