optimization-algorithms-wiki

Population-optimization benchmark (Andrey Dik’s MQL5 series)

The comparative benchmark that connects this wiki’s founding sources: andrey-dik‘s long MQL5 series implements ~45 population-based optimization algorithms in MQL5 and scores them on a common set of standard test functions across several dimensionalities (low-dim through high-dim, e.g. 5D / 25D / 500D), producing a relative ranking (score as a % of maximum).

A practitioner benchmark, not a peer-reviewed one — its value here is as the shared yardstick across the founding sources; corroborate against independent suites (CEC/BBOB) where possible.

Independent counterpart: the academic standard is test-functions-for-optimization (Rastrigin, Rosenbrock, Ackley, …) underlying the CEC/BBOB(COCO) suites. Tellingly, cma-es rates near the top on BBOB yet only ~38/45 here — same algorithm, different problem distribution. We record both and flag the tension (no-free-lunch-theorem; synthesis); don’t read either as absolute.

Methodology evolved — two non-comparable scoring schemes

A subtlety the wiki must respect: Dik’s benchmark changed over the years, so scores from different articles aren’t on one scale.

• Mature rating (current): a % of MAX aggregated over Hilly / Forest / Megacity functions across ~45 algorithms. This is the table the founding four and evolution-strategies report.
• Early rating (~2022–early 2023): an absolute 0–1 score over Skin / Forest / Megacity in a small field (~6 algorithms, often vs. an RND random baseline). This is what PSO, GWO, ACO and ABC report — not comparable to the %-of-MAX column.

The benchmark’s own evolution is itself a no-free-lunch-theorem lesson: even one author’s “score” isn’t a fixed yardstick.

Mature %-of-MAX results (comparable; see no-free-lunch-theorem)

The spread is the point: a famous evolution strategy (cma-es) sits mid-low while a 1970s elitist ES ((μ+λ)-ES) leads the whole suite; a simpler archive-based method (BSA) beats CMA-ES; and dimensionality matters (CMA-ES is strong at low-D but fails at 500-D). Rankings are suite-, dimension-, and implementation-dependent — never read as absolute quality.

Early small-field results (different scheme — do not compare to the % column)

These four share a pattern: strong on smooth, low-dimensional functions, poor scalability to high-dim and discrete landscapes — and PSO famously losing to random search here is the most pointed no-free-lunch-theorem datum in the corpus.

Related

andrey-dik · metaheuristic-optimization · no-free-lunch-theorem · cma-es · backtracking-search-algorithm · exchange-market-algorithm · deterministic-oscillatory-search · evolution-strategies · particle-swarm-optimization · grey-wolf-optimizer · ant-colony-optimization · artificial-bee-colony