Enhancing Explainability and Reliable Decision-Making in Particle Swarm Optimization through Communication Topologies

Anupam Yadav; Bapi Dutta; Indu Bala; Luis Mart\'inez; Nitin Gupta

REVIEW 4 major objections 5 minor 1 cited by

Enhancing Explainability and Reliable Decision-Making in Particle Swarm Optimization through Communication Topologies

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper claims that a particle swarm’s communication topology changes which hyperparameter settings work best, and derives task-specific rules for choosing topology and coefficients.

desk verdict A reproducible but thinly supported XAI-for-PSO companion: the new application is fine, but the headline guidelines rest on an undefined R2 metric and in-sample comparisons. read the letter →

arxiv 2504.12803 v1 pith:4G6FR65M submitted 2025-04-17 cs.LG cs.AI

Nitin Gupta , Indu Bala , Bapi Dutta , Luis Martínez , Anupam Yadav This is my paper · ORCID

classification cs.LGcs.AI

keywords particleswarmoptimizationcommunicationtopologyringstargridexplainableAIhyperparameteranalysisbenchmarkfunctions

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to show that a particle swarm optimizer’s communication topology is not a neutral detail: it changes which hyperparameters matter, how fast the swarm converges, and which problem shapes the algorithm handles well. The authors run an explainable benchmarking pipeline over 1,728 configurations of a 2-dimensional, 24-function benchmark suite and use attribution values to read off the effect of each setting. Their reported pattern is consistent: a low cognitive coefficient $c_1$ helps and a high one hurts, small swarms suit unimodal problems under the ring topology while larger swarms suit multimodal ones, and the ring topology gives the best fit for regression-style tasks. If these findings hold, practitioners could replace trial-and-error tuning with task-class rules for choosing topology and coefficients.

What carries the argument

The central object is the communication topology—the graph that decides which particles exchange their best-known positions—because it determines which term in the PSO velocity update dominates the search. The argument runs through an adapted explainable benchmarking pipeline: configurations are sampled from the hyperparameter grid, each is run on the 24-function benchmark suite, performance is scored by the area over the convergence curve (AOCC), and attribution values are computed to isolate each hyperparameter’s marginal contribution. That pipeline is what converts raw convergence numbers into the paper’s configuration rules.

What would settle it

Run the same 1,728-configuration sweep in dimensions 5, 10, and 30 with a 1,000-iteration budget and check whether low $c_1$ still dominates and whether the ring topology still gives the highest $R^2$; either flip would refute the paper’s guidance.

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Extended reading notes

Core claim

On its own terms, the paper establishes that the effect of each PSO hyperparameter depends on communication topology. In the velocity update $v_i(t+1)=w v_i(t)+c_1 r_1(p_{best,i}-x_i(t))+c_2 r_2(g_{best}-x_i(t))$, the $c_1$ term is the consistent driver: lower values of $c_1$ improve area-over-the-convergence-curve performance across functions and topologies, while larger values worsen it. The paper reports that the ring topology yields the highest $R^2$ when fitting performance across the benchmark set, making it the recommended choice for regression-oriented tasks, while the star topology converges fastest but risks early stagnation and the grid topology is the most time-efficient. For unimodal functions a small swarm of 50 particles works best in the ring, for multimodal functions a larger swarm of 100 works better, and the star benefits from small swarms on highly multimodal functions.

Load-bearing premise

The guidelines rest on the assumption that swarm behavior in two dimensions with a 100-iteration budget transfers to the higher-dimensional, longer-running optimization tasks that practitioners actually face.

Editorial extensions

If this is right

For unimodal problems, use a small swarm ($n=50$) with the ring topology; for multimodal problems, use a larger swarm ($n=100$), and keep $c_1$ low.
The ring topology is the best default among the three for regression-style tasks where fit quality, measured by $R^2$, is the goal.
The star topology should be expected to converge quickly but to stagnate on difficult multimodal landscapes, making it a poor choice when local optima are dense.
The grid topology is the most compute-efficient information-sharing structure at this budget, useful when per-run cost matters.
Attribution-based explanation turns PSO configuration into readable rules: each hyperparameter’s effect can be stated as a sign and magnitude rather than a tuned value.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the attribution signs flip across topologies, a single global hyperparameter default is likely suboptimal; an automated tuner that conditions on topology should outperform one that ignores it.
The $R^2$ used to rank topologies is fit on the benchmark evaluation itself, so the ring recommendation should be tested on held-out functions or real regression problems before being adopted as a general rule.
The same pipeline could test adaptive or dynamic topologies, for example starting with the star for fast progress and switching to the ring later, to see whether the reported trade-offs can be combined in one run.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: this is a 4-page GECCO Companion paper that applies IOHxplainer/SHAP to PSO hyperparameters under three topologies. It's a legitimate new application, and the authors provide code and data. But the two practical guidelines — "lower c1 always helps" and "Ring is best for regression tasks" — are not actually supported by the numbers as reported. The stress-test note is on target: R2 train appears in Table 2 but is never defined, and the c1 claim is made from SHAP swarm plots without any per-c1 performance table.

What's new: using SHAP attribution on PSO topology/hyperparameter search is a reasonable and fairly novel use of an existing tool. The experimental setup is standard (BBOB, 24 functions, 5 instances, 5 seeds) and reimplementation-friendly. The paper is honest about its limits: it explicitly says scaling to higher dimensions is future work, and the GitHub link is a plus.

What's soft: (1) The central topology ranking relies on R2 train, which is undefined; if it's an in-sample regression R2 from the hyperparameter model, then it's not evidence of optimization performance. The actual AOCC means differ by ~0.001-0.03 with overlapping stds, so the "Ring is superior" conclusion could be noise. (2) No significance tests or confidence intervals anywhere, despite "statistical analysis" in the abstract. (3) Single-best and avg-best configs are selected and evaluated on the same runs, so the comparisons are in-sample. (4) The c1 claim isn't backed by a table of mean AOCC per c1 level per function; "consistently" is doing too much work. (5) The 2D/100-iteration limit is acknowledged, but that doesn't fix the within-setting issues.

There's also an apparent typo in Table 2 f12 Von Neumann "all mean" (1.36E-01 vs 1.35E-02), which makes me trust the table a bit less.

Who it's for: practitioners who want a quick, qualitative read on how PSO hyperparameters interact with topology, and people working on XAI-for-algorithms. It's not yet reliable as quantitative guidance.

Recommendation: send to peer review as a borderline. The flaws are fixable with held-out validation, per-level tables, significance tests, and defining R2. For a 4-page companion, the contribution is modest but real.

Referee Report

4 major / 5 minor

Summary. The paper applies an adapted IOHxplainer framework with SHAP to study how three PSO communication topologies (Ring, Star, Von Neumann) affect performance on the 24 noiseless BBOB functions at dimension 2 with a budget of 100 iterations. It reports AOCC-based performance for 1,728 configurations, presents SHAP swarm plots to interpret hyperparameter effects, and derives practical guidelines: lower c1 improves performance, and Ring topology is best for regression tasks based on an R2 value. The authors also report runtime comparisons among topologies and provide a GitHub repository with data.

Significance. If the central claims were established, the paper would provide useful, practically actionable guidance for topology and hyperparameter selection in PSO, and it would demonstrate a promising use of XAI tools for algorithm configuration. Strengths include the use of a standard BBOB benchmark setup, a clearly described experimental grid, and the availability of code and full results in a public repository. The main limitation is that the headline conclusions currently rest on undefined or in-sample performance summaries and on qualitative SHAP readings, with no significance testing; the conclusions therefore need substantially stronger quantitative support before they can be relied upon.

major comments (4)

[Section 4.1, Table 2] The conclusion that 'the Ring topology is the superior choice for regression tasks focused on maximizing the R2 value' is based on the column labeled 'R2 train', but this metric is never defined. As labeled, it appears to be an in-sample goodness-of-fit statistic, not an optimizer performance measure, so its relationship to AOCC and to regression-task suitability is unclear. Moreover, the AOCC differences between topologies in the 'all mean' column are typically 0.001 to 0.03 with overlapping standard deviations, so without a definition of the regression target, a significance test, or a held-out evaluation, the Ring-topology ranking cannot be considered established.
[Section 4, hyperparameter claims] The statement that 'a lower c1 value consistently improves performance, while a larger c1 worsens it' is supported only by qualitative SHAP swarm plots. The text does not report mean AOCC per c1 level, per function, per topology, or any statistical comparison across c1 values, so 'consistently' is not verifiable from the reported evidence. The SHAP attributions themselves are not validated: the paper does not specify the model being explained, the background distribution, the baseline value, or any measure of attribution accuracy, so the SHAP plots cannot substitute for a direct quantitative analysis.
[Section 4.1, single-best and avg-best selection] The 'single-best' and 'avg-best' configurations are selected on the same benchmark runs whose AOCC values are then reported in Table 2. This in-sample selection makes the reported means optimistic and the comparisons between topologies potentially circular. The paper should either perform a separate evaluation of the selected configurations on independent runs or report paired differences with confidence intervals across the 24 functions, as the current presentation does not allow the reader to distinguish genuine topology effects from selection noise.
[Section 3 and Section 5] All experiments are run only in 2 dimensions with a budget of 100 iterations, and Section 5 explicitly lists 'scaling to higher dimensions' as future work, yet the conclusions are phrased as general guidelines for choosing topologies and hyperparameters for different types of optimization problems. The paper provides no evidence that the c1 effect or the topology ranking persists at higher dimensions or larger budgets, so the practical guidelines should either be restricted to the tested regime or accompanied by at least one higher-dimensional check.

minor comments (5)

[Section 2.2, Figure 1] The reference to 'AOCC 3' in the text should be 'AOCC (Equation 3)' or a citation to the metric definition, rather than an unexpanded label.
[Table 2, f12 Von Neumann row] The 'all mean' value of 1.36E-01 for Von Neumann on f12 appears to be an outlier that is inconsistent with the other values in that row; please verify the decimal point and the underlying data.
[Section 1, references] The paper would benefit from citing the original IOHxplainer paper and the IOHexperimenter/COCO documentation more precisely, as the current references do not clearly identify where the adapted framework originates.
[Throughout] The text contains several colloquial or vague phrases, such as 'promoting structure' for the Von Neumann topology and 'you can find a more detailed explanation of the framework in Figure 1'; these should be tightened to formal, precise descriptions.
[Section 4.1] The runtime comparison is based on wall-clock hours on a single machine, which is sensitive to machine load and implementation details; consider reporting per-run CPU time or normalized runtime to make the comparison reproducible.

Circularity Check

1 steps flagged · score 6.0 of 10

Central topology recommendation reduces to in-sample R2 train; no independent prediction is made.

fitted input called prediction [Section 4.1, Table 2]
"We identified the best configuration per BBOB function (“single-best mean”) and the best overall (“avg-best mean”), comparing them with average performance and standard deviations. ... Based on Table 2 settings, the Ring topology outperforms the Von Neumann and Star topologies in terms of the R2 value, which typically indicates a better fit for regression tasks. ... the Ring topology is the superior choice for regression tasks focused on maximizing the R2 value."

The 'single-best' and 'avg-best' configurations are selected on the same BBOB runs whose statistics are then tabulated, and the decisive column is explicitly labeled 'R2 train'. No held-out split, validation set, or significance test is described. The conclusion that Ring is 'superior for regression tasks' therefore restates the in-sample R2 train values produced by the same fitting/selection procedure rather than predicting performance on independent data. Since 'train' denotes the fitting data, the topology ranking is by construction a summary of the fit, not an out-of-sample forecast.

full rationale

The paper does not rely on load-bearing self-citations or imported uniqueness theorems; its empirical material is self-contained. The central circularity concern is in Section 4.1: the 'single-best' and 'avg-best' configurations are identified on the same benchmark runs, and Table 2 reports 'R2 train' for those configurations. Using an explicitly in-sample R2 column to rank topologies and then recommending Ring for regression tasks turns a fitted summary into a design guideline, which is the fitted-input-called-prediction pattern. The c1 guideline in Section 4 is also a post hoc SHAP read of the same AOCC data rather than a validated forecast, though it is a descriptive interpretation more than a circular reduction. These issues are compounded by the undefined 'R2 train' metric and the absence of significance tests or confidence intervals, so the headline practical claims are statistically forced by the in-sample data. Overall score 6: partial circularity, not a definitional equivalence.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claims rest on the chosen hyperparameter grid, the 2D and 100-iteration evaluation budget, and the assumption that SHAP attributions over AOCC are meaningful explanations. No fitted model parameters appear, but the single-best configuration selection is an in-sample fit to the benchmark results. No new entities are introduced.

free parameters (2)

Hyperparameter search grid = c1 in {0.3,0.5,0.7,0.9}; c2 in {0.2,0.4,0.6,0.7}; w in {0.9,1.2,0.4}; n in {50,100,150}; k in {1,2,3}; p in {1,2}; r…
All conclusions about which hyperparameters matter are conditioned on these hand-picked ranges; no sensitivity analysis or justification for the ranges is provided.
Evaluation budget and instance count = d=2, 100 iterations, 5 initial instances x 5 independent runs
The guidelines are derived entirely within this narrow budget; the paper itself lists scaling to higher dimensions as future work.

assumptions (4)

domain assumption BBOB noiseless benchmark functions are representative of real-world optimization problems.
Section 3 evaluates only the 24 BBOB functions in 2D, yet the abstract promises practical guidelines for optimization tasks in general.
domain assumption SHAP attributions computed on AOCC performance data faithfully explain PSO hyperparameter influence.
Section 4 interprets SHAP dot plots as contributions without validating the attribution model or checking SHAP assumptions for this algorithm class.
domain assumption AOCC is a sufficient scalar metric for comparing convergence and exploration behavior.
Equation 3 defines AOCC and it is the sole performance metric, but no argument shows it captures the exploration and exploitation trade-off claimed.
domain assumption Unstated PSO implementation details do not affect the relative topology conclusions.
Only Equations 1 and 2 are given; initialization, velocity bounds, and termination behavior are unspecified, and these can materially change PSO behavior.

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Cite this review

Pith. "Pith review of Enhancing Explainability and Reliable Decision-Making in Particle Swarm Optimization through Communication Topologies." pith.science (2026). https://pith.science/paper/4G6FR65M

@misc{pith2026250412803,
  author       = {Pith},
  title        = {Pith review of: Enhancing Explainability and Reliable Decision-Making in Particle Swarm Optimization through Communication Topologies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4G6FR65M}},
  note         = {Machine review of arXiv:2504.12803}
}

read the original abstract

Swarm intelligence effectively optimizes complex systems across fields like engineering and healthcare, yet algorithm solutions often suffer from low reliability due to unclear configurations and hyperparameters. This study analyzes Particle Swarm Optimization (PSO), focusing on how different communication topologies Ring, Star, and Von Neumann affect convergence and search behaviors. Using an adapted IOHxplainer , an explainable benchmarking tool, we investigate how these topologies influence information flow, diversity, and convergence speed, clarifying the balance between exploration and exploitation. Through visualization and statistical analysis, the research enhances interpretability of PSO's decisions and provides practical guidelines for choosing suitable topologies for specific optimization tasks. Ultimately, this contributes to making swarm based optimization more transparent, robust, and trustworthy.

Figures

Figures reproduced from arXiv: 2504.12803 by the authors.

**Figure 2.** Hyper-parameter contributions per benchmark function for d=2 for PSO using Star Topology. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

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Reference graph

Works this paper leans on

15 extracted references · 12 canonical work pages · cited by 1 Pith paper

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

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Suyog Chandramouli, Yifan Zhu, and Antti Oulasvirta. 2023. Interactive Person- alization of Classifiers for Explainability using Multi-Objective Bayesian Opti- mization. In Proceedings of the 31st ACM Conference on User Modeling, Adaptation and Personalization. 34–45

work page 2023

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Nikolaus Hansen, Anne Auger, Dimo Brockhoff, and Tea Tušar. 2022. Any- time performance assessment in blackbox optimization benchmarking. IEEE Transactions on Evolutionary Computation 26, 6 (2022), 1293–1305

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Essam H Houssein, Ahmed G Gad, Kashif Hussain, and Ponnuthurai Nagaratnam Suganthan. 2021. Major advances in particle swarm optimization: theory, analysis, and application. Swarm and Evolutionary Computation 63 (2021), 100868

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James Kennedy and Russell Eberhart. 1995. A new optimizer using particle swarm theory. In Proceedings of the sixth international symposium on micro machine and human science, Vol. 3943. Nagoya, Japan: IEEE

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Marius Lindauer, Katharina Eggensperger, Matthias Feurer, André Biedenkapp, Joshua Marben, Philipp Müller, and Frank Hutter. 2019. Boah: A tool suite for multi-fidelity bayesian optimization & analysis of hyperparameters. arXiv preprint arXiv:1908.06756 (2019)

arXiv 2019