VLJ_ALGO

VLJ_ALGO sets the algorithm(s) used during the tensor-LEED optimization using the viperleed-jax plugin. When an algorithm is specified as a flag, that parameters settings can specified instead.

Default: CMAES, SLSQP

Syntax:

! setting the algorithm to use
VLJ_ALGO = CMAES          ! use only the CMA-ES algorithm
VLJ_ALGO = CMAES, BFGS    ! use a two-step optimization with CMA-ES and BFGS
VLJ_ALGO = SLSQP          ! use only the SLSQP algorithm

! settings for the algorithms
VLJ_ALGO CMAES = pop 50, gens 100, ftol 1e-4
VLJ_ALGO SLSQP = grad False

When using VLJ_ALGO without a flag, one or two algorithms can be specified on the right-hand side, separated by commas. If two algorithms are specified, a two-phase optimization will be performed where the second algorithm starts from the best result of the first phase. This can be useful to combine the global search capabilities of CMA-ES with the local refinement capabilities of gradient-based algorithms such as BFGS or SLSQP.

On a separate line, any of the algorithms can be specified as a flag to specify settings to be used for the optimization using that algorithm. See below for the allowed flags and their values for each algorithm.

VLJ_CONFIG precondition

CMAES

The CMA-ES (Covariance Matrix Adaptation Evolution Strategy) algorithm is a global optimization algorithm that is well-suited for high-dimensional and noisy optimization problems. viperleed-jax uses the implementation of CMA-ES from the Wanzenböck et al. [27] library.

Default: pop 30, gens 200, ftol 1e-3

Syntax:

! settings for the algorithms
VLJ_ALGO CMAES = pop 50, gens 100, ftol 1e-4
VLJ_ALGO CMAES = gens 400, ftol 1e-5

Available setting for CMAES are:

  • pop: Population size, i.e. number of samples per generation.

  • gens: Maximum number of generations to run the algorithm. If the algorithm converges before reaching this number, it will stop early.

  • ftol: The convergence criterion on the R-factor value. The algorithm will stop standard deviation of the best R-factor values over the last convergence_gens generations is below this value.

  • convergence_gens: The number of generations to consider when evaluating convergence based on the ftol criterion.

SLSQP

The SLSQP (Sequential Least Squares Programming) algorithm is a gradient-based optimization algorithm that is well-suited for constrained optimization problems. viperleed-jax uses the implementation of SLSQP from the SciPy library.

Default: grad True, grad_damping 0.1

Available setting for SLSQP are:

  • grad: Toggle calculation of gradients using automatic differentiation.

  • grad_damping: A factor applied to the computed gradient which can help to avoid the algorithm jumping outside of the basin around the global minimum.

BFGS

The BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm is a different gradient-based optimization algorithm well suited to high-dimensional problems. Unlike SLSQP it always evaluates the gradient at every step. viperleed-jax uses the implementation of BFGS from the SciPy library.

Default: grad True

Available setting for BFGS are:

  • grad: Toggle calculation of gradients using automatic differentiation.

Note

The grad switch for the SLSQP and BFGS algorithms can have significant impact on the performance of the optimization. If set to False, the algorithm will use finite differences to approximate gradients. If set to True, the algorithm will use automatic differentiation to compute gradients, which can be more efficient, but may significantly increase memory usage due to the need to store intermediate results for gradient calculation.