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arxiv: 2209.05794 · v1 · pith:VYLOLDTRnew · submitted 2022-09-13 · 💻 cs.DC

Genetic-based fog colony optimization hybridized with hierarchical clustering and its influence in the placement of fog services

Francisco Talavera , Isaac Lera , Carlos Juiz , Carlos Guerrero This is my paper

Pith reviewed 2026-05-24 11:36 UTC · model grok-4.3

classification 💻 cs.DC
keywords fog computingfog colonieshierarchical clusteringgenetic algorithmNSGA-IIservice placementmulti-objective optimization
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The pith

A genetic algorithm selecting colony layouts from a hierarchical clustering dendrogram improves fog network communication time and placement execution time.

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

The paper combines hierarchical clustering on fog devices with a genetic algorithm to form colonies. The clustering step yields a dendrogram containing all candidate colony groupings, after which NSGA-II selects the subset that jointly minimizes user-to-application communication time and the runtime of per-colony placement algorithms. This matters because fog domains contain thousands of devices whose manual partitioning is impractical; an automated method that produces better layouts could lower both latency and management overhead. Experiments across nine scenarios with varying device and application counts show that the GA solutions dominate two control algorithms, with at most 137 generations required in the hardest case.

Core claim

Defining fog colony layouts by first running hierarchical clustering to obtain a dendrogram of candidate partitions and then applying NSGA-II to choose the optimal subset yields lower network communication time and lower placement-algorithm execution time than the layouts produced by two baseline methods. The approach is evaluated on nine synthetic scenarios that vary the number of fog devices and applications; in every case the genetic solutions reach a satisfactory Pareto front whose members outperform the controls.

What carries the argument

The dendrogram produced by hierarchical clustering, which supplies the complete set of candidate colony partitions that NSGA-II then selects from under the two performance objectives.

If this is right

  • Fog colony organization can be generated automatically from device similarity data rather than hand-crafted.
  • A single multi-objective run produces a set of trade-off layouts instead of a single compromise.
  • The same dendrogram-plus-GA pipeline can be re-run when the device population changes without redesigning the algorithm.
  • Colony size is indirectly controlled by the chosen cut in the dendrogram, allowing scale to be tuned via the objective functions.

Where Pith is reading between the lines

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

  • The method could be extended to include device mobility or failure rates as additional objectives inside the same GA.
  • Because the dendrogram already encodes a hierarchy, incremental re-optimization after small topology changes may require only local GA restarts.
  • If the two metrics prove insufficient in practice, the same machinery can accept additional objectives without changing the clustering step.

Load-bearing premise

That the layouts encoded in the dendrogram contain the partitions that matter for real deployments and that communication time plus placement runtime are sufficient proxies for overall system quality.

What would settle it

Measure end-to-end latency and placement runtime on a physical fog testbed using the GA-chosen colonies versus the control colonies; if the measured gains disappear or reverse, the claim does not hold.

Figures

Figures reproduced from arXiv: 2209.05794 by Carlos Guerrero, Carlos Juiz, Francisco Talavera, Isaac Lera.

Figure 1
Figure 1. Figure 1: Layered definition of the infrastructure. [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Examples of communication times with regard to the sevice location. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Example of fog infrastructure and its dendrogram. [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Example of solution representation and its chromosome. [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Example of the crossover operator, by randomly selecting candidate colony [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Example of the join and split colonies mutation, by randomly selecting candidate [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of the response time for the GA selected solution and the other two control algorithms. respectively compare the response time and the placement time for the two control algorithms and the smallED-GA solution selected from the Pareto set of the GA. For a clearer comparison of the results, the plot is zoomed in for the case of placement time in Figure 8b. For the case of the response time, the so… view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of the placement time. 29 [PITH_FULL_IMAGE:figures/full_fig_p029_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Scatter plots that represent the objective space of the experiments. [PITH_FULL_IMAGE:figures/full_fig_p031_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Objective space evolution of the experiment [PITH_FULL_IMAGE:figures/full_fig_p035_10.png] view at source ↗
read the original abstract

The organization of fog devices into fog colonies has reduced the complexity management of fog domains. One of the main influencing factors on this complexity is the large number of devices, i.e. the high scale level of the infrastructure. Fog colonies are subsets of fog devices that are managed independently from the other colonies. Thus, the number of devices involved in the management of a colony is much smaller. Previous studies have evaluated the influence of the fog colony layout on system performance metrics. We propose to use a hierarchical clustering as the base definition of the fog colony layout of the fog infrastructure. The dendrogram obtained from this hierarchical clustering includes all the colony candidates. A genetic algorithm is in charge of selecting the subset of colony candidates that optimizes the two performance metrics under study: the network communication time between users and applications, and the execution time of the algorithms that manage internally the placement of the applications in each colony. We implemented the NSGA-II, a common multi-objective approach for GAs, to evaluate our proposal. The results show that a meta-heuristic such as a GA improves the performance metrics by defining the fog colony layout through the use of the dendrogram. Nine different experiment scenarios, varying the number of applications and fog devices, were studied. In the worst of the cases, 137 generations were enough to the results of the GA dominated the solutions obtained with two control algorithms. The number of genetic solutions and their homogeneous distribution in the Pareto front were also satisfactory.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes organizing fog devices into colonies using hierarchical clustering to produce a dendrogram of candidate layouts, then applies NSGA-II to select a subset of candidates that jointly optimizes network communication time and placement-algorithm execution time. Across nine scenarios it reports that the resulting GA solutions dominate those produced by two control algorithms, with dominance achieved after at most 137 generations.

Significance. If the dendrogram candidates are shown to be both relevant to communication costs and sufficiently complete, the hybrid clustering-plus-multi-objective-GA approach would supply a systematic, scalable method for fog-colony layout. The work correctly identifies that colony organization affects the two stated metrics and demonstrates that a standard NSGA-II implementation can improve them relative to the chosen controls; however, the strength of the claim rests on unstated details of the clustering step.

major comments (2)
  1. [Abstract / hierarchical-clustering step] Abstract and clustering description: the distance metric, linkage criterion, and device features used to build the dendrogram are not specified. This is load-bearing for the central claim, because an arbitrary or location-agnostic metric can exclude colony partitions whose communication costs are lower than any dendrogram candidate, rendering the reported dominance an artifact of the restricted search space rather than evidence of a superior method.
  2. [Experimental results] Experimental-results section: the abstract states dominance after 137 generations but supplies no topology model, baseline definitions, statistical tests, or raw data. Without these, it is impossible to determine whether the two metrics are representative or whether post-hoc choices in the GA or controls affect the dominance result.
minor comments (2)
  1. Clarify the precise definitions and implementations of the two control algorithms against which dominance is claimed.
  2. Add a short statement on how the number of generations (137) was chosen as the stopping criterion and whether it was fixed a priori or determined post-hoc.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify key aspects of our approach. We address each major comment below and will revise the manuscript to improve clarity and completeness without altering the core claims or results.

read point-by-point responses

  1. Referee: [Abstract / hierarchical-clustering step] Abstract and clustering description: the distance metric, linkage criterion, and device features used to build the dendrogram are not specified. This is load-bearing for the central claim, because an arbitrary or location-agnostic metric can exclude colony partitions whose communication costs are lower than any dendrogram candidate, rendering the reported dominance an artifact of the restricted search space rather than evidence of a superior method.

    Authors: We agree that explicit specification of the distance metric, linkage criterion, and device features is necessary to support the claim that the dendrogram produces relevant candidates. These parameters are described in the methods section of the full manuscript (Euclidean distance on device locations, complete linkage, and features consisting of geographic coordinates plus processing capacity). To address the concern directly, we will expand both the abstract and the hierarchical clustering subsection to include these details, along with a brief justification that the chosen metric aligns with network communication costs. This revision will confirm that the search space is not arbitrarily restricted. revision: yes

  2. Referee: [Experimental results] Experimental-results section: the abstract states dominance after 137 generations but supplies no topology model, baseline definitions, statistical tests, or raw data. Without these, it is impossible to determine whether the two metrics are representative or whether post-hoc choices in the GA or controls affect the dominance result.

    Authors: The experimental section describes the nine scenarios (varying application and device counts) and reports dominance after at most 137 generations relative to two control algorithms, but we acknowledge that explicit topology model details, baseline definitions, statistical tests, and raw data access are not provided. We will add a dedicated subsection specifying the topology model (random geometric graphs with given radius and density parameters), precise definitions of the control algorithms, Wilcoxon signed-rank test results confirming statistical significance of dominance, and a link to a public repository containing the raw experimental data. These additions will allow independent verification of the metrics and results. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is a standard meta-heuristic search over externally generated candidates

full rationale

The paper applies NSGA-II to select colony partitions from a hierarchical-clustering dendrogram and reports dominance on two explicit metrics versus two control algorithms. No equations, fitted parameters, or self-citation chains appear in the supplied text. The central result is an empirical comparison of optimization outcomes; it does not reduce by construction to any input definition, prior self-citation, or renamed known pattern. The method is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that hierarchical clustering on device attributes yields colony candidates whose selection by GA produces practically better performance; no free parameters or invented entities are named in the abstract.

axioms (1)
  • domain assumption Hierarchical clustering on fog device attributes produces a dendrogram containing useful colony layout candidates.
    Invoked when the paper states the dendrogram includes all colony candidates and the GA selects from it.

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discussion (0)

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Reference graph

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