Differential Evolution (DE)
DE is a population-based, gradient-free metaheuristic for continuous optimization, introduced by Storn & Price (1995, formal pub. 1997). Its signature is vector-difference mutation: new candidates are built from the scaled difference between existing population members, so the search step self-scales to the population’s current spread. Source: Wikipedia (an authoritative, non-andrey-dik source — see synthesis on benchmark independence).
How it works
For each agent x, pick three distinct members a, b, c and form a donor:
y = a + F·(b − c)
then binomial crossover (rate CR) mixes donor and parent coordinates, and greedy selection
keeps the trial only if it improves: “if f(y) ≤ f(x) then replace … with y.” Control parameters:
NP (population size, ~10·n), F (differential weight, ~0.8, range [0,2]), CR (~0.9). Higher
F → more exploration; lower CR → more exploitation (exploration-vs-exploitation).
Why it matters here
DE is the population-based optimizer the Dik corpus most conspicuously lacked, and a standard CEC- competition baseline — its self-scaling difference vector is a different answer to the same explore/exploit problem than cma-es‘s covariance adaptation or particle-swarm-optimization‘s velocity. Closely related to evolution-strategies and genetic-algorithm. Wikipedia notes only that “variants of the DE algorithm are continually being developed” — no single ranking, consistent with the no-free-lunch-theorem.
Related
metaheuristic-optimization · exploration-vs-exploitation · no-free-lunch-theorem · genetic-algorithm · evolution-strategies · cma-es · particle-swarm-optimization · test-functions-for-optimization