DESn

DESn, or Differential Evolution with Stochastic Neighborhoods, is an optimization algorithm that combines the principles of differential evolution with stochastic neighborhood search. It was introduced to address the limitations of traditional differential evolution in handling complex, high-dimensional optimization problems.

The algorithm works by maintaining a population of candidate solutions, each of which is a vector in the search space. It iteratively improves these solutions by generating new candidate solutions through a process of mutation, crossover, and selection. The mutation process in DESn introduces stochasticity by selecting neighborhood solutions based on a probability distribution, rather than deterministically. This stochastic neighborhood selection helps to explore the search space more effectively and escape local optima.

The crossover operation in DESn combines the mutated vector with a target vector to produce a trial vector. The selection process then determines which vector, the trial or the target, will survive to the next generation based on their fitness values. This process is repeated for a predefined number of generations or until a satisfactory solution is found.

DESn has been shown to outperform traditional differential evolution on a variety of benchmark problems, particularly those with complex landscapes and high-dimensional search spaces. Its stochastic neighborhood selection mechanism allows it to balance exploration and exploitation more effectively, leading to improved optimization performance. However, like all optimization algorithms, DESn's performance can be sensitive to the choice of its parameters, and further research is needed to fully understand and optimize its behavior.