ctrl-freak: User Function Contracts

This document specifies the exact contracts for user-provided functions and strategy protocols in ctrl-freak.

Philosophy

User thinks about individuals. Framework handles populations.

You write functions that operate on a single individual. The framework:

Calls your functions in a loop over the population
Handles parent selection via customizable selection strategies
Manages algorithm-specific survival logic (Pareto ranking, fitness-based selection, etc.)
Orchestrates the generational cycle

This separation keeps user code simple and domain-focused while the framework handles algorithmic complexity.

The framework supports both single-objective optimization (via ga()) and multi-objective optimization (via nsga2()), with extensible selection and survival strategies.

Algorithm Selection

ctrl-freak provides two main algorithms:

Algorithm	Function	Objectives	Default Selection	Default Survival
NSGA-II	`nsga2()`	Multi-objective	Crowded tournament	NSGA-II (fronts + crowding)
Standard GA	`ga()`	Single-objective	Fitness tournament	Elitist

Both algorithms accept the same user-defined functions (init, evaluate, crossover, mutate) but differ in how they handle selection and survival.

Objective Direction

All objectives are minimized.

To maximize an objective, negate it:

def evaluate(x: np.ndarray) -> np.ndarray:
    accuracy = compute_accuracy(x)      # Want to maximize
    latency = compute_latency(x)        # Want to minimize
    return np.array([-accuracy, latency])  # Negate accuracy

Function Contracts

`init(rng: np.random.Generator) -> np.ndarray`

Generates the decision variables for one individual.

Aspect	Specification
Input	`rng`: A seeded `numpy.random.Generator` instance
Output	`np.ndarray` with shape `(n_vars,)` and dtype `float64`
User responsibilities	Generate values within valid bounds; ensure returned array has correct shape
Framework responsibilities	Provides a seeded RNG for reproducibility; calls `init` once per individual

Example:

def init(rng: np.random.Generator) -> np.ndarray:
    # Continuous variables in [0, 1]
    continuous = rng.uniform(0, 1, size=5)

    # Integer variables in {0, 1, 2, 3, 4}
    integers = rng.integers(0, 5, size=3).astype(float)

    return np.concatenate([continuous, integers])

Notes:

Always use the provided rng for randomness (not np.random.random())
The framework does not validate bounds; out-of-bounds values propagate silently
All decision variables must be numeric (float64)

`evaluate(x: np.ndarray) -> np.ndarray | float`

Computes objective values for one individual.

Multi-Objective Evaluation (for nsga2())

Aspect	Specification
Input	`x`: `np.ndarray` with shape `(n_vars,)` containing decision variables
Output	`np.ndarray` with shape `(n_obj,)` containing objective values to minimize
User responsibilities	Return finite values; handle constraints via penalties; negate objectives to maximize
Framework responsibilities	Automatic lifting to population via `lift()`; never modifies input

Example:

def evaluate(x: np.ndarray) -> np.ndarray:
    # Two objectives
    f1 = x[0] ** 2 + x[1] ** 2          # Sphere
    f2 = (x[0] - 1) ** 2 + x[1] ** 2    # Shifted sphere
    return np.array([f1, f2])

Requirements:

Return values must be finite (np.isfinite(obj).all() must be True)
All objectives must be returned in consistent order across calls
Shape must be exactly (n_obj,), not (n_obj, 1) or (1, n_obj)

Invalid outputs:

np.inf or -np.inf (breaks crowding distance calculation)
np.nan (breaks dominance comparisons)
Wrong shape (causes stacking errors)

Parallel execution requirements:

When using n_workers > 1, the evaluate function must be picklable:

Define functions at module level (not inside other functions)
Avoid closures over unpicklable objects (file handles, database connections)
Lambda functions work if they don't capture unpicklable state

Single-Objective Evaluation (for ga())

When using the ga() function for single-objective optimization, evaluate returns a scalar:

Aspect	Specification
Input	`x`: `np.ndarray` with shape `(n_vars,)`
Output	`float` — single objective value to minimize

Example:

def evaluate(x: np.ndarray) -> float:
    """Sphere function: minimize sum of squares."""
    return float(np.sum(x ** 2))

`crossover(p1: np.ndarray, p2: np.ndarray) -> np.ndarray`

Combines two parent individuals to produce one child.

Aspect	Specification
Input	`p1`, `p2`: Each `np.ndarray` with shape `(n_vars,)`
Output	`np.ndarray` with shape `(n_vars,)` representing one child
User responsibilities	Preserve bounds if needed; preserve constraint invariants if needed
Framework responsibilities	Selects parents via binary tournament; provides two distinct parents

Example (SBX-like):

def crossover(p1: np.ndarray, p2: np.ndarray) -> np.ndarray:
    # Simulated binary crossover (simplified)
    eta = 20  # Distribution index
    u = np.random.random(len(p1))

    beta = np.where(
        u <= 0.5,
        (2 * u) ** (1 / (eta + 1)),
        (1 / (2 * (1 - u))) ** (1 / (eta + 1))
    )

    child = 0.5 * ((1 + beta) * p1 + (1 - beta) * p2)
    return np.clip(child, 0, 1)  # Enforce bounds

Example (uniform):

def crossover(p1: np.ndarray, p2: np.ndarray) -> np.ndarray:
    mask = np.random.random(len(p1)) < 0.5
    return np.where(mask, p1, p2)

Notes:

Always produces exactly one child (not two)
Parents may be identical (handle gracefully)
Bounds enforcement is user responsibility

`mutate(x: np.ndarray) -> np.ndarray`

Mutates one individual.

Aspect	Specification
Input	`x`: `np.ndarray` with shape `(n_vars,)`
Output	`np.ndarray` with shape `(n_vars,)` representing mutated individual
User responsibilities	Enforce bounds (clip); repair constraint violations; control mutation rate
Framework responsibilities	None. Full control given to user.

Example (Gaussian):

def mutate(x: np.ndarray) -> np.ndarray:
    mutation_rate = 0.1
    sigma = 0.1

    # Mutate each gene with probability mutation_rate
    mask = np.random.random(len(x)) < mutation_rate
    noise = np.random.normal(0, sigma, len(x))
    mutated = x + mask * noise

    return np.clip(mutated, 0, 1)  # Enforce bounds

Example (polynomial):

def mutate(x: np.ndarray) -> np.ndarray:
    eta = 20  # Distribution index
    lower, upper = 0.0, 1.0

    mutated = x.copy()
    for i in range(len(x)):
        if np.random.random() < 0.1:  # Mutation probability
            delta = min(x[i] - lower, upper - x[i]) / (upper - lower)
            u = np.random.random()

            if u < 0.5:
                deltaq = (2 * u + (1 - 2 * u) * (1 - delta) ** (eta + 1)) ** (1 / (eta + 1)) - 1
            else:
                deltaq = 1 - (2 * (1 - u) + 2 * (u - 0.5) * (1 - delta) ** (eta + 1)) ** (1 / (eta + 1))

            mutated[i] = x[i] + deltaq * (upper - lower)

    return np.clip(mutated, lower, upper)

Critical requirements:

Always return values within valid bounds
The framework does not clip or validate output
Out-of-bounds values propagate through the entire algorithm

Strategy Protocols

The framework uses protocols to define extensible selection and survival strategies. These allow you to customize algorithm behavior while maintaining type safety.

ParentSelector Protocol

Parent selectors choose which individuals become parents for reproduction.

from typing import Protocol
import numpy as np
from ctrl_freak import Population

class ParentSelector(Protocol):
    def __call__(
        self,
        pop: Population,
        n_parents: int,
        rng: np.random.Generator,
        **kwargs: np.ndarray,
    ) -> np.ndarray:
        """
        Select parent indices from the population.

        Args:
            pop: Population to select from
            n_parents: Number of parents to select
            rng: Random number generator for reproducibility
            **kwargs: Algorithm-specific metadata (e.g., rank, crowding_distance, fitness)

        Returns:
            np.ndarray of shape (n_parents,) containing selected indices
        """
        ...

Contract:

Must return exactly n_parents indices
Indices must be valid (0 <= idx < len(pop))
Must use provided rng for any randomness
May select the same individual multiple times

Built-in implementations:

crowded_tournament(tournament_size=2) — For NSGA-II, uses rank and crowding distance
fitness_tournament(tournament_size=2) — For GA, uses fitness values
roulette_wheel() — Fitness-proportionate selection

SurvivorSelector Protocol

Survivor selectors determine which individuals survive to the next generation.

class SurvivorSelector(Protocol):
    def __call__(
        self,
        pop: Population,
        n_survivors: int,
        **kwargs: np.ndarray,
    ) -> tuple[np.ndarray, dict[str, np.ndarray]]:
        """
        Select survivors and compute algorithm-specific state.

        Args:
            pop: Combined population (parents + offspring)
            n_survivors: Number of individuals to keep
            **kwargs: Algorithm-specific inputs (e.g., parent_size, fitness)

        Returns:
            Tuple of:
            - np.ndarray of shape (n_survivors,) containing survivor indices
            - dict mapping state names to arrays (e.g., {'rank': ..., 'fitness': ...})
        """
        ...

Contract:

Must return exactly n_survivors indices
Indices must be valid (0 <= idx < len(pop))
State dict keys and values are algorithm-specific
For NSGA-II: returns {'rank': ..., 'crowding_distance': ...}
For GA: returns {'fitness': ...}

Built-in implementations:

nsga2_survival() — Non-dominated sorting with crowding distance
truncation_survival() — Keep best k by fitness
elitist_survival(elite_count=1) — Preserve elite parents, fill with best offspring

Implementing Custom Strategies

Custom Parent Selector

import numpy as np
from ctrl_freak import Population

def rank_proportionate_selection(
    pop: Population,
    n_parents: int,
    rng: np.random.Generator,
    **kwargs: np.ndarray,
) -> np.ndarray:
    """Select parents with probability inversely proportional to rank."""
    rank = kwargs.get('rank')
    if rank is None:
        raise ValueError("rank_proportionate_selection requires 'rank' kwarg")

    # Lower rank = higher probability
    max_rank = rank.max()
    weights = (max_rank - rank + 1).astype(float)
    weights /= weights.sum()

    return rng.choice(len(pop), size=n_parents, p=weights).astype(np.intp)


# Usage
result = nsga2(..., select=rank_proportionate_selection)

Custom Survivor Selector

def age_based_survival(
    pop: Population,
    n_survivors: int,
    **kwargs: np.ndarray,
) -> tuple[np.ndarray, dict[str, np.ndarray]]:
    """Survival favoring younger individuals (lower index = older)."""
    fitness = kwargs.get('fitness')
    if fitness is None:
        if pop.objectives is None or pop.objectives.shape[1] != 1:
            raise ValueError("Requires fitness kwarg or single-objective population")
        fitness = pop.objectives[:, 0]

    # Favor younger individuals by adding age penalty
    age_penalty = np.arange(len(pop)) * 0.01
    adjusted_fitness = fitness + age_penalty

    indices = np.argsort(adjusted_fitness)[:n_survivors]
    return indices.astype(np.intp), {'fitness': fitness[indices]}


# Usage
result = ga(..., survive=age_based_survival)

Contract Summary Table

User Functions

Function	Input Shape	Output Shape	User Enforces	Framework Provides
`init`	(seeded RNG)	`(n_vars,)`	Bounds	Seeded RNG
`evaluate`	`(n_vars,)`	`(n_obj,)` or `float`	Finite values, constraints	Lifting to population
`crossover`	`(n_vars,)`, `(n_vars,)`	`(n_vars,)`	Bounds preservation	Tournament-selected parents
`mutate`	`(n_vars,)`	`(n_vars,)`	Bounds (clip)	Nothing

Strategy Protocols

Protocol	Input	Output	Built-in Implementations
`ParentSelector`	pop, n_parents, rng, **kwargs	indices array	crowded_tournament, fitness_tournament, roulette_wheel
`SurvivorSelector`	pop, n_survivors, **kwargs	(indices, state_dict)	nsga2_survival, truncation_survival, elitist_survival

Constraint Handling Strategies

The framework is constraint-agnostic. Users implement constraint handling through their functions.

Design Philosophy: Feasibility is User Responsibility

All user functions must return feasible individuals. This is a consistent contract across init, crossover, and mutate. The framework does not provide a repair parameter — if you need to repair solutions, compose your operators with a repair function:

from ctrl_freak import sbx_crossover, polynomial_mutation

# Your domain-specific repair function
def repair(x: np.ndarray) -> np.ndarray:
    # Example: enforce x[0] + x[1] <= 1
    if x[0] + x[1] > 1:
        scale = 1 / (x[0] + x[1])
        x = x.copy()
        x[0] *= scale
        x[1] *= scale
    return x

# Compose repair with standard operators
sbx = sbx_crossover(eta=15.0, bounds=(0.0, 1.0), seed=42)
poly_mut = polynomial_mutation(eta=20.0, bounds=(0.0, 1.0), seed=42)

crossover = lambda p1, p2: repair(sbx(p1, p2))
mutate = lambda x: repair(poly_mut(x))

# Use composed operators
result = nsga2(
    init=lambda rng: repair(rng.uniform(0, 1, size=10)),
    evaluate=evaluate,
    crossover=crossover,
    mutate=mutate,
    pop_size=100,
    n_generations=50,
)

This approach keeps the framework simple and gives you full control over when and how repair is applied.

Hard Constraints (must be satisfied)

Strategy 1: Repair in mutation

def mutate(x: np.ndarray) -> np.ndarray:
    mutated = x + np.random.normal(0, 0.1, len(x))
    mutated = np.clip(mutated, lower_bounds, upper_bounds)  # Box constraints

    # Repair constraint: x[0] + x[1] <= 1
    if mutated[0] + mutated[1] > 1:
        scale = 1 / (mutated[0] + mutated[1])
        mutated[0] *= scale
        mutated[1] *= scale

    return mutated

Strategy 2: Preserve in crossover

def crossover(p1: np.ndarray, p2: np.ndarray) -> np.ndarray:
    # Both parents satisfy constraint; convex combination also satisfies
    alpha = np.random.random()
    return alpha * p1 + (1 - alpha) * p2  # Preserves convex constraints

Strategy 3: Rejection in init

def init(rng: np.random.Generator) -> np.ndarray:
    while True:
        x = rng.uniform(0, 1, size=N_VARS)
        if constraint_satisfied(x):
            return x

Soft Constraints (penalty-based)

Add constraint violations as additional objectives:

def evaluate(x: np.ndarray) -> np.ndarray:
    # Original objectives
    f1 = objective_1(x)
    f2 = objective_2(x)

    # Constraint violations (0 when satisfied, positive when violated)
    g1 = max(0, x[0] + x[1] - 1)           # x[0] + x[1] <= 1
    g2 = max(0, 0.5 - x[2])                 # x[2] >= 0.5

    # Option A: Sum all violations into one penalty objective
    return np.array([f1, f2, g1 + g2])

    # Option B: Each constraint as separate objective (higher dimensional Pareto front)
    return np.array([f1, f2, g1, g2])

Mixed Strategy

Combine repair for simple constraints with penalties for complex ones:

def mutate(x: np.ndarray) -> np.ndarray:
    mutated = x + np.random.normal(0, 0.1, len(x))
    # Repair simple box constraints
    mutated = np.clip(mutated, 0, 1)
    return mutated

def evaluate(x: np.ndarray) -> np.ndarray:
    f1 = compute_cost(x)
    f2 = compute_time(x)

    # Complex nonlinear constraint as penalty
    violation = max(0, nonlinear_constraint(x))
    return np.array([f1, f2, violation])

Common Pitfalls

Shape Errors

# Wrong: returns (n_obj, 1) instead of (n_obj,)
def evaluate(x):
    return np.array([[f1], [f2]])  # Shape (2, 1)

# Correct
def evaluate(x):
    return np.array([f1, f2])      # Shape (2,)

Non-finite Values

# Wrong: can return inf
def evaluate(x):
    return np.array([1 / x[0], x[1]])  # inf when x[0] = 0

# Correct: handle edge cases
def evaluate(x):
    f1 = 1 / x[0] if x[0] != 0 else 1e10  # Large but finite
    return np.array([f1, x[1]])

Ignoring the Provided RNG

# Wrong: not reproducible
def init(rng):
    return np.random.random(N_VARS)  # Uses global state

# Correct
def init(rng):
    return rng.random(N_VARS)        # Uses provided generator

Forgetting Bounds Enforcement

# Wrong: mutation can escape bounds
def mutate(x):
    return x + np.random.normal(0, 0.1, len(x))

# Correct
def mutate(x):
    mutated = x + np.random.normal(0, 0.1, len(x))
    return np.clip(mutated, lower, upper)

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ctrl-freak: User Function Contracts

Philosophy

Algorithm Selection

Objective Direction

Function Contracts

`init(rng: np.random.Generator) -> np.ndarray`

`evaluate(x: np.ndarray) -> np.ndarray | float`

Multi-Objective Evaluation (for nsga2())

Single-Objective Evaluation (for ga())

`crossover(p1: np.ndarray, p2: np.ndarray) -> np.ndarray`

`mutate(x: np.ndarray) -> np.ndarray`

Strategy Protocols

ParentSelector Protocol

SurvivorSelector Protocol

Implementing Custom Strategies

Custom Parent Selector

Custom Survivor Selector

Contract Summary Table

User Functions

Strategy Protocols

Constraint Handling Strategies

Design Philosophy: Feasibility is User Responsibility

Hard Constraints (must be satisfied)

Soft Constraints (penalty-based)

Mixed Strategy

Common Pitfalls

Shape Errors

Non-finite Values

Ignoring the Provided RNG

Forgetting Bounds Enforcement

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ctrl-freak: User Function Contracts

Philosophy

Algorithm Selection

Objective Direction

Function Contracts

init(rng: np.random.Generator) -> np.ndarray

evaluate(x: np.ndarray) -> np.ndarray | float

Multi-Objective Evaluation (for nsga2())

Single-Objective Evaluation (for ga())

crossover(p1: np.ndarray, p2: np.ndarray) -> np.ndarray

mutate(x: np.ndarray) -> np.ndarray

Strategy Protocols

ParentSelector Protocol

SurvivorSelector Protocol

Implementing Custom Strategies

Custom Parent Selector

Custom Survivor Selector

Contract Summary Table

User Functions

Strategy Protocols

Constraint Handling Strategies

Design Philosophy: Feasibility is User Responsibility

Hard Constraints (must be satisfied)

Soft Constraints (penalty-based)

Mixed Strategy

Common Pitfalls

Shape Errors

Non-finite Values

Ignoring the Provided RNG

Forgetting Bounds Enforcement

`init(rng: np.random.Generator) -> np.ndarray`

`evaluate(x: np.ndarray) -> np.ndarray | float`

`crossover(p1: np.ndarray, p2: np.ndarray) -> np.ndarray`

`mutate(x: np.ndarray) -> np.ndarray`