Euclidean Distance Calculation Method and Source Code

Euclidean distance is a classical method for measuring the straight-line distance between two points in multidimensional space, commonly used in genetic algorithms and machine learning to calculate similarity between individuals. Its core concept originates from the Pythagorean theorem in geometry.

Calculation Principle Given two n-dimensional vectors A=(a₁,a₂,...,aₙ) and B=(b₁,b₂,...,bₙ), the Euclidean distance formula requires: Summing the squared differences across all dimensions Taking the square root of the sum Smaller values indicate higher similarity between vectors, with 0 representing perfect overlap.

Application in Genetic Algorithms Population diversity assessment: Evaluating population distribution density by calculating inter-individual distances Selection operation optimization: Preventing premature convergence caused by excessive reproduction of similar individuals Cluster analysis: Differentiating individuals with distinct characteristics when combined with elitism strategy

Implementation Key Points Handle exceptions for vectors with inconsistent dimensions Normalize high-dimensional data before processing Utilize matrix operations for acceleration in large-scale computations

Although intuitive, this distance metric may become ineffective in ultra-high-dimensional data (curse of dimensionality), where alternatives like cosine similarity or Mahalanobis distance can be considered. In genetic algorithms, it typically collaborates with other fitness functions to guide evolutionary direction.