Evolution Strategies — (μ,λ)-ES and (μ+λ)-ES

Evolution Strategies (ES) are among the oldest population-based optimizers, developed by Ingo Rechenberg and colleagues in 1960s Germany; the (μ+λ) variant came from Schwefel (and J. Reichenbacher) in the 1970s. They are the classical ancestors of cma-es. Source: andrey-dik's MQL5 implementation, with recombination letting offspring "inherit the characteristics of all parents."

How it works — comma vs. plus

μ parents generate λ offspring via recombination + (self-adaptive) mutation; the two variants differ in who survives:

• (μ,λ)-ES ("comma") — select the best μ from the λ offspring only; parents always die. New children "compete with their parents for a limited number of places, which can lead to premature convergence to a local optimum."
• (μ+λ)-ES ("plus") — select the best μ from parents ∪ offspring combined; good parents persist, giving "a broader exploration of the solution space." A textbook exploration-vs-exploitation knob: elitist retention (plus) vs. forced turnover (comma).

Benchmark (context-relative)

Reported on the mature %-of-MAX rating (Hilly/Forest/Megacity) — the same scale as the founding four, so directly comparable:

(μ+λ)-ES achieved "phenomenal results" — "ahead of its nearest competitor SDSm by almost 10%", and above all four founding algorithms (best of those: BSA at 55.10%). It led the suite from its 2026-06 ingest until 2026-07-25, when DOAm (73.63%) edged past it by 1.45 points. A 1970s elitist strategy holding the top of the modern field for that long is a sharp no-free-lunch-theorem twist: the "plus" tweak (keep parents) outperforms decades of newer metaphors, and the thing that finally beat it was a three-line correction to an existing metaphor algorithm rather than a new mechanism. The comma variant lands mid-pack, showing the survival rule alone swings rank by ~20 points.

Why T2 (re-tiered 2026-08-25)

Held at T3 since ingest, which graded the venue — MQL5, a broker's community article site — rather than what the page rests on. This page's load-bearing claims are a mechanism description of an algorithm published by Rechenberg and Schwefel (1960s–70s) and a comparative score, both from andrey-dik, who did not write the algorithm and has no stake in where it lands. That is somebody measuring somebody else's work, which QUALITY.md's ladder puts at T2.

The spoke's standing finding — that in this field the scorer is usually the author — is real and does not apply here; it applies to DOAm, which stays T3 because there Dik is scoring his own modification. The confound that does remain is implementation: Dik re-implements each optimizer in MQL5, so his figure grades his code as much as the method, and his scoring scheme changed mid-series (population-optimization-benchmark). Both stay flagged in prose, where a methodological limit belongs — not in the tier.

Note the floor is unmoved by this: T1 ÷ tiered counts T1 against the same denominator either way, so the change alters the tier mix and not the spoke's floor of 0.18.

Related

metaheuristic-optimization · exploration-vs-exploitation · population-optimization-benchmark · no-free-lunch-theorem · andrey-dik · cma-es · backtracking-search-algorithm