Note

This page was generated from docs/tutorials/11_using_classical_optimization_solvers_and_models.ipynb.

Using Classical Optimization Solvers and Models with Qiskit Optimization#

We can use classical optimization solvers (CPLEX and Gurobi) with Qiskit Optimization. Docplex and Gurobipy are the Python APIs for CPLEX and Gurobi, respectively. We can load and save an optimization model by Docplex and Gurobipy and can apply CPLEX and Gurobi to QuadraticProgram.

If you want to use the CPLEX solver, you need to install pip install 'qiskit-optimization[cplex]'. Docplex is automatically installed, as a dependent, when you install Qiskit Optimization.

If you want to use Gurobi and Gurobipy, you need to install pip install 'qiskit-optimization[gurobi]'.

Note: these solvers, that are installed via pip, are free versions and come with some limitations, such as number of variables. The following links provide further details:

CplexSolver and GurobiSolver#

Qiskit Optimization supports the classical solvers of CPLEX and Gurobi as CplexSolver and GurobiSolver, respectively. We can solve QuadraticProgram with CplexSolver and GurobiSolver as follows.

[1]:

from qiskit_optimization.problems import QuadraticProgram

# define a problem
qp = QuadraticProgram()
qp.binary_var("x")
qp.integer_var(name="y", lowerbound=-1, upperbound=4)
qp.maximize(quadratic={("x", "y"): 1})
qp.linear_constraint({"x": 1, "y": -1}, "<=", 0)
print(qp.prettyprint())

Problem name:

Maximize
  x*y

Subject to
  Linear constraints (1)
    x - y <= 0  'c0'

  Integer variables (1)
    -1 <= y <= 4

  Binary variables (1)
    x

[2]:

from qiskit_optimization.algorithms import CplexOptimizer, GurobiOptimizer

cplex_result = CplexOptimizer().solve(qp)
gurobi_result = GurobiOptimizer().solve(qp)

print("cplex")
print(cplex_result.prettyprint())
print()
print("gurobi")
print(gurobi_result.prettyprint())

Restricted license - for non-production use only - expires 2025-11-24

cplex
objective function value: 4.0
variable values: x=1.0, y=4.0
status: SUCCESS

gurobi
objective function value: 4.0
variable values: x=1.0, y=4.0
status: SUCCESS

We can set the solver parameter of CPLEX as follows. We can display the solver message of CPLEX by setting disp=True. See Parameters of CPLEX for details of CPLEX parameters.

[3]:

result = CplexOptimizer(disp=True, cplex_parameters={"threads": 1, "timelimit": 0.1}).solve(qp)
print(result.prettyprint())

Version identifier: 22.1.0.0 | 2022-03-25 | 54982fbec

CPXPARAM_Read_DataCheck                          1

CPXPARAM_Threads                                 1

CPXPARAM_TimeLimit                               0.10000000000000001

Found incumbent of value 0.000000 after 0.00 sec. (0.00 ticks)

Found incumbent of value 4.000000 after 0.00 sec. (0.00 ticks)


Root node processing (before b&c):

  Real time             =    0.00 sec. (0.00 ticks)

Sequential b&c:

  Real time             =    0.00 sec. (0.00 ticks)

                          ------------

Total (root+branch&cut) =    0.00 sec. (0.00 ticks)

objective function value: 4.0
variable values: x=1.0, y=4.0
status: SUCCESS

We get the same optimal solution by QAOA as follows.

[4]:

from qiskit_optimization.algorithms import MinimumEigenOptimizer

from qiskit_algorithms import QAOA
from qiskit_algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler

meo = MinimumEigenOptimizer(QAOA(sampler=Sampler(), optimizer=COBYLA(maxiter=100)))
result = meo.solve(qp)
print(result.prettyprint())
print("\ndisplay the best 5 solution samples")
for sample in result.samples[:5]:
    print(sample)

objective function value: 4.0
variable values: x=1.0, y=4.0
status: SUCCESS

display the best 5 solution samples
SolutionSample(x=array([1., 4.]), fval=4.0, probability=0.041944773933828096, status=<OptimizationResultStatus.SUCCESS: 0>)
SolutionSample(x=array([1., 3.]), fval=3.0, probability=0.07443253202894709, status=<OptimizationResultStatus.SUCCESS: 0>)
SolutionSample(x=array([1., 2.]), fval=2.0, probability=0.13540988877110383, status=<OptimizationResultStatus.SUCCESS: 0>)
SolutionSample(x=array([1., 1.]), fval=1.0, probability=0.12258577937645261, status=<OptimizationResultStatus.SUCCESS: 0>)
SolutionSample(x=array([0., 0.]), fval=0.0, probability=0.0735318504545516, status=<OptimizationResultStatus.SUCCESS: 0>)

Translators between `QuadraticProgram` and Docplex/Gurobipy#

Qiskit Optimization can load QuadraticProgram from a Docplex model and a Gurobipy model.

First, we define an optimization problem by Docplex and Gurobipy.

[5]:

# docplex model
from docplex.mp.model import Model

docplex_model = Model("docplex")
x = docplex_model.binary_var("x")
y = docplex_model.integer_var(-1, 4, "y")
docplex_model.maximize(x * y)
docplex_model.add_constraint(x <= y)
docplex_model.prettyprint()

// This file has been generated by DOcplex
// model name is: docplex
// single vars section
dvar bool x;
dvar int y;

maximize
 [ x*y ];

subject to {
 x <= y;

}

[6]:

# gurobi model
from io import StringIO
from tempfile import NamedTemporaryFile
from os import remove

import gurobipy as gp


def gpy_display(mdl):
    """Convenience function to pretty-print a Gurobipy-Model."""
    with NamedTemporaryFile(suffix=".lp") as tmp_file:
        mdl.write(tmp_file.name)

        with open(tmp_file.name, "r") as f:
            print(f.read())


gurobipy_model = gp.Model("gurobi")
x = gurobipy_model.addVar(vtype=gp.GRB.BINARY, name="x")
y = gurobipy_model.addVar(vtype=gp.GRB.INTEGER, lb=-1, ub=4, name="y")
gurobipy_model.setObjective(x * y, gp.GRB.MAXIMIZE)
gurobipy_model.addConstr(x - y <= 0)
gurobipy_model.update()
gpy_display(gurobipy_model)

\ Model gurobi
\ LP format - for model browsing. Use MPS format to capture full model detail.
Maximize
 [ 2 x * y ] / 2
Subject To
 R0: x - y <= 0
Bounds
 -1 <= y <= 4
Binaries
 x
Generals
 y
End

We can generate QuadraticProgram object from both Docplex and Gurobipy models. We see that the two QuadraticProgram objects generated from Docplex and Gurobipy are identical.

[7]:

from qiskit_optimization.translators import from_docplex_mp, from_gurobipy

qp = from_docplex_mp(docplex_model)
print("QuadraticProgram obtained from docpblex")
print(qp.prettyprint())
print("-------------")
print("QuadraticProgram obtained from gurobipy")
qp2 = from_gurobipy(gurobipy_model)
print(qp2.prettyprint())

QuadraticProgram obtained from docpblex
Problem name: docplex

Maximize
  x*y

Subject to
  Linear constraints (1)
    x - y <= 0  'c0'

  Integer variables (1)
    -1 <= y <= 4

  Binary variables (1)
    x

-------------
QuadraticProgram obtained from gurobipy
Problem name: gurobi

Maximize
  x*y

Subject to
  Linear constraints (1)
    x - y <= 0  'R0'

  Integer variables (1)
    -1 <= y <= 4

  Binary variables (1)
    x

We can generate a Docplex model and a Gurobipy model from QuadraticProgram too.

[8]:

from qiskit_optimization.translators import to_gurobipy, to_docplex_mp

gmod = to_gurobipy(from_docplex_mp(docplex_model))
print("convert docplex to gurobipy via QuadraticProgram")
gpy_display(gmod)

dmod = to_docplex_mp(from_gurobipy(gurobipy_model))
print("\nconvert gurobipy to docplex via QuadraticProgram")
print(dmod.export_as_lp_string())

convert docplex to gurobipy via QuadraticProgram
\ Model docplex
\ LP format - for model browsing. Use MPS format to capture full model detail.
Maximize
 [ 2 x * y ] / 2
Subject To
 c0: x - y <= 0
Bounds
 -1 <= y <= 4
Binaries
 x
Generals
 y
End


convert gurobipy to docplex via QuadraticProgram
\ This file has been generated by DOcplex
\ ENCODING=ISO-8859-1
\Problem name: gurobi

Maximize
 obj: [ 2 x*y ]/2
Subject To
 R0: x - y <= 0

Bounds
 0 <= x <= 1
 -1 <= y <= 4

Binaries
 x

Generals
 y
End

Indicator constraints of Docplex#

from_docplex_mp supports indicator constraints, e.g., u = 0 => x + y <= z (u: binary variable) when we convert a Docplex model into QuadraticProgram. It converts indicator constraints into linear constraints using the big-M formulation.

[9]:

ind_mod = Model("docplex")
x = ind_mod.binary_var("x")
y = ind_mod.integer_var(-1, 2, "y")
z = ind_mod.integer_var(-1, 2, "z")
ind_mod.maximize(3 * x + y - z)
ind_mod.add_indicator(x, y >= z, 1)
print(ind_mod.export_as_lp_string())

\ This file has been generated by DOcplex
\ ENCODING=ISO-8859-1
\Problem name: docplex

Maximize
 obj: 3 x + y - z
Subject To
 lc1: x = 1 -> y - z >= 0

Bounds
 0 <= x <= 1
 -1 <= y <= 2
 -1 <= z <= 2

Binaries
 x

Generals
 y z
End

Let’s compare the solutions of the model with an indicator constraint by

applying CPLEX directly to the Docplex model (without translating it to QuadraticProgram. CPLEX solver natively supports the indicator constraints),
applying QAOA to QuadraticProgram obtained by from_docplex_mp.

We see the solutions are same.

[10]:

qp = from_docplex_mp(ind_mod)
result = meo.solve(qp)  # apply QAOA to QuadraticProgram
print("QAOA")
print(result.prettyprint())
print("-----\nCPLEX")
print(ind_mod.solve())  # apply CPLEX directly to the Docplex model

QAOA
objective function value: 6.0
variable values: x=1.0, y=2.0, z=-1.0
status: SUCCESS
-----
CPLEX
solution for: docplex
objective: 6
status: OPTIMAL_SOLUTION(2)
x=1
y=2
z=-1

[11]:

import tutorial_magics

%qiskit_version_table
%qiskit_copyright

Version Information

Software	Version
`qiskit`	1.0.1
`qiskit_algorithms`	0.3.0
`qiskit_optimization`	0.6.1
System information
Python version	3.8.18
OS	Linux
Wed Feb 28 03:00:52 2024 UTC

This code is a part of a Qiskit project

This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.

Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.

Using Classical Optimization Solvers and Models with Qiskit Optimization#

CplexSolver and GurobiSolver#

Translators between QuadraticProgram and Docplex/Gurobipy#

Indicator constraints of Docplex#

Version Information

This code is a part of a Qiskit project

Translators between `QuadraticProgram` and Docplex/Gurobipy#