Differential Evolution › Summary

Differential Evolution builds a continuous population search from donor differences. DE/rand/1/bin draws three distinct donors excluding the target, scales one difference, adds it to a random base donor, and chooses trial coordinates with a binomial mask. A forced mask entry ensures mutant inheritance, although the resulting trial can still duplicate the target.

For a fixed deterministic objective, greedy replacement with our tie-accepting convention makes retained slot costs non-increasing. Freezing the old population gives the deferred implementation used here. Neither a contracting population nor a flat incumbent trace certifies a global optimum; box repair also does not establish feasibility for other constraints.

Our synthetic comparison counts every candidate, including initialization and rejected proposals, stops exactly at its budget, validates final box membership, and reports repeated-run outcomes. The known Rastrigin minimum helps interpret those outcomes; it does not turn DE into an optimality proof. Parameter choices, local-search baselines, noise handling, and the costs of any polishing or warm start remain part of an honest comparison.