Modifying a value during optimisation

General
1

Hello,
In order to carry out topology optimisation simulations in fluid mechanics using the density based method, I need to modify a q value over the iterations, used in the k function:
def k(alpha):
return k_max + (k_min - k_max) * alpha * (1. + q) / (alpha + q)
However, I can’t get the optimisation to take account of the change in the value of q. I get exactly the same result without changing the value of q. I also tried to define k as def(k,q) but without success.

Here is part of the code:

# Initial setup for topology optimization
alpha = interpolate(Constant(f_V-0.01), A) # Initial guess for the design variable
set_working_tape(Tape())              # Clear all annotations and restart the adjoint model

# Solve the simulation
u = solve_forward_problem(alpha)

# Visualization files
alpha_pvd_file = File("%s/alpha_iterations.pvd" %(output_folder)); alpha_viz = Function(A, name = "AlphaVisualisation")
dj_pvd_file = File("%s/dj_iterations.pvd" %(output_folder)); dj_viz = Function(A, name = "dJVisualisation")

# Callback during topology optimization
global current_iteration
current_iteration = 0
def derivative_cb_post(j, dj, current_alpha):
    global current_iteration
    if current_iteration >=10:
        q = 0.1
    print("\n [Iteration: %d] J = %1.7e, q = %1.2f\n" %(current_iteration, j, q))
    obj.append(j)
    ité.append(current_iteration)
    current_iteration += 1
    # Save for visualization
    alpha_viz.assign(current_alpha); alpha_pvd_file << alpha_viz
    dj_viz.assign(dj); dj_pvd_file << dj_viz

if current_iteration >=10:
    q = 0.1

# Objective function
u_split = split(u); v = u_split[0]
J = assemble((1/2.*(mu_)*inner(grad(v) + grad(v).T, grad(v) + grad(v).T) + inner(k(alpha) * v, v))*dx)
#J = assemble(w_ud*dot(v - u_target, v - u_target) * dx(6) + inner(k(alpha) * v, v)*dx)

print(" Current objective function value: %1.7e" %(J))

# Set the topology optimization problem and solver
alpha_C = Control(alpha)
Jhat = ReducedFunctional(J, alpha_C, derivative_cb_post = derivative_cb_post)
problem_min = MinimizationProblem(Jhat, bounds = (0.0, 1.0), constraints = [UFLInequalityConstraint((f_V - alpha)*dx, alpha_C)])

solver_opt = IPOPTSolver(problem_min, parameters = {'maximum_iterations': 50 })

# Perform topology optimization
alpha_opt = solver_opt.solve()
alpha.assign(alpha_opt); alpha_viz.assign(alpha)
alpha_pvd_file << alpha_viz

Thank you !

2

Your code snippet is quite incomplete, making it somewhat difficult to help you. Is this code within a loop? And where are you defining the k function, inside or outside that loop? The variable scopes may be a bit tricky.

If this is indeed a single iteration of a (for/while) loop, and you are indeed re-assembling J in each iteration, then it doesn’t seem likely that the indifference to a change in your q parameter is a FEniCS issue.

Have you tried taking ridiculous q values to see if there is a change in results? Or even whether it stops converging, just to test if the variable affects anything.

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3

I finally succeeded in restarting the optimisation after changing q. Thanks a lot!

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