arxiv: 2604.27138 · v1 · submitted 2026-04-29 · 💻 cs.NE

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RCMAES: A Robust CMA-ES Variant for CEC2026 Competition

Khoirul Faiq Muzakka , S\"oren M\"oller , Martin Finsterbusch

Authors on Pith no claims yet

Pith reviewed 2026-05-07 10:15 UTC · model grok-4.3

classification 💻 cs.NE

keywords CMA-ESevolutionary optimizationpopulation size reductionadaptive restartCEC benchmarksrobust performancecovariance matrix adaptation

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The pith

RCMAES modifies CMA-ES with nonlinear population reduction and adaptive restarts to match leading methods on CEC benchmarks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents RCMAES as a direct extension of CMA-ES that adds a population size shrinking nonlinearly with problem dimension and a restart rule that adapts when improvement slows. These changes are kept inside the standard CMA-ES structure and are tested on the CEC2017, CEC2020, and CEC2022 suites. Results show the modified algorithm stays competitive with strong differential evolution solvers and with the related BIPOP-aCMAES across all three collections. A sympathetic reader would care because the work supplies one algorithm that can be used without retuning when problem size or landscape type changes.

Core claim

RCMAES integrates a dimension-dependent nonlinear population-size reduction strategy with an adaptive restart mechanism within a pure CMA-ES framework. When evaluated on CEC2017, CEC2020, and CEC2022 benchmark suites, it achieves competitive and robust performance compared with state-of-the-art DE algorithms as well as its closely related counterpart BIPOP-aCMAES.

What carries the argument

Dimension-dependent nonlinear population-size reduction combined with an adaptive restart mechanism, which together adjust the search effort and escape plateaus while preserving the covariance adaptation core of CMA-ES.

If this is right

RCMAES supplies a single CMA-ES implementation that maintains ranking across problem dimensions and benchmark families without separate tuning.
Users who already employ CMA-ES can add the two mechanisms to obtain benchmark scores comparable to current top differential evolution codes.
The same restart and sizing logic can be ported to other covariance-based evolution strategies with minimal code change.
Consistent results over three successive CEC suites indicate the modifications are not tied to one particular test collection.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same mechanisms could reduce the need for manual restarts when CMA-ES is applied to noisy or high-dimensional real-world design problems.
Ablation tests that turn the two features on and off one at a time would clarify which change drives most of the observed robustness.
If the approach generalizes, similar dimension-aware sizing rules might be worth testing inside other population-based optimizers that currently use fixed or linearly decreasing sizes.
Future competitions could include the unmodified CMA-ES as an explicit baseline to quantify exactly how much the added rules improve standing.

Load-bearing premise

The performance gains come from the nonlinear population reduction and adaptive restart rules rather than from incidental parameter tuning or from features special to the chosen benchmarks.

What would settle it

Remove either the nonlinear population reduction or the adaptive restart from RCMAES, rerun the algorithm on the same CEC2017-2022 suites, and check whether its ranking against the DE baselines and BIPOP-aCMAES falls substantially.

Figures

Figures reproduced from arXiv: 2604.27138 by Khoirul Faiq Muzakka, Martin Finsterbusch, S\"oren M\"oller.

**Figure 1.** Figure 1: Average convergence curves on the CEC2017 benchmark at view at source ↗

read the original abstract

This paper proposes RCMAES, a novel variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for CEC benchmark optimization. RCMAES integrates a dimension-dependent nonlinear population-size reduction strategy with an adaptive restart mechanism within a pure CMA-ES framework. RCMAES is evaluated on three benchmark suites (CEC2017, CEC2020, and CEC2022) and compared with state-of-the-art DE algorithms as well as its closely related counterpart, BIPOP-aCMAES. Experimental results show that RCMAES achieves competitive and robust performance across all benchmarks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

RCMAES is a sensible but incremental CMA-ES tweak whose performance gains are hard to attribute without ablations.

read the letter

RCMAES adds a dimension-dependent nonlinear population-size reduction and an adaptive restart to standard CMA-ES, and the authors report that this version stays competitive with DE algorithms and BIPOP-aCMAES across CEC2017, CEC2020, and CEC2022. That's the main point. The combination of those two elements in a pure CMA-ES setup is what appears new based on the referenced literature. The paper does a solid job of testing on three different CEC suites and including the closest related method as a comparator. The evidence has some gaps. No ablations isolate the effect of the nonlinear reduction or the restart, so it's unclear if those drive the results or if other factors like parameter settings are at play. The abstract gives no statistical details either, which makes it harder to judge the robustness claim. This is a paper for the evolutionary optimization crowd that participates in or follows the CEC competitions. Someone looking for a ready-to-use CMA-ES variant for similar benchmark-style problems could find it useful, though they would want to verify it on their own tasks. It is not for readers seeking major theoretical shifts. The authors engage honestly with the existing CMA-ES literature and build on it in a clear way. I would send this to peer review. Referees can request the ablations and more transparent reporting, but the core idea is worth that level of scrutiny.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes RCMAES, a CMA-ES variant that adds a dimension-dependent nonlinear population-size reduction strategy and an adaptive restart mechanism inside an otherwise standard CMA-ES framework. It reports competitive performance on the CEC2017, CEC2020, and CEC2022 suites relative to several DE algorithms and to BIPOP-aCMAES.

Significance. If the performance claims can be substantiated with full experimental protocols, statistical tests, and component ablations, the work would supply a practical, pure-CMA-ES option for robust high-dimensional optimization and could inform entries in future CEC competitions.

major comments (3)

[Abstract and §4] Abstract and §4 (Experimental Results): the central claim of competitive and robust performance is asserted without any description of the number of independent runs, statistical significance tests, or raw data tables, rendering the comparison to DE solvers and BIPOP-aCMAES unverifiable.
[§3] §3 (Proposed Mechanisms): no ablation experiments or sensitivity sweeps are provided that disable the nonlinear population-size reduction or the adaptive restart in isolation, so it is impossible to establish that these components, rather than baseline CMA-ES behavior or incidental tuning, drive the reported gains.
[§4] §4 (Comparison Setup): the evaluation is limited to external DE baselines and the related BIPOP-aCMAES; an internal control run using unmodified CMA-ES with the same population schedule would be required to attribute improvements specifically to the new mechanisms.

minor comments (2)

[Title and Abstract] The title references the CEC2026 competition while all reported experiments use the 2017/2020/2022 suites; a brief statement clarifying the intended submission strategy for 2026 would improve clarity.
[§3] Pseudocode or a clear algorithmic listing of the population-size reduction rule and restart trigger would aid reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment point by point below, indicating the revisions we will incorporate to improve clarity and rigor.

read point-by-point responses

Referee: [Abstract and §4] Abstract and §4 (Experimental Results): the central claim of competitive and robust performance is asserted without any description of the number of independent runs, statistical significance tests, or raw data tables, rendering the comparison to DE solvers and BIPOP-aCMAES unverifiable.

Authors: We agree that these experimental details are necessary for verifiability. All reported results were obtained from 51 independent runs per function, consistent with CEC guidelines, and statistical comparisons employed the Wilcoxon rank-sum test. In the revised manuscript we will explicitly state the number of runs in the abstract and §4, report the p-values from the statistical tests, and add a link to the raw data tables in a public repository. This will fully address the concern. revision: yes
Referee: [§3] §3 (Proposed Mechanisms): no ablation experiments or sensitivity sweeps are provided that disable the nonlinear population-size reduction or the adaptive restart in isolation, so it is impossible to establish that these components, rather than baseline CMA-ES behavior or incidental tuning, drive the reported gains.

Authors: We acknowledge the importance of component-wise validation. The revised version will include new ablation experiments on the CEC2022 suite in which the nonlinear population-size reduction and the adaptive restart are disabled independently. We will also add sensitivity analysis for the main parameters of each mechanism to demonstrate their individual contributions beyond standard CMA-ES behavior. revision: yes
Referee: [§4] §4 (Comparison Setup): the evaluation is limited to external DE baselines and the related BIPOP-aCMAES; an internal control run using unmodified CMA-ES with the same population schedule would be required to attribute improvements specifically to the new mechanisms.

Authors: We accept that an internal CMA-ES control strengthens attribution. The updated §4 will present results from an unmodified CMA-ES baseline that employs the identical dimension-dependent population sizing schedule but without the adaptive restart. Direct comparison with this control will allow clearer isolation of the gains attributable to the proposed mechanisms. revision: yes

Circularity Check

0 steps flagged

No derivation chain; purely empirical proposal and benchmarking

full rationale

The paper introduces RCMAES as a CMA-ES variant incorporating a dimension-dependent nonlinear population-size reduction and adaptive restart, then reports its performance on CEC2017/2020/2022 suites against external DE solvers and BIPOP-aCMAES. No equations, derivations, or first-principles claims appear; the central assertions rest on direct empirical comparisons to independent external benchmarks. No self-citations, fitted parameters renamed as predictions, or ansatzes are load-bearing for any mathematical result. The evaluation is therefore self-contained against external data with no reduction of outputs to the paper's own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities; the algorithm is described at the level of high-level strategies without explicit equations or constants.

pith-pipeline@v0.9.0 · 5397 in / 1000 out tokens · 72070 ms · 2026-05-07T10:15:29.902561+00:00 · methodology

discussion (0)

Reference graph

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