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
RNDrandom 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)
| Algorithm | Rank (this suite) | Score |
|---|---|---|
| dingo-optimization-algorithm (DOAm) | suite leader (2026-07) | 73.63% |
| evolution-strategies — (μ+λ)-ES | 2nd; leader until 2026-07 | 72.18% |
| backtracking-search-algorithm (BSA) | 20 / 45 | 55.10% |
| evolution-strategies — (μ,λ)-ES | mid-pack | 51.22% |
| cma-es | ~38 / 45 | 48.33% |
| exchange-market-algorithm (EMA) | 45 / 45 | 37.40% |
| deterministic-oscillatory-search (DOS) | 45th | 32.36% |
The spread is the point: a famous evolution strategy (cma-es) sits mid-low while a 1970s elitist ES ((μ+λ)-ES) led the whole suite until 2026-07; 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.
Leader change, 2026-07-25. DOAm took the top slot at 73.63%. Both results stand as recorded; note that DOAm is andrey-dik‘s own modification of a published algorithm, so the suite leader is now an entrant tuned by the suite’s author — the sharpest reason yet to treat this table as one practitioner’s yardstick rather than a neutral ranking. Also in the 2026-07 table: ANS 68.15%, CLA 67.86%, AMOm 66.52%, random walk 26.09%.
Early small-field results (different scheme — do not compare to the % column)
| Algorithm | Early score (Skin/Forest/Megacity) | Field note |
|---|---|---|
| ant-colony-optimization (ACO) | 0.54688 | 1st of its small field |
| artificial-bee-colony (ABC) | 0.49447 / 0.50836 (mod.) | 4th; excels at ≤2 vars |
| particle-swarm-optimization (PSO) | 0.47695 | below RND baseline (0.51254) |
| grey-wolf-optimizer (GWO) | 0.4158 | 4th of 6 |
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