Skip to content

DEEM

DEEM — base algorithm

j-machacek/DEEM

`DEEM` — base algorithm¶

from DEEM.DEEM import DEEM

The base optimiser. Construct it with the objective and bounds, then call update() to run the optimisation loop.

Constructor¶

DEEM(
    function, lower_bound, upper_bound, X0=None,
    nparticles_max=50, nparticles_min=50,
    nswarm_max=10, nswarm_min=2,
    maxiter=1000, maxfev=100000000,
    sampling_method='LHS',
    nworkers=1,
    tolerance=1e-6, termination='iterations',
    maxiter_below_tolerance=30, log_interval=1,
    method_subswarm_reduction='sigmoid-3',
    method_boundary='damping',
    method_subswarm_creation='equally-distributed',
    method_reset='density',
    niter_reset_global=None,
    penalty=1e22,
)

Required arguments¶

Argument	Type	Description
`function`	callable	Objective \(f(\mathbf{x})\) to minimise; takes a 1-D array, returns a float.
`lower_bound`	array-like	Lower bounds \(\mathbf{LB}\), length \(n_D\).
`upper_bound`	array-like	Upper bounds \(\mathbf{UB}\), length \(n_D\).

Population and sub-populations¶

Argument	Default	Description
`X0`	`None`	Optional initial guess; used as the first candidate's start position.
`nparticles_max`	`50`	Maximum population size \(n_c\).
`nparticles_min`	`50`	Minimum population size (set `< max` for L-SHADE-style shrinking).
`nswarm_max`	`10`	Maximum number of sub-populations \(n_s\).
`nswarm_min`	`2`	Minimum number of sub-populations.
`method_subswarm_reduction`	`'sigmoid-3'`	Schedule for reducing \(n_s\): `constant`, `linear`, `exponential`, `sigmoid-2`, `sigmoid-3`.
`method_subswarm_creation`	`'equally-distributed'`	Sub-population creation: `equally-distributed`, `fitness-focused`.

Budget and termination¶

Argument	Default	Description
`maxiter`	`1000`	Maximum number of iterations \(n_i^{max}\).
`maxfev`	`1e8`	Maximum number of function evaluations \(n_f^{max}\).
`termination`	`'iterations'`	`'iterations'` runs the full `maxiter`; `'tolerance'` stops early.
`tolerance`	`1e-6`	Early-termination tolerance \(TOL\).
`maxiter_below_tolerance`	`30`	Iterations below \(TOL\) before stopping (\(n_i^{TOL}\)).
`niter_reset_global`	`None`	Restart threshold \(n_i^{res}\); defaults to `maxiter // 10`.

Sampling, boundaries, restart, misc¶

Argument	Default	Description
`sampling_method`	`'LHS'`	Initial sampling: `LHS`, `Random-Uniform`, `Sobol`, `Halton`, `Grid`.
`method_boundary`	`'damping'`	Boundary handling: `clip`, `random`, `damping`, `periodic`, `damping-periodic`, `damping-periodic-random`, `damping-periodic-clip`.
`method_reset`	`'density'`	Restart strategy (base algorithm: `density`).
`nworkers`	`1`	Parallel workers for evaluation (`1` = serial).
`log_interval`	`1`	Iterations between log lines.
`penalty`	`1e22`	Value treated as the penalty/infeasible marker.

Methods¶

`update()`¶

Runs the full optimisation loop until a termination criterion is met. Updates the result attributes in place.

optimizer.update()

Result attributes¶

After update() returns, read the result from:

Attribute	Description
`XBEST`	Best position found, \(\mathbf{x}_{GB}\).
`FBEST`	Best objective value found.
`fev`	Number of function evaluations performed.
`XBEST_history`, `FBEST_history`	History of improvements to the global best.
`iters`	Number of iterations executed.

Objective convention

DEEM minimises. For a maximisation problem, pass the negated objective and negate FBEST afterwards.