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### multiobj.py

#!/usr/bin/env python3.11

# Copyright 2024, 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(f"Optimization was stopped with status {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(f"El{e}" for e in selected))

# Print number of solutions stored
nSolutions = model.SolCount
print(f"Number of solutions found: {nSolutions}")

# Print objective values of solutions
if nSolutions > 10:
nSolutions = 10
print(f"Objective values for first {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(f"\tSet{i}" + "".join(f" {objval:6g}" for objval in objvals[:3]))

except gp.GurobiError as e:
print(f"Error code {e.errno}: {e}")

except AttributeError as e:
print(f"Encountered an attribute error: {e}")


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