HimmelblausFunction

class HimmelblausFunction(A=-11, B=-7, objective='minimize', modifiers: List[BaseModifier] | None = None, memory=False, collect_data=True, callbacks=None, catch_errors=None)

Himmelblau’s two-dimensional test function.

A multimodal function with four identical global minima.

The function is defined as:

\[f(x, y) = (x^2 + y + A)^2 + (x + y^2 + B)^2\]

where \(A = -11\) and \(B = -7\) by default.

The four global minima are:

• \(f(3.0, 2.0) = 0\)

• \(f(-2.805118, 3.131312) = 0\)

• \(f(-3.779310, -3.283186) = 0\)

• \(f(3.584428, -1.848126) = 0\)

Parameters:

• A (float, default=-11) – First constant term.

• B (float, default=-7) – Second constant term.

• objective (str, default="minimize") – Either “minimize” or “maximize”.

• modifiers (list of BaseModifier, optional) – List of modifiers to apply to function evaluations.

n_dim

Number of dimensions (always 2).

Type:

int

Examples

>>> from surfaces.test_functions import HimmelblausFunction
>>> func = HimmelblausFunction()
>>> result = func({"x0": 3.0, "x1": 2.0})
>>> abs(result) < 1e-10
True

__call__(params: Dict[str, Any] | ndarray | list | tuple | None = None, *, fidelity: float | None = None, **kwargs)

Evaluate the objective function.

Args:

params: Parameter values as dict, array, list, or tuple fidelity: Optional fidelity level in (0, 1]. Controls evaluation

cost vs accuracy trade-off for multi-fidelity optimization (e.g. Hyperband, BOHB). None means full-fidelity evaluation. Only supported by ML test functions; ignored by algebraic functions.

**kwargs: Parameters as keyword arguments (only with dict input)

Returns:

The objective function value

batch(X: ArrayLike) → ArrayLike

Evaluate multiple parameter sets in a single call.

Parameters:

X (ArrayLike) – 2D array of shape (n_points, n_dim) where each row is a parameter set.

Returns:

1D array of shape (n_points,) with evaluation results.

Return type:

ArrayLike

Raises:

• NotImplementedError – If the function does not implement _batch_objective.

• ValueError – If X has wrong number of dimensions or wrong n_dim.

property callbacks

Callback management (CallbackAccessor).

property data

Evaluation data (DataAccessor).

property errors

Error handler management (ErrorAccessor).

property memory

Memory cache management (MemoryAccessor).

property meta: MetaSpec

Instance display/identity metadata (a frozen MetaSpec).

Metadata is fully static today, so this returns the class-level MetaSpec resolved at class-definition time.

property modifiers

Modifier management (ModifierAccessor).

property plot

Access plotting methods for this function.

pure(params: Dict[str, Any] | ndarray | list | tuple | None = None, *, fidelity: float | None = None, **kwargs)

Evaluate the function without modifiers.

Returns the true (deterministic) function value, bypassing any configured modifiers. Does not update search_data, n_evaluations, or callbacks. Ignores memory caching.

Parameters:

• params (dict, array, list, or tuple) – Parameter values to evaluate.

• fidelity (float or None) – Fidelity level in (0, 1] for multi-fidelity evaluation.

• **kwargs (dict) – Parameters as keyword arguments.

Returns:

The true function value without modifiers, with direction applied.

Return type:

float or np.ndarray

reset() → None

Reset all state including collected data and memory cache.

property search_space: Dict[str, Any]

Search space for this function (read-only public API).

property spec: FunctionSpec

Instance-resolved function specification (a frozen FunctionSpec).

type(self)._spec is the static class-level template. This property overlays the fields that genuinely vary per instance (n_dim, n_objectives, f_global, x_global) by lifting them off the instance, so that func.spec.n_dim reflects this instance’s value. It is resolved on every access rather than cached, because some functions (e.g. BBOB) read spec during __init__ before the optimum has been computed, and a cached early value would go stale.