GurobiError: Invalid argument to LinExpr multiplication

Hello I am getting the following error: GurobiError: Invalid argument to LinExpr multiplication

here is my code;

from gurobipy import GRB,Model,quicksum #*
import numpy as np # array kullanmak için
import pandas as pd #excel'i taşımak için


def Output(m):  
    # Print the result
    status_code = {1:'LOADED', 2:'OPTIMAL', 3:'INFEASIBLE', 4:'INF_OR_UNBD', 5:'UNBOUNDED'} #this is how a 'dictionary' 
                                                                                            #is defined in Python
    status = m.status
    
    print('The optimization status is ' + status_code[status])
    if status == 2:    
        # Retrieve variables value
        print('Optimal solution:')
        for v in m.getVars():
            print(str(v.varName) + " = " + str(v.x))    
        print('Optimal objective value: ' + str(m.objVal) + "\n")
        
model = Model("CPL_model");

n=5 #number of stations
first_station_set = range(n) # i / i and j # n+1 
#second_station_set = range(5) # j

bigM = 1000
m = 3 #number of vehicles
q = [[80,90,110,120,100,120]] #demand of stations
Q=[200,200,200] #capacity of the vehicle
cost=[[5,3,4,6,7,8]]


# Add Decision Varibales

#m = mdl.addVar(lb = 0, vtype = GRB.INTEGER, name = 'm') # vehicle amount
#q = mdl.addVars(first_station_set, vtype = GRB.INTEGER,name = 'Q') # station request
x = model.addVars(first_station_set, first_station_set, vtype=GRB.BINARY, name=["x_"+str(i+1) + "," +str(j+1) 
                                                                                for i in first_station_set for j in first_station_set]) 

u= model.addVars(first_station_set, lb = 0,vtype = GRB.INTEGER,name = ['u_'+str(i) for i in first_station_set])
#Add constraint

# Constraint 2
model.addConstrs((quicksum(x[i,j] for i in first_station_set) == 1 for j in range(1,n)), name = 'C2')


# Constraint 3
model.addConstrs((quicksum(x[j,i] for i in first_station_set) == 1 for j in range(1,n)), name = 'C3')

# Constraint 4
model.addConstr((quicksum(x[0,j] for j in first_station_set) <= m), name = 'C4')

# Constraint 5
model.addConstr(((quicksum(x[0,j] for j in range(1,n))) == (quicksum(x[j,0] for j in range(1,n)))), name = 'C5')


#BURADA YAZIYORUZ UUUUUUYU
model.addConstrs(((u[i]-u[j] + Q *x[i,j]  <= Q - q[j]) for i in range(n) for j in range(n)), name = 'C11')

#Objective FUnction

model.setObjective((quicksum(cost[i][j] * x[i][j] for i in range(n) for j in range(n))),GRB.MINIMIZE)


model.optimize()

model.write("DellAmico1.lp") # LP dosyası ürettirmek

status = model.status
object_Value = model.objVal
print()
print("model status is: ", status)
print()
print("Objective value is: ", object_Value)

Can you help me with this error please. Thanks in advance.

Jaromił Najman

Gurobi Staff

December 01, 2022 09:05

The error occurs because you are trying to multiply (and add) a list of values with an optimization variable while constructing a constraint.

model.addConstrs(((u[i]-u[j] + Q *x[i,j]  <= Q - q[j]) for i in range(n) for j in range(n)), name = 'C11')

Here \(\texttt{Q * x[i,j]}\) and \(\texttt{Q - q[j]}\) are the problem. Since all vehicle capacities are equal, you could just replace \(\texttt{Q}\) by 200.

Then you try to subtract a list of lists \(\texttt{q}\). I am not sure what you want to achieve here. I would guess that \(\texttt{q}\) should be

q = [80,90,110,120,100,120]

but then it still has 1 entry to many (which does not result in an error).

Then, there is another issue with the list of lists \(\texttt{cost}\)

cost=[[5,3,4,6,7,8]]

which you are trying to access via

cost[i][j] * x[i][j] for i in range(n) for j in range(n)

This will not work because there is only 1 dimension in the i-axis (and again 6 entries in the j-axis which are 1 too many given your n=5). You could fix it either by adding cost lists for all remaining i entries

cost=[[5,3,4,6,7,8],[5,3,4,6,7,8],[5,3,4,6,7,8],[5,3,4,6,7,8],[5,3,4,6,7,8]]

or using only one dimensional costs

cost=[5,3,4,6,7,8]

and adjusting the objective

model.setObjective((quicksum(cost[i] * x[i][j] for i in range(n) for j in range(n))),GRB.MINIMIZE)

Additionally, \(\texttt{x[i][j]}\) should read \(\texttt{x[i,j]}\)

model.setObjective((quicksum(cost[i] * x[i,j] for i in range(n) for j in range(n))),GRB.MINIMIZE)

With all the above fixes, you can execute the optimization. The model you generated is infeasible. Please have a look at How do I determine why my model is infeasible? for more information. A first start would be to analyze the IIS computed by Gurobi

model.optimize()

model.write("DellAmico1.lp") # LP dosyası ürettirmek

if model.status == GRB.INFEASIBLE:
  model.computeIIS()
  model.write("iis.ilp")
  exit()

Best regards,
Jaromił

GurobiError: Invalid argument to LinExpr multiplication

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