How to use gurobi variable as a power on a constant

[Asif Arain]

Hi, 

I am using Gurobi with Python to solve the following problem.

max. (1-Var(3^{-VC})) * (mean(VC)) s. t. sum(C) <= 3 and C in {0,1}

Whereas, C is a binary decision vector of length n. V is a coefficient (information) matrix of size mxn (m<=n). 

Here is my python code:

from gurobipy import *

import numpy as np

# EXAMPLE DATA SET

# ----------------------------------------------

V = np.matrix((

            (1,1,1,1,0,0),

            (0,1,1,1,1,0),

            (1,1,0,0,0,1),

            (0,0,0,1,1,1)))

V = V.tolist()

# LOCAL FUNCTIONS

# ----------------------------------------------

# V times C

def V_x_C(V,C):

    VC = {}

    for i in range(np.shape(V)[0]):

        ij_sum = 0;

        for j in range(len(C)):

            ij_sum +=  V[i][j]*C[j]

        VC[i] = ij_sum

    return VC

   

# Square

def sqr(vec):

    sqr_vec = {}

    for i in range(len(vec)):

        sqr_vec[i] = vec[i]*vec[i]    

    return sqr_vec

   

# Variance

def variance(vec):

    mean_vec = sum(vec)/len(vec)

    diff_vec = vec-mean_vec

    sqdf_vec = sqr(diff_vec)

    var_vec  = (sum(sqdf_vec))/len(vec)

    return var_vec

# Power

def pwr(scalr,vec):

    reslt = {}

    for i in range(len(vec)):

        reslt[i] = scalr**vec[i]

    return reslt

# ObjVar

def objVar(V,C):

    VC = V_x_C(V,C)

    negVC = np.dot(-1,VC.values())

    pwrVC = pwr(3,negVC)

    varVC = variance(1-pwrVC)

    return varVC

# ObjMean

def objMean(V,C):

    VC = V_x_C(V,C)

    sumVC = 0

    for i in range(len(VC)):

        sumVC += VC[i]

    meanVC = float(sumVC)/len(VC)

    return meanVC

   

# OPTIMIZATION

# ----------------------------------------------

# Create a new model

m = Model("My Model")

# Optimization Variables

C = {}

for i in range(np.shape(V)[1]):

    C[i] = m.addVar(vtype=GRB.BINARY)

# The objective is to maximize the costs

m.modelSense = GRB.MAXIMIZE

   

# Integrate new variables

m.update()

# Objective Function

m.setObjective( (1-objVar(V,C))*(objMean(V,C)) )

# Constraint

m.addConstr( quicksum ([C[i] for i in range(np.shape(V)[1])]) <= 3)

m.optimize()

# Publish results

for v in m.getVars():

    print('%s %g' % (v.varName, v.x))

I am getting following error:

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>

  File "/home/asif/anaconda/lib/python2.7/site-packages/spyderlib/widgets/externalshell/sitecustomize.py", line 682, in runfile

    execfile(filename, namespace)

  File "/home/asif/anaconda/lib/python2.7/site-packages/spyderlib/widgets/externalshell/sitecustomize.py", line 78, in execfile

    builtins.execfile(filename, *where)

  File "/media/Win7/DATA/MPS-GSMR/PLANNER/TestPython/question_gurobi_form.py", line 83, in <module>

    m.setObjective( (1-objVar(V,C))*(objMean(V,C)) )

  File "/media/Win7/DATA/MPS-GSMR/PLANNER/TestPython/question_gurobi_form.py", line 52, in objVar

    pwrVC = pwr(3,negVC) 

  File "/media/Win7/DATA/MPS-GSMR/PLANNER/TestPython/question_gurobi_form.py", line 45, in pwr

    reslt[i] = scalr**vec[i]

TypeError: unsupported operand type(s) for ** or pow(): 'int' and 'LinExpr'

 

Apparently, the main issue is how to use gurobi variable as power on a constant. Please suggest me to address the bug in particular and the overall implementation in general.