Summary

There is already a rust crate here:

• https://docs.rs/differential-evolution/latest/differential_evolution/

Full description

Differential Evolution (DE) is a powerful and versatile population-based optimization algorithm designed to solve complex, non-linear, and non-differentiable continuous optimization problems. Developed by Rainer Storn and Kenneth Price in 1995, DE has gained popularity due to its simplicity, efficiency, and robustness.

Key features of Differential Evolution:

• Population-based: DE maintains a population of candidate solutions, allowing for parallel exploration of the search space.
• Self-organizing: The algorithm adapts its search strategy based on the population's distribution, requiring minimal parameter tuning.
• Mutation strategy: DE uses vector differences between randomly selected population members to generate new candidate solutions, promoting diversity and exploration.
• Crossover: The algorithm combines information from multiple solutions to create offspring, balancing exploration and exploitation.
• Selection: DE employs a simple one-to-one selection mechanism, ensuring that the population improves or maintains its quality over generations.

The basic DE algorithm follows these steps:

1. Initialize a population of candidate solutions randomly within the search space.
2. For each member of the population:
   • Select three distinct individuals from the population
   • Create a mutant vector by adding the weighted difference of two vectors to a third
   • Perform crossover between the mutant vector and the current individual
   • Evaluate the fitness of the resulting trial vector
   • Replace the current individual with the trial vector if it performs better
3. Repeat steps 2-3 until a termination criterion is met (e.g., maximum iterations or desired fitness achieved).

Differential Evolution has been successfully applied to various optimization problems, including engineering design, machine learning, and financial modeling. Its effectiveness in finding global optima, even in complex, multimodal landscapes, makes it a popular choice among researchers and practitioners in the field of optimization.