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### multiobj.py

#!/usr/bin/env python3.7

# Copyright 2020, Gurobi Optimization, LLC

# Want to cover three different sets but subject to a common budget of
# elements allowed to be used. However, the sets have different priorities to
# be covered; and we tackle this by using multi-objective optimization.

import gurobipy as gp
from gurobipy import GRB
import sys

try:
# Sample data
Groundset = range(20)
Subsets = range(4)
Budget = 12
Set = [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1],
[0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0],
[0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0]]
SetObjPriority = [3, 2, 2, 1]
SetObjWeight = [1.0, 0.25, 1.25, 1.0]

# Create initial model
model = gp.Model('multiobj')

# Initialize decision variables for ground set:
# x[e] == 1 if element e is chosen for the covering.

# Constraint: limit total number of elements to be picked to be at most
# Budget

# Set global sense for ALL objectives
model.ModelSense = GRB.MAXIMIZE

# Limit how many solutions to collect
model.setParam(GRB.Param.PoolSolutions, 100)

# Set and configure i-th objective
for i in Subsets:
objn = sum(Elem[k]*Set[i][k] for k in range(len(Elem)))
model.setObjectiveN(objn, i, SetObjPriority[i], SetObjWeight[i],
1.0 + i, 0.01, 'Set' + str(i))

# Save problem
model.write('multiobj.lp')

# Optimize
model.optimize()

model.setParam(GRB.Param.OutputFlag, 0)

# Status checking
status = model.Status
if status in (GRB.INF_OR_UNBD, GRB.INFEASIBLE, GRB.UNBOUNDED):
print("The model cannot be solved because it is infeasible or "
"unbounded")
sys.exit(1)

if status != GRB.OPTIMAL:
print('Optimization was stopped with status ' + str(status))
sys.exit(1)

# Print best selected set
print('Selected elements in best solution:')
selected = [e for e in Groundset if Elem[e].X > 0.9]
print(" ".join("El{}".format(e) for e in selected))

# Print number of solutions stored
nSolutions = model.SolCount
print('Number of solutions found: ' + str(nSolutions))

# Print objective values of solutions
if nSolutions > 10:
nSolutions = 10
print('Objective values for first ' + str(nSolutions) + ' solutions:')
for i in Subsets:
model.setParam(GRB.Param.ObjNumber, i)
objvals = []
for e in range(nSolutions):
model.setParam(GRB.Param.SolutionNumber, e)
objvals.append(model.ObjNVal)

print('\tSet{} {:6g} {:6g} {:6g}'.format(i, *objvals))

except gp.GurobiError as e:
print('Error code ' + str(e.errno) + ": " + str(e))

except AttributeError as e:
print('Encountered an attribute error: ' + str(e))