New Genetic Algorithm solution for Knapsack problem

DIRECTORY.md

@@ -195,6 +195,7 @@
     * [Permutations](data_structures/arrays/permutations.py)
     * [Prefix Sum](data_structures/arrays/prefix_sum.py)
     * [Product Sum](data_structures/arrays/product_sum.py)
+    * [Rotate Array](data_structures/arrays/rotate_array.py)
     * [Sparse Table](data_structures/arrays/sparse_table.py)
     * [Sudoku Solver](data_structures/arrays/sudoku_solver.py)
   * Binary Tree
@@ -460,6 +461,7 @@
 
 ## Genetic Algorithm
   * [Basic String](genetic_algorithm/basic_string.py)
+  * [Knapsack](genetic_algorithm/knapsack.py)
 
 ## Geodesy
   * [Haversine Distance](geodesy/haversine_distance.py)

genetic_algorithm/knapsack.py

@@ -0,0 +1,345 @@
+"""Did you know that Genetic Algorithms can be used to quickly approximate
+combinatorial optimization problems such as knapsack?
+
+It is commonly known that combinatorial optimization problems can be solved using
+dynamic programming. It is lesser known that genetic algorithms (or evolutionary
+computing in general) can reach the best solution fairly quickly in a lot of cases.
+Otherwise, it can still approximate a very good solution (in life, good is good
+enough).
+
+Genetic algorithms: https://en.wikipedia.org/wiki/Genetic_algorithm
+Evolutionary computation: https://en.wikipedia.org/wiki/Evolutionary_computation
+Knapsack problem: https://en.wikipedia.org/wiki/Knapsack_problem
+
+Run doctests:
+    python -m doctest -v knapsack.py
+"""
+
+import random
+from dataclasses import dataclass
+
+random.seed(42)
+
+# =========================== Problem setup: Knapsack ===========================
+
+KNAPSACK_N_ITEMS: int = 42  # Number of items in the knapsack problem
+KNAPSACK_VALUE_RANGE: tuple[int, int] = (10, 100)  # Range of item values
+KNAPSACK_WEIGHT_RANGE: tuple[int, int] = (5, 50)  # Range of item weights
+KNAPSACK_CAPACITY_RATIO: float = 0.5  # Capacity as a fraction of total weight
+
+
+@dataclass
+class Item:
+    value: int
+    weight: int
+
+
+def generate_knapsack_instance(
+    n_items: int,
+    value_range: tuple[int, int],
+    weight_range: tuple[int, int],
+    capacity_ratio: float,
+) -> tuple[list[Item], int]:
+    """
+    Generates a random knapsack problem instance.
+
+    Returns a tuple: (items, capacity), where items is a list of Item(value, weight)
+    and capacity is an int computed as floor(capacity_ratio * total_weight).
+
+    Examples
+    --------
+    Use a tiny, deterministic instance to validate shape and capacity range:
+
+    >>> random.seed(0)
+    >>> items, cap = generate_knapsack_instance(
+    ...     n_items=3,
+    ...     value_range=(5, 5),
+    ...     weight_range=(10, 10),
+    ...     capacity_ratio=0.5
+    ... )
+    >>> len(items), cap
+    (3, 15)
+    >>> all(isinstance(it, Item) for it in items)
+    True
+    >>> [it.value for it in items], [it.weight for it in items]
+    ([5, 5, 5], [10, 10, 10])
+    """
+    items = []
+    for _ in range(n_items):
+        value = random.randint(*value_range)
+        weight = random.randint(*weight_range)
+        items.append(Item(value=value, weight=weight))
+    # Capacity as a fraction of total weight
+    capacity = int(sum(it.weight for it in items) * capacity_ratio)
+    return items, capacity
+
+
+# Example instance (guarded by __main__ below for printing)
+items, capacity = generate_knapsack_instance(
+    n_items=KNAPSACK_N_ITEMS,
+    value_range=KNAPSACK_VALUE_RANGE,
+    weight_range=KNAPSACK_WEIGHT_RANGE,
+    capacity_ratio=KNAPSACK_CAPACITY_RATIO,
+)
+
+# ============================== GA Representation ==============================
+
+# HYPERPARAMETERS (For tuning the GA)
+
+POPULATION_SIZE = 120
+GENERATIONS = 200
+CROSSOVER_PROBABILITY = 0.9
+MUTATION_PROBABILITY = 0.01
+TOURNAMENT_K = 3
+ELITISM = 2
+
+OVERWEIGHT_PENALTY_FACTOR = 10
+
+genome_t = list[int]  # An index list where 1 means item is included, 0 means excluded
+
+
+def evaluate(genome: genome_t, items: list[Item], capacity: int) -> tuple[int, int]:
+    """
+    Calculates fitness (value) and weight of a candidate solution. If overweight,
+    the returned value is penalized; weight is the actual summed weight.
+
+    Returns (value, weight).
+
+    Examples
+    --------
+    Feasible genome (no penalty):
+
+    >>> it = [Item(10, 4), Item(7, 3), Item(5, 2)]
+    >>> genome = [1, 0, 1]  # take items 0 and 2
+    >>> evaluate(genome, it, capacity=7)
+    (15, 6)
+
+    Overweight genome (penalty applies):
+    Total value = 10+7+5 = 22, total weight = 9, capacity = 7, overflow = 2
+    Penalized value = max(0, 22 - 2 * OVERWEIGHT_PENALTY_FACTOR) = 2
+
+    >>> genome = [1, 1, 1]
+    >>> evaluate(genome, it, capacity=7)
+    (2, 9)
+    """
+    total_value = 0
+    total_weight = 0
+    for gene, item in zip(genome, items):
+        if gene:
+            total_value += item.value
+            total_weight += item.weight
+    if total_weight > capacity:
+        overflow = total_weight - capacity
+        total_value = max(0, total_value - overflow * OVERWEIGHT_PENALTY_FACTOR)
+    return total_value, total_weight
+
+
+def random_genome(length: int) -> genome_t:
+    """
+    Generates a random genome (list of 0/1) of length n.
+
+    Examples
+    --------
+    Check length and content are 0/1 bits:
+
+    >>> random.seed(123)
+    >>> g = random_genome(5)
+    >>> len(g), set(g).issubset({0, 1})
+    (5, True)
+    """
+    return [random.randint(0, 1) for _ in range(length)]
+
+
+def selection(
+    population: list[genome_t], fitnesses: list[int], tournament_k: int
+) -> genome_t:
+    """
+    Performs tournament selection to choose a genome from the population.
+
+    Note that other selection strategies exist such as roulette wheel, rank-based, etc.
+
+    Examples
+    --------
+    Deterministic tournament with fixed seed (k=2):
+
+    >>> random.seed(1)
+    >>> pop = [[0,0,0], [1,0,0], [1,1,0], [1,1,1]]
+    >>> fits = [0, 5, 9, 7]
+    >>> parent = selection(pop, fits, tournament_k=2)
+    >>> parent in pop
+    True
+    """
+    contenders = random.sample(list(zip(population, fitnesses)), tournament_k)
+    return max(contenders, key=lambda contender: contender[1])[0][:]
+
+
+def crossover(
+    genome_1: genome_t, genome_2: genome_t, p_crossover: float
+) -> tuple[genome_t, genome_t]:
+    """
+    Performs single-point crossover between two genomes.
+    If crossover does not occur (random > p_crossover) or genomes are too short,
+    returns copies of the parents.
+
+    Note: other crossover strategies exist (two-point, uniform, etc.).
+
+    Examples
+    --------
+    Force crossover with p=1.0 and fixed RNG; verify lengths and bit content:
+
+    >>> random.seed(2)
+    >>> a, b = [0,0,0,0], [1,1,1,1]
+    >>> c1, c2 = crossover(a, b, p_crossover=1.0)
+    >>> len(c1) == len(a) == len(c2) == len(b)
+    True
+    >>> set(c1).issubset({0,1}) and set(c2).issubset({0,1})
+    True
+
+    No crossover if p=0.0:
+
+    >>> c1, c2 = crossover([0,0,0], [1,1,1], p_crossover=0.0)
+    >>> c1, c2
+    ([0, 0, 0], [1, 1, 1])
+    """
+    min_length = min(len(genome_1), len(genome_2))
+    if random.random() > p_crossover or min_length < 2:
+        return genome_1[:], genome_2[:]
+    cutoff_point = random.randint(1, min_length - 1)
+    return genome_1[:cutoff_point] + genome_2[cutoff_point:], genome_2[
+        :cutoff_point
+    ] + genome_1[cutoff_point:]
+
+
+def mutation(genome: genome_t, p_mutation: float) -> genome_t:
+    """
+    Performs bit-flip mutation on a genome. Each bit flips with probability p_mutation.
+
+    Note: other mutation strategies exist (swap, scramble, etc.).
+
+    Examples
+    --------
+    With probability 1.0, every bit flips:
+
+    >>> mutation([0, 1, 1, 0], p_mutation=1.0)
+    [1, 0, 0, 1]
+
+    With probability 0.0, nothing changes:
+
+    >>> mutation([0, 1, 1, 0], p_mutation=0.0)
+    [0, 1, 1, 0]
+    """
+    return [(1 - gene) if random.random() < p_mutation else gene for gene in genome]
+
+
+def run_ga(
+    items: list[Item],
+    capacity: int,
+    pop_size: int = POPULATION_SIZE,
+    generations: int = GENERATIONS,
+    p_crossover: float = CROSSOVER_PROBABILITY,
+    p_mutation: float = MUTATION_PROBABILITY,
+    tournament_k: int = TOURNAMENT_K,
+    elitism: int = ELITISM,
+) -> dict:
+    """
+    Runs the genetic algorithm to (approximately) solve the knapsack problem.
+
+    Returns a dict with keys:
+      - 'best_genome' (genome_t)
+      - 'best_value' (int)
+      - 'best_weight' (int)
+      - 'capacity' (int)
+      - 'best_history' (list[int])
+      - 'avg_history' (list[float])
+
+    Examples
+    --------
+    Use a tiny instance and few generations to validate structure and lengths:
+
+    >>> random.seed(1234)
+    >>> tiny_items = [Item(5,2), Item(6,3), Item(2,1), Item(7,4)]
+    >>> cap = 5
+    >>> out = run_ga(
+    ...     tiny_items, cap,
+    ...     pop_size=10, generations=5,
+    ...     p_crossover=0.9, p_mutation=0.05,
+    ...     tournament_k=2, elitism=1
+    ... )
+    >>> len(out['best_fitness_history']) == 5 and len(out['avg_fitness_history']) == 5
+    True
+    >>> isinstance(out['best_genome'], list) and isinstance(out['best_value'], int)
+    True
+    >>> out['capacity'] == cap
+    True
+    """
+    population = [random_genome(len(items)) for _ in range(pop_size)]
+    best_fitness_history: list[int] = []  # track best fitness per generation
+    avg_fitness_history: list[float] = []
+    best_genome_overall: genome_t = []
+    best_fitness_overall: int = -1
+
+    for _ in range(generations):
+        fitnesses = [evaluate(genome, items, capacity)[0] for genome in population]
+        best_fit = max(fitnesses)
+        best_idx = fitnesses.index(best_fit)
+        best_fitness_history.append(best_fit)
+        avg_fit = sum(fitnesses) / pop_size
+        avg_fitness_history.append(avg_fit)
+
+        if best_fit > best_fitness_overall:
+            best_fitness_overall = best_fit
+            best_genome_overall = population[best_idx][:]
+
+        # Elitism
+        sorted_indices = sorted(range(pop_size), key=lambda idx: fitnesses[idx])
+        elite_indices = sorted_indices[::-1][:elitism]  # reverse and take top indices
+        elites = [population[idx][:] for idx in elite_indices]
+
+        # New generation
+        new_pop = elites[:]
+        while len(new_pop) < pop_size:
+            parent1 = selection(population, fitnesses, tournament_k=tournament_k)
+            parent2 = selection(population, fitnesses, tournament_k=tournament_k)
+            child1, child2 = crossover(parent1, parent2, p_crossover)
+            child1 = mutation(child1, p_mutation)
+            child2 = mutation(child2, p_mutation)
+            new_pop.extend([child1, child2])
+        population = new_pop[:pop_size]
+
+    # Final evaluation of the best
+    best_value, best_weight = evaluate(best_genome_overall, items, capacity)
+    return {
+        "best_genome": best_genome_overall,
+        "best_value": best_value,
+        "best_weight": best_weight,
+        "capacity": capacity,
+        "best_fitness_history": best_fitness_history,
+        "avg_fitness_history": avg_fitness_history,
+    }
+
+
+# ================================ Script entry =================================
+
+if __name__ == "__main__":
+    result = run_ga(items, capacity)
+    best_value, best_weight = result["best_value"], result["best_weight"]
+
+    print(f"Knapsack capacity: {result['capacity']}")
+    print(f"Best solution: value = {best_value}, weight = {best_weight}")
+    # # Uncomment to inspect chosen items:
+    # best_items = [
+    #     items[idx] for idx, bit in enumerate(result["best_genome"]) if bit == 1
+    # ]
+    # print("Items included in the best solution:", best_items)
+
+    # # Optional: plot fitness curves
+    # import matplotlib.pyplot as plt
+    # plt.figure()
+    # plt.plot(result["best_fitness_history"], label="Best fitness")
+    # plt.plot(result["avg_fitness_history"], label="Average fitness")
+    # plt.title("GA on Knapsack: Fitness over Generations")
+    # plt.xlabel("Generation")
+    # plt.ylabel("Fitness")
+    # plt.legend()
+    # plt.tight_layout()
+    # plt.show()