Optimizers

class lumopt.optimizers.generic_optimizers.ScipyOptimizers(max_iter, method='L-BFGS-G', scaling_factor=1.0, pgtol=1e-05, ftol=1e-12, target_fom=0, scale_initial_gradient_to=None)

Wrapper for the optimizers in SciPy’s optimize package:

Some of the optimization algorithms available in the optimize package (‘L-BFGS-G’ in particular) can approximate the Hessian from the different optimization steps (also called Quasi-Newton Optimization). While this is very powerfull, the figure of merit gradient calculated from a simulation using a continuous adjoint method can be noisy. This can point Quasi-Newton methods in the wrong direction, so use them with caution.

Parameters:
  • max_iter – maximum number of iterations; each iteration can make multiple figure of merit and gradient evaluations.
  • method – string with the chosen minimization algorithm.
  • scaling_factor – scalar or a vector of the same length as the optimization parameters; typically used to scale the optimization parameters so that they have magnitudes in the range zero to one.
  • pgtol – projected gradient tolerance paramter ‘gtol’ (see ‘BFGS’ or ‘L-BFGS-G’ documentation).
  • ftol – tolerance paramter ‘ftol’ which allows to stop optimization when changes in the FOM are less than this
  • target_fom – A target value for the figure of merit. This allows to print/plot the distance of the current design from a target value
  • scale_initial_gradient_to –
class lumopt.optimizers.fixed_step_gradient_descent.FixedStepGradientDescent(max_dx, max_iter, all_params_equal, noise_magnitude, scaling_factor)

Gradient descent with the option to add noise and a parameter scaling. The update equation is:

Delta p_i =

rac{ rac{dFOM}{dp_i}}{max_j(| rac{dFOM}{dp_j}|)}Delta x + ext{noise}_i

If all_params_equal = True, then the update equation is:

Delta p_i = sign(

rac{dFOM}{dp_i})Delta x + ext{noise}_i

If the optimization has many local optima: noise = rand([-1,1])*noise_magnitude.

param max_dx:maximum allowed change of a parameter per iteration.
param max_iter:maximum number of iterations to run.
param all_params_equal:
 if true, all parameters will be changed by +/- dx depending on the sign of their associated shape derivative.
param noise_magnitude:
 amplitude of the noise.
param scaling_factor:
 scalar or vector of the same length as the optimization parameters; typically used to scale the optimization parameters so that they have magnitudes in the range zero to one.
class lumopt.optimizers.adaptive_gradient_descent.AdaptiveGradientDescent(max_dx, min_dx, max_iter, dx_regrowth_factor, all_params_equal, scaling_factor)

Almost identical to FixedStepGradientDescent, except that dx changes according to the following rule:

dx = min(max_dx,dx*dx_regrowth_factor) while newfom < oldfom dx = dx / 2 if dx < min_dx:

dx = min_dx return newfom
Parameters:
  • max_dx – maximum allowed change of a parameter per iteration.
  • min_dx – minimum step size (for the largest parameter changing) allowed.
  • dx_regrowth_factor – by how much dx will be increased at each iteration.
  • max_iter – maximum number of iterations to run.
  • all_params_equal – if true, all parameters will be changed by +/- dx depending on the sign of their associated shape derivative.
  • scaling_factor – scalar or vector of the same length as the optimization parameters; typically used to scale the optimization parameters so that they have magnitudes in the range zero to one.