Minimize volume with maximum compliance

This is a variation of the standart design optimisation problem where the minimum volume structure is seeked given a maximum compliance.  It illustrate the modularity of how Functions is implemented in HydrOpTop and can be used either as a constrain or a main objective.

import numpy as np

from HydrOpTop.Functions.verification import Mechanical_Compliance, Volume_Percentage
from HydrOpTop.Functions import Volume_Percentage
from HydrOpTop.Materials import SIMP
from HydrOpTop.Filters import Density_Filter, Heaviside_Filter
from HydrOpTop.Crafter import Steady_State_Crafter
from HydrOpTop.Solvers import Linear_Elasticity_2D

#create solver simulation object
sim = Linear_Elasticity_2D("cantilever")

#get cell ids in the region to optimize and parametrize permeability
#same name than in pflotran input file
young_modulus = SIMP(cell_ids_to_parametrize="all", property_name="YOUNG_MODULUS", bounds=[0, 2000], power=3)

#define cost function
max_vol = Volume_Percentage("parametrized_cell")

#define maximum compliance
MC = Mechanical_Compliance(ids_to_consider="everywhere")
MC.constraint_tol = 5e-2

#define filter
dfilter = Density_Filter(0.3)
hfilter = Heaviside_Filter(0.5, 1)

#craft optimization problem
#i.e. create function to optimize, initiate IO array in classes...
crafted_problem = Steady_State_Crafter(max_vol, sim, [young_modulus], [MC], filters=[dfilter, hfilter])
crafted_problem.IO.output_every_iteration(2)
crafted_problem.IO.define_output_format("vtu")

#initialize optimizer
p_ini = np.ones(crafted_problem.get_problem_size(),dtype='f8')

#optimize in several pass to reach discrete distribution
out = crafted_problem.optimize(optimizer="nlopt-mma", action="minimize", max_it=50, ftol=1e-10, initial_guess=p_ini)

hfilter.stepness = 2
out = crafted_problem.optimize(optimizer="nlopt-mma", action="minimize",
                               max_it=20, initial_guess=out.p_opt)
hfilter.stepness = 4
out = crafted_problem.optimize(optimizer="nlopt-mma", action="minimize",
                               max_it=20, initial_guess=out.p_opt)
hfilter.stepness = 8
out = crafted_problem.optimize(optimizer="nlopt-mma", action="minimize",
                               max_it=20, initial_guess=out.p_opt)
hfilter.stepness = 20
out = crafted_problem.optimize(optimizer="nlopt-mma", action="minimize",
                               max_it=30, initial_guess=out.p_opt)

crafted_problem.IO.write_fields_to_file([out.p_opt_filtered], "./out.vtu", ["Filtered_density"])