[Paper] Quantifying the Impact of Modules and Their Interactions in the PSO-X Framework

Source: arXiv - 2601.04100v1

Overview

The paper investigates how individual components (modules) and their interactions shape the performance of Particle Swarm Optimization (PSO) algorithms within the highly configurable PSO‑X framework. By analysing thousands of algorithm variants on a standard benchmark, the authors reveal that only a handful of modules truly drive success, offering a roadmap for practitioners who need to pick the right building blocks for their optimisation tasks.

Key Contributions

• Large‑scale empirical study: Evaluated 1 424 PSO‑X algorithm instances on the 25‑function CEC’05 benchmark (10‑ and 30‑dimensional).
• Quantitative attribution: Applied functional ANOVA to measure the marginal and interaction effects of each module on optimisation quality.
• Problem‑class profiling: Linked module importance to problem characteristics such as multimodality, separability, and dimensionality.
• Cluster analysis of problem classes: Grouped benchmark functions that share similar module‑effect patterns, exposing “families” of problems that respond alike to specific PSO components.
• Practical insight: Demonstrated that PSO performance is dominated by a few high‑impact modules, reducing the perceived combinatorial explosion when configuring PSO‑X.

Methodology

1. Modular PSO‑X definition – The framework consists of dozens of interchangeable modules (e.g., inertia weight strategies, velocity update rules, topology, mutation operators). Each module can be toggled on/off or swapped with alternatives, yielding a combinatorial space of algorithms.
2. Algorithm generation – The authors automatically instantiated every feasible combination, ending up with 1 424 distinct PSO variants.
3. Benchmarking – Each variant was run on the CEC’05 suite (a widely‑used set of continuous optimisation problems) at two dimensionalities (10 D, 30 D). Standard performance metrics (best‑found fitness, convergence speed) were recorded over multiple independent runs to ensure statistical robustness.
4. Functional ANOVA (fANOVA) – This statistical technique decomposes the total variance in performance into contributions from individual modules and their interactions, yielding a percentage of explained variance for each factor.
5. Cluster analysis – Using the module‑effect profiles, the authors performed hierarchical clustering on the 25 benchmark functions, revealing groups of problems that share similar sensitivity to the same modules.

The whole pipeline is fully reproducible: the authors provide the configuration scripts, the generated algorithm pool, and the analysis code.

Results & Findings

In short, most PSO‑X configurations behave similarly, and performance differences can be traced back to a handful of well‑understood components.

Practical Implications

• Simplified algorithm selection – Developers can focus on tuning the few high‑impact modules instead of wrestling with the full combinatorial space, cutting configuration time by orders of magnitude.
• Automated hyper‑parameter optimisation – Meta‑optimisers (e.g., Bayesian optimisation) can be constrained to the influential modules, leading to faster convergence and lower computational budgets.
• Domain‑specific presets – Based on the identified problem clusters, libraries can ship ready‑made PSO‑X presets (e.g., “multimodal‑heavy”, “high‑dimensional”) that already embed the most effective modules for that class.
• Transfer learning across problems – Since module importance patterns are stable across similar problem families, knowledge gained on one benchmark can be transferred to real‑world optimisation tasks (e.g., hyper‑parameter tuning for deep nets, engineering design).
• Framework design guidance – Future modular optimisation frameworks can prioritize adding new modules that target the uncovered gaps (e.g., novel diversity‑preserving operators) rather than proliferating redundant options.

Limitations & Future Work

• Benchmark scope – The study is limited to the CEC’05 suite; real‑world problems may exhibit additional complexities (constraints, noisy evaluations) that could shift module importance.
• Static module set – Only the modules already present in PSO‑X were examined; introducing entirely new operators (e.g., surrogate‑based guidance) might change the variance landscape.
• Scalability to higher dimensions – Experiments capped at 30 D; ultra‑high‑dimensional problems (≥100 D) could reveal new interaction effects.
• Dynamic adaptation – The analysis treats modules as static choices; exploring runtime switching or adaptive composition could further boost performance.

The authors suggest extending the methodology to other modular meta‑heuristic families (e.g., DE, CMA‑ES) and to multi‑objective settings, where module interactions may be more pronounced.

Authors

• Christian L. Camacho-Villalón
• Ana Nikolikj
• Katharina Dost
• Eva Tuba
• Sašo Džeroski
• Tome Eftimov

Paper Information

• arXiv ID: 2601.04100v1
• Categories: cs.NE, cs.AI
• Published: January 7, 2026
• PDF: Download PDF