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### poolsearch.py

#!/usr/bin/python

# Copyright 2018, Gurobi Optimization, LLC

# We find alternative epsilon-optimal solutions to a given knapsack
# problem by using PoolSearchMode

from __future__ import print_function
from gurobipy import *

try:
# Sample data
Groundset    = range(10)
objCoef      = [32, 32, 15, 15, 6, 6, 1, 1, 1, 1]
knapsackCoef = [16, 16,  8,  8, 4, 4, 2, 2, 1, 1]
Budget       = 33

# Create initial model
model = Model("poolsearch")

# Create dicts for tupledict.prod() function
objCoefDict = dict(zip(Groundset, objCoef))
knapsackCoefDict = dict(zip(Groundset, knapsackCoef))

# Initialize decision variables for ground set:
# x[e] == 1 if element e is chosen
Elem = model.addVars(Groundset, vtype=GRB.BINARY, name='El')

# Set objective function
model.ModelSense = GRB.MAXIMIZE
model.setObjective(Elem.prod(objCoefDict))

# Constraint: limit total number of elements to be picked to be at most
# Budget
model.addConstr(Elem.prod(knapsackCoefDict) <= Budget, name='Budget')

# Limit how many solutions to collect
model.setParam(GRB.Param.PoolSolutions, 1024)
# Limit the search space by setting a gap for the worst possible solution that will be accepted
model.setParam(GRB.Param.PoolGap, 0.10)
# do a systematic search for the k-best solutions
model.setParam(GRB.Param.PoolSearchMode, 2)

# save problem
model.write('poolsearch.lp')

# Optimize
model.optimize()

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

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

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

# Print best selected set
print('Selected elements in best solution:')
print('\t', end='')
for e in Groundset:
if Elem[e].X > .9:
print(' El%d' % e, end='')
print('')

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

# Print objective values of solutions
for e in range(nSolutions):
model.setParam(GRB.Param.SolutionNumber, e)
print('%g ' % model.PoolObjVal, end='')
if e % 15 == 14:
print('')
print('')

# print fourth best set if available
if (nSolutions >= 4):
model.setParam(GRB.Param.SolutionNumber, 3);

print('Selected elements in fourth best solution:')
print('\t', end='')
for e in Groundset:
if Elem[e].Xn > .9:
print(' El%d' % e, end='')
print('')

except GurobiError as e:
print('Gurobi error ' + str(e.errno) + ": " + str(e.message))

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


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