Optimizers

The package provides two families of optimization algorithms:

Gradient-based Optimizers

All gradient-based optimizers inherit from _OptimizerBase and compute numerical gradients via finite differences.

Common Inputs

All gradient-based optimizers share these inputs:

• parameters (Dict): optimization parameters, including initial_parameters and algorithm_settings

• itmax (Int, default 100): maximum number of iterations

• get_best (Bool, default True): whether to return the best result node PK

• structure (StructureData, optional): structure for lattice optimization

Common Outputs

• optimized_parameters (List): the optimized parameter vector

• final_value (Float): the final objective function value

• history (List): iteration history

• result_node_pk (Int, optional): PK of the best AiiDA node

Convergence and Robustness

All gradient-based optimizers include:

• Step clamping: limits step size to max_step (default 0.1) to prevent instability

• Rollback on worse objective: reverts parameters if the objective increases

• Learning rate decay: reduces the step rate when stuck

• Random jump escape: adds random perturbation when stuck for allowed_stuck consecutive iterations

Adam

Adaptive moment estimation optimizer.

Algorithm settings (inside algorithm_settings):

Parameter	Type	Default
learning_rate	float	5e-2
beta1	float	0.5
beta2	float	0.999
tolerance	float	1e-3
epsilon	float	1e-7
delta	float	1e-6

RMSprop

Root mean square propagation optimizer.

Algorithm settings:

Parameter	Type	Default
learning_rate	float	1e-3
rho	float	0.9
tolerance	float	1e-3
epsilon	float	1e-7
delta	float	1e-6

Conjugate Gradient (Polak-Ribiere)

Conjugate gradient optimizer with dynamic learning rate and periodic restarts.

Algorithm settings:

Parameter	Type	Default
learning_rate	float	1e-2
lr_min	float	1e-8
lr_max	float	1.0
lr_increase	float	1.1
lr_decrease	float	0.5
restart_interval	int	10
tolerance	float	1e-3
epsilon	float	1e-7
delta	float	1e-6

BFGS

BFGS quasi-Newton optimizer with backtracking line search (Armijo condition).

Algorithm settings:

Parameter	Type	Default
alpha	float	1.0
beta	float	0.5
sigma	float	1e-4
linesearch_max_iter	int	20
tolerance	float	1e-3
epsilon	float	1e-7
delta	float	1e-6

PyMOO Optimizers

PyMOO_Optimizer wraps algorithms from the PyMOO library in an AiiDA WorkChain. It uses an ask-evaluate-tell loop where each iteration submits a batch of evaluations.

Inputs

• algorithm_name (Str): name of the PyMOO algorithm

• parameters (Dict): contains bounds, algorithm_settings, and optional tol

• itmax (Int): maximum number of iterations

• itmin (Int, default 10): minimum iterations before early stopping via tol

• structure (StructureData, optional): structure for lattice optimization

• get_best (Bool, default True): whether to return the best result PK

Early Stopping

If tol is specified, the optimizer stops when the spread of the best objective values over 3 consecutive iterations falls below tol (after at least itmin iterations).

Bounds

bounds can be:

• A scalar multiplier b: each parameter p gets bounds ((1-b)*p, (1+b)*p)

• A list of [low, high] pairs: explicit bounds for each variable

The number of optimized variables is inferred automatically from the Bravais lattice (when a structure is provided), from initial_parameters, or from the length of the bounds list.

Supported Algorithms

Algorithm Settings

Each algorithm accepts specific keyword arguments inside algorithm_settings (see AlgorithmBuilder). Use string names for operators (e.g., "SBX" for crossover, "FRS" for sampling, "TOS" for selection).

AlgorithmBuilder

Parameter Normalization