Lernen Parameter Tuning and Convergence

Definition

Parameter tuning in genetic algorithms refers to selecting and adjusting key values such as mutation rate, crossover probability, and population size to control algorithm behavior and improve convergence.

Static vs. Dynamic Parameter Tuning

Two main approaches exist for controlling parameters in genetic algorithms:

Static parameter tuning: parameters such as mutation rate, crossover probability, and population size are fixed before the algorithm starts and remain constant during execution;
Dynamic (adaptive) parameter tuning: parameters are adjusted automatically based on population feedback or algorithm progress. Adaptive tuning helps maintain diversity and avoid premature convergence.

Static tuning is simple but may be suboptimal when optimal settings change over time.
Dynamic tuning provides flexibility, improving both convergence speed and robustness.


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import numpy as np

def adaptive_mutation_rate(population, min_rate=0.01, max_rate=0.2):
    """
    Adjusts mutation rate based on population diversity.
    Diversity is measured as the average Hamming distance between individuals.
    """
    def hamming_distance(ind1, ind2):
        return sum(a != b for a, b in zip(ind1, ind2))
    
    n = len(population)
    if n < 2:
        return min_rate  # No diversity in a single-individual population
    
    # Compute average Hamming distance
    distances = []
    for i in range(n):
        for j in range(i + 1, n):
            distances.append(hamming_distance(population[i], population[j]))
    avg_distance = np.mean(distances)
    max_distance = len(population[0])
    
    # Normalize diversity
    diversity = avg_distance / max_distance if max_distance else 0
    
    # Inverse relationship: lower diversity -> higher mutation
    mutation_rate = max_rate - (max_rate - min_rate) * diversity
    return np.clip(mutation_rate, min_rate, max_rate)

When population diversity drops, individuals become too similar, and the algorithm risks stagnation. Increasing the mutation rate in these moments injects new genetic material, helping escape local optima. When diversity is high, lowering mutation allows more focused exploitation of good solutions. This adaptive control balances exploration and exploitation dynamically, improving convergence stability.


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import matplotlib.pyplot as plt

# Simulate parameter and fitness changes for illustration
generations = np.arange(1, 51)
mutation_rates = np.linspace(0.2, 0.01, 50) + 0.02 * np.random.randn(50)
avg_fitness = np.linspace(10, 90, 50) + 5 * np.random.randn(50)

plt.figure(figsize=(10, 5))
plt.subplot(1, 2, 1)
plt.plot(generations, mutation_rates, label="Mutation Rate")
plt.xlabel("Generation")
plt.ylabel("Mutation Rate")
plt.title("Adaptive Mutation Rate Over Time")
plt.legend()

plt.subplot(1, 2, 2)
plt.plot(generations, avg_fitness, color="green", label="Average Fitness")
plt.xlabel("Generation")
plt.ylabel("Average Fitness")
plt.title("Population Fitness Over Time")
plt.legend()

plt.tight_layout()
plt.show()

Monitoring and Convergence

To achieve reliable convergence and performance in genetic algorithms:

Start with parameter ranges from literature or previous experiments;
Use static parameters for simple tasks, but prefer adaptive tuning for complex problems;
Monitor metrics such as population diversity, best and average fitness;
Adjust parameters dynamically to maintain balance between exploration and exploitation.

Which statements about parameter tuning and convergence in genetic algorithms are correct? Select all that apply.

Select the correct answer

You should always use static parameter settings and never change them, regardless of the problem or observed performance.

Dynamic parameter tuning can help maintain diversity and adapt to different phases of the search process.

Increasing the mutation rate when population diversity is low helps inject new genetic material and avoid premature convergence.

Static parameter tuning means adjusting parameters during the run based on feedback from the algorithm.

Adaptive mutation rates are used to make the algorithm converge faster by always increasing the mutation rate over generations.

Monitoring metrics such as average fitness and diversity helps detect stagnation and guide parameter adjustments.

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