What was added

This PR continues the work started in #14, where population initialization schemes were added to Population.

The goal now is to make these schemes part of the hyper-heuristic search process as well. In practice, the hyper-heuristic off CUSTOMHYS can now choose not only the sequence of perturbation operators, but also how the initial population should be created.

The implementation follows @jcrvz’s suggestion in issue #16: treating initializers as first-class operators within the heuristic space itself, while distinguishing them from perturbation operators through an explicit classification.

Main changes

operators.py — initializers as operators

The initialization schemes added in #14 are now also available as operator functions:

• initialize_random
• initialize_sobol
• initialize_halton
• initialize_grid
• initialize_lhs
• initialize_beta
• initialize_normal
• initialize_lognormal
• initialize_exponential
• initialize_rayleigh

These functions were added to __all__, along with their respective aliases.

A simple prefix-based role classification was also introduced through _ROLE_PREFIXES:

_ROLE_PREFIXES: dict[str, str] = {
    "initialize_": "initialize",
}

def _get_role(op_tuple) -> str:
    name = op_tuple[0]
    for prefix, role in _ROLE_PREFIXES.items():
        if name.startswith(prefix):
            return role
    return "perturb"

With this approach, the role of each operator is derived directly from its name. This avoids adding an extra field to the tuples and keeps role-related strings centralized.

It also makes future extensions straightforward. If new operator types are introduced later, such as adapt_ or select_, they can be supported by adding a single new prefix to the dictionary.

customhys/collections/default_initializers.txt

A new collection file was added with the initialization operators in the framework’s standard 3-tuple format.

This file can be loaded by Hyperheuristic together with any perturbation operator collection.

hyperheuristic.py — initializer support in the SA loop

When the heuristic space contains operators with role "initialize", the hyper-heuristic now treats position 0 of each candidate solution as the selected initializer.

The remaining positions continue to represent the perturbation operator sequence.

The main changes include:

• initialization_operators: a new property that lists the initialization operators available in the heuristic space, along with their indices.
• Candidate generation: position 0 is always filled with an initialization operator, while the rest of the solution is generated normally.
• SA mutations: actions such as Swap, Mirror, Roll, Shift, Remove, and similar ones were updated to operate only on the tail of the solution, preserving the initializer at the head.
• ChangeInitOperator: a new action that replaces the initialization operator at position 0 with another available initializer. This action is enabled only when at least two initializers exist in the space.
• evaluate_candidate_solution: the initialization operator is extracted from the head of the solution, converted into initial_scheme, and passed to Metaheuristic, which then forwards it to Population.initialise_positions().
• Compatibility preserved: Metaheuristic still receives only the tail 3-tuples, so the existing perturbation behavior remains unchanged.
• Bugfix: Remove and RemoveMany now return the current solution unchanged when the cardinality is already at the minimum with initializers present, instead of raising HyperheuristicError.

Tests

Two new test files were added, with a total of 95 tests.

tests/test_initialization_operators.py

Covers:

• _get_role
• _ROLE_PREFIXES
• process_operators
• all initialize_* functions
• the different Population.initialise_positions() variants

tests/test_hyperheuristic_initialization.py

Covers:

• the initialization_operators property
• the ChangeInitOperator action
• initializer preservation at the head of the solution across mutations
• evaluate_candidate_solution with an initialization operator
• build_operators
• integration tests with the full SA loop using Sphere, Rastrigin, and Ackley1 from benchmark_func

Backward compatibility

Heuristic spaces without initialization operators continue to work as before.

In these cases, _get_role returns "perturb" by default, and all initializer-specific behavior remains disabled.

Obs: need suport for vertex init in future