#!/usr/bin/env python3
"``naginterfaces.library.mip.handle_solve_minlp`` Python Example."
# NAG Copyright 2018-2020.
# pylint: disable=invalid-name
from naginterfaces.base import utils
from naginterfaces.library import opt, mip
[docs]def main():
"""
Example for :func:`naginterfaces.library.mip.handle_solve_minlp`.
Nonlinear programming with some integer constraints.
>>> main()
naginterfaces.library.mip.handle_solve_minlp Python Example Results.
Solve a portfolio selection problem.
Final objective value is 2.9250000e+00
"""
print(
'naginterfaces.library.mip.handle_solve_minlp Python Example Results.'
)
print('Solve a portfolio selection problem.')
# The portfolio parameters:
rho = 10.
p = 3
# The nonlinear objective:
cb_objfun = lambda x, inform: (
(
x[0]*(4.*x[0]+3.*x[1]-x[2]) +
x[1]*(3.*x[0]+6.*x[1]+x[2]) +
x[2]*(x[1]-x[0]+10.*x[2])
),
0,
)
def cb_objgrd(x, fdx, inform):
"""The gradient of the objective."""
fdx[0] = 8.*x[0] + 6.*x[1] - 2.*x[2]
fdx[1] = 6.*x[0] + 12.*x[1] + 2.*x[2]
fdx[2] = 2.*(x[1]-x[0]) + 20.*x[2]
fdx[3] = 0.
return 0
# The nonlinear constraints function:
cb_confun = lambda x, _ncnln, inform: (
[
8.*x[0] + 9.*x[1] + 12.*x[2] + 7.*x[3] - rho,
p - x[4] - x[5] - x[6] - x[7],
],
0,
)
def cb_congrd(x, gdx, inform):
"""The Jacobian of the nonlinear constraints."""
gdx[:4] = [8., 9., 12., 7.]
return inform
# The problem size:
n = 8
# The initial guess:
x = [1., 1., 1., 1., 0., 0., 0., 0.]
# Create a handle for the problem:
handle = opt.handle_init(nvar=n)
# Define the bounds:
opt.handle_set_simplebounds(
handle,
bl=[0.]*n,
bu=[1000., 1000., 1000., 1000., 1., 1., 1., 1.],
)
# Define the non-linear objective:
opt.handle_set_nlnobj(
handle,
idxfd=[1, 2, 3, 4],
)
# Define the linear constraints:
opt.handle_set_linconstr(
handle,
bl=[1.] + [0.]*4,
bu=[1.] + [1.e20]*4,
irowb=[
1, 1, 1, 1,
2, 2,
3, 3,
4, 4,
5, 5,
],
icolb=[
1, 2, 3, 4,
1, 5,
2, 6,
3, 7,
4, 8
],
b=[
1., 1., 1., 1.,
-1., 1,
-1., 1,
-1., 1,
-1., 1
],
)
# Define the nonlinear constraints:
opt.handle_set_nlnconstr(
handle,
bl=[0., 0.], bu=[0., 1.e20],
irowgd=[1, 1, 1, 1], icolgd=[1, 2, 3, 4],
)
# Set integer variables
opt.handle_set_property(handle=handle, ptype='Bin', idx=[5, 6, 7, 8])
# Set some algorithmic options.
for option in [
'Verify Derivatives = Yes',
'Print Level = 0',
]:
opt.handle_opt_set(handle, option)
# Use an explicit I/O manager for abbreviated iteration output:
iom = utils.FileObjManager(locus_in_output=False)
# Solve the problem.
soln = mip.handle_solve_minlp(
handle, x,
objfun=cb_objfun, objgrd=cb_objgrd, confun=cb_confun, congrd=cb_congrd,
io_manager=iom)
print('Final objective value is {:.7e}'.format(soln.rinfo[0]))
# Destroy the handle:
opt.handle_free(handle)
if __name__ == '__main__':
import doctest
import sys
sys.exit(
doctest.testmod(
None, verbose=True, report=False,
optionflags=doctest.ELLIPSIS | doctest.REPORT_NDIFF,
).failed
)
