Do Bio-Inspired Algorithms Save Energy in Data Centres? Separating Server Packing from Migration Search in Virtual Machine Consolidation

Do Bio-Inspired Algorithms Save Energy in Data Centres? Separating Server Packing from Migration Search in Virtual Machine Consolidation Short title: Separating packing from search in VM consolidation Aun Yichieta,*

Woo Yu Hanga

a Faculty of Information and Communication Technology, Universiti Tunku Abdul Rahman, Jalan Universiti,

Bandar Barat, 31900 Kampar, Perak, Malaysia * Corresponding author. Aun Yichiet, Faculty of Information and Communication Technology, Universiti

arXiv:2610.34102v1 [cs.DC] 25 Oct 2026

Tunku Abdul Rahman, Jalan Universiti, Bandar Barat, 31900 Kampar, Perak, Malaysia. Email: aunyc@utar.edu.my Abstract Energy-efficient virtual machine (VM) consolidation matters as data centre electricity demand rises. Bio-inspired metaheuristics, including ant colony optimisation (ACO), particle swarm optimisation (PSO), and genetic algorithms, have reported substantial energy savings. However, these improvements are commonly evaluated against conventional allocation policies that differ in both initial VM placement and subsequent migration optimisation, making it difficult to determine the contribution of metaheuristic search. This study reproduces an existing consolidation implementation in CloudSim Plus and introduces a matched control that retains the same initial packing and empty-host deactivation mechanisms but excludes migration search. ACO, PSO, and a modified genetic algorithm (MGA) are evaluated across two fleet configurations and four workload regimes, with ten stochastic replications per condition. The matched control achieves energy savings of 0.8–81.4% relative to the spreading baseline, the amount available falling sharply as load rises, without migrations or incomplete workload execution. Across 24 comparisons, metaheuristic search increases energy consumption in 11 cases, produces identical outcomes in seven, and reduces consumption in six. Of these, ten increases and five reductions remain statistically significant after Holm correction. Five of the six apparent reductions coincide with unfinished tasks and disappear after normalisation by delivered computational work. Only ACO under light heterogeneous load retains a 3.22-percentage-point improvement (95% CI 2.96–3.47). These findings demonstrate that initial packing and host deactivation account for most of the measured energy savings in the examined implementations, highlighting the importance of matched control conditions and workload-completion measures for reliable evaluation of VM consolidation algorithms. Keywords: virtual machine placement; server consolidation; data centre energy; ant colony optimisation; particle swarm optimisation; controlled experiment

1. Introduction Global data centre electricity consumption reached 415 TWh in 2024 and is projected to approach 945 TWh by 2030 [1]. Efficiency gains at the facility level can no longer absorb this growth, as the industry-weighted Power Usage Effectiveness has remained near 1.54 for six consecutive years [2], indicating that the overhead layer is close to its practical limit. Alternative avenues for optimisation can therefore be explored within the information technology layer itself, where computational work is assigned to physical machines. Scope for such optimisation arises from the way server power scales with load. A powered but idle host draws between 50% and 70% of its peak demand [3], so a fleet operating at low utilisation consumes a

disproportionate share of its rated power. Energy is conserved not by distributing load evenly across the fleet, but by concentrating it onto fewer hosts and deactivating the remainder. Virtualisation makes such concentration possible, and the resulting optimisation problem, virtual machine (VM) consolidation, has become the principal information technology intervention available for data centre energy management. The scale at which these policies will be applied is growing fastest outside the established markets, and Southeast Asia is where the question is most immediate. In Johor, Malaysia, 38 data centre projects hold Electricity Supply Agreements totalling 5.9 GW of maximum demand against an actual drawn load of 405 MW in December 2024 [4], so contracted demand there exceeds realised demand by more than an order of magnitude. Most of that capacity has yet to be energised, which means that the consolidation policies governing its eventual efficiency remain design decisions rather than installed facts. VM consolidation is formulated as multi-dimensional bin packing, in which virtual machines with processor, memory and bandwidth requirements are assigned to hosts of finite capacity so as to minimise the number of active hosts. The problem is NP-hard, and its solution space grows combinatorially with fleet size. Exact methods therefore cannot satisfy the timescales required for online allocation, while constructive heuristics such as first-fit and best-fit execute in near-linear time but leave capacity stranded in fragments too small to allocate. Bio-inspired metaheuristics occupy the interval between these extremes. They require no gradient information, operate directly on discrete assignment spaces, and return a usable solution at any point at which they are interrupted, which suits an allocator that must respond within a scheduling interval. Their population-based structure further allows several candidate configurations to be maintained and compared within a single iteration, providing a mechanism for escaping the local optima that greedy packing produces. Three families have dominated this literature, and each corresponds to a different structural feature of the problem. Ant colony optimisation constructs assignments incrementally and retains a pheromone memory across iterations, which suits a problem in which virtual machines are allocated in sequence and earlier decisions constrain later ones [5]. Particle swarm optimisation represents a complete allocation as a position vector and converges rapidly, although host indices are categorical and must be recovered through discretisation [6]. Genetic algorithms recombine parent solutions through crossover, an operator capable of preserving well-packed groups of virtual machines as intact units, and therefore well matched to grouping problems [7]. Bio-inspired algorithms have been reported to reduce energy consumption by as much as 47% relative to conventional allocation policies [8,11], with others in the same line reporting gains below 15% [5,10]. Those policies, however, differ from the proposed methods in two respects simultaneously: the rule governing where virtual machines are initially placed, and the presence of a subsequent search for beneficial migrations. Only the second is contributed by the metaheuristic, and a comparison that varies both cannot determine which is responsible for the observed saving. This study develops and applies a controlled experimental framework that distinguishes the energy effect of initial consolidation from the effect attributable to metaheuristic search, and evaluates whether reported improvements persist under matched initial conditions and workload-delivery requirements. An existing consolidation implementation of ant colony optimisation, particle swarm optimisation and a modified genetic algorithm is reproduced in CloudSim Plus and evaluated against a matched control that applies the same initial packing rule and the same empty-host deactivation behaviour, but performs no migration search. An artificial bee colony implementation is carried through the same design as a structural diagnostic. The contrast between the conventional baseline and this control measures the effect of packing and deactivation; 2

the contrast between the control and each metaheuristic measures the effect of search. Cryptographic fingerprints verify that all policy arms receive identical virtual machine sets and task assignments, so that neither contrast is confounded by workload variation. Energy is reported alongside workload completion throughout, which allows apparent reductions obtained by leaving tasks unfinished to be identified rather than credited. The framework is applied across two fleet configurations and four workload regimes, and three implementation-level properties of the reproduced system are documented where they bear on the interpretation of published results. The remainder of this paper is organised as follows. Section 2 examines the comparison structure of representative studies. Section 3 specifies the system model and the decomposition. Section 4 describes the controlled framework and the measured implementation. Section 5 details the experimental design. Section 6 reports the results, Section 7 discusses them, and Section 8 concludes.

2. Related Work The theoretical basis for consolidation is the observation of Barroso and Hölzle that servers are not energy-proportional: an idle but powered machine draws a large fixed fraction of its peak demand, so energy is conserved by emptying machines and deactivating them rather than by balancing load [3]. Beloglazov and Buyya translated this argument into the adaptive-threshold heuristics and linear power model that most simulation-based work in this area inherits, including the implementation reproduced here [12]. Cambazard et al. subsequently formalised the cost structure as bin packing with linear usage costs, comprising a fixed cost for each opened bin and a cost linear in its load, and derived lower bounds for this application [13]. The matched control introduced in Section 4 measures how closely an ordinary best-fit heuristic approaches that bound without any search. The energy-efficient ant colony system of Liu et al. is the reference point for ACO applied to static placement [5], and the dynamic consolidation formulation of Ferdaus et al. is the corresponding reference for ACO applied to the migration of running virtual machines [8]. Genetic and swarm formulations are comparably developed, and recent work extends them with reinforcement-learning hybrids [14], renewable- and carbon-aware objectives [15], and container-level placement [16]. Baydoun and Zekri published three treatments of this problem during 2025, including an ACO-initialised PSO hybrid for energy- and carbon-efficient consolidation [9-11]. Across this body of work the proposed methods differ considerably, but their evaluation structure does not. Table 1 classifies the experimental sections of three studies in this line, together with the implementation reproduced here and the control introduced here, along the properties that determine what a comparison identifies. Each surveyed study compares its proposed method against a policy that differs from it in both respects at once, so the quantity measured in each is the joint effect of placement and search. The reported outcomes are energy and, in some cases, service-level violation rates, and establishing that the arms delivered equal work additionally requires a completion count, since an energy reduction obtained by leaving work unfinished is otherwise indistinguishable from one obtained by consolidating efficiently. Both properties belong to the experimental designs rather than to the algorithms, and both are removable at the cost of one additional arm and one additional metric. This issue is distinct from the incommensurability documented in the wider methodological literature.

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Table 1. Comparison structure of representative energy-aware consolidation studies, the reproduced implementation, and the present study. Study

Comparator(s)

Comparator shares proposed initial placement

Migration search

Completion reported

Liu et al. [5]

No

Yes

No

Baydoun and Zekri [11]a Reproduced implementation

BFD, FFD, UACS, the authors’ prior ACO CloudSim Plus default allocation policy

Not stated; comparators retain their own published settings Not stated; all arms begin from a randomly generated load-balanced state Not stated

No; static placement

Ferdaus et al. [8]

FFD, RGGA, ACO, MACO, HACOPSO; CPLEX for bounds FFDL1; MMDVMC

Yes

No

Yes

No

This study

Spreading baseline and the matched control

No; the default policy spreads, the metaheuristics pack Yes, by construction

Yes; disabled in the control

Yes, per run

a Characterised from the openly available version of the two-stage ACO-PSO approach, the immediate predecessor of [9], which

carries the same two stated innovations. Entries describe the experimental sections of the cited works as published. “Not stated” indicates that the information is not given there, and is not an assertion that the conditions differed.

Sörensen’s analysis of metaphor-driven algorithm proliferation [17], Kudela’s demonstration that widely used benchmark suites carry artefacts affecting substantial bodies of published comparison [18], and the synthesis by Molina et al. [19] each argue that the incentive structure of the field rewards proposing algorithms more than comparing them, and Mann’s survey states the domain-specific form of the argument, that published variants of the problem differ sufficiently that reported numbers are not commensurable between papers [20]. Incommensurability limits what can be concluded by comparing two papers; an unmatched control limits what can be concluded within one. The remedy is correspondingly narrower, requiring no standard benchmark or shared workload, only that one arm differ from the proposed method in a single respect.

3. System Model 3.1 Placement, migration and workload A simulated data centre in this study comprises a fixed set of physical hosts and a stream of virtual machines that arrive to run on them. Each host offers processing elements, memory, storage and network bandwidth. Each virtual machine requests a quantity of each and carries a share of the user workload, expressed as cloudlets, which are units of computation measured in millions of instructions. Two decisions govern where that work runs. Placement occurs when a virtual machine arrives: the allocation policy selects a host with sufficient free capacity to accept it. Migration occurs afterwards: the policy may move a running virtual machine from its current host to another, which allows virtual machines spread across many lightly loaded hosts to be gathered onto fewer hosts so that the remainder can be powered down. Placement is decided once per virtual machine on arrival, whereas migration is reconsidered at every scheduling interval for the lifetime of the simulation. Both decisions are taken by one component, the allocation policy, and both are where the metaheuristics examined here act: ant colony optimisation, particle swarm optimisation and the modified genetic algorithm each supply a rule applied at admission together with a search that proposes migrations at every subsequent interval. Section 4 specifies the rules and the searches used.

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All four resources are reserved at admission. A host accepts a virtual machine only while its uncommitted memory, storage, bandwidth and aggregate processing capacity each meet the request, and VmSchedulerTimeShared enforces the last of these by testing the host’s remaining unallocated MIPS against the virtual machine’s full nominal demand. What time-sharing permits is that the number of virtual processing elements resident on a host exceed its physical count, since each virtual element draws a share of the host’s aggregate capacity rather than owning a core. Capacity in MIPS therefore bounds how densely a host can be packed, while the count of virtual elements does not. Formally, let P be the set of physical hosts and V the set of virtual machines, with C the set of cloudlets representing user workload. An allocation is a mapping A : V → P. The reservation constraint on memory, storage and bandwidth is VM rj ≤ PMir

∑

for all i, r ∈ {m, s, b}.

(1)

j : A(VM j )=PMi

(a)

(b) running cloudlet

VM

i

ii

v

iv

iii

capacity Reserved

capacity

h2

migrate

deactivate

h1 after

requested

Time-shared

h1

h2 after, deactivated

place v1

place v2 , cloudlets start

cloudlet in v1 ends

capacity

migrate v2 out

Fig. 1. The simulated system. (a) Hosts have finite capacity, drawn as the rail along the foot of each host. A virtual machine is a reservation against that capacity, drawn as a block whose width is the share it holds; cloudlets are units of work that execute inside a VM. A running VM may be migrated to another host, and a host left with no VMs is deactivated and stops drawing power. (b) The two resource classes, for one host across five intervals. Memory, storage and bandwidth are reserved when the VM is placed and released only when it leaves: the upper row steps up at each placement, steps down at the migration, and does not move when the cloudlet ends. They cannot be over-committed, so a host whose free memory is below a VM’s request is not a candidate for it and the reserved row can never cross the capacity line. Processing is time-shared: the lower row is zero in interval ii, where a VM is resident but idle, rises only while cloudlets execute, and in interval iii shows demand exceeding the host’s processing capacity, with the delivered rate capped and the surplus deferred. The fleets are 20 hosts of 256 GB with 48, 56 or 24 processing elements at 3.0, 2.7 or 2.4 GHz; the three VM classes reserve 2, 4 and 8 GB against requests of 1000, 4000 and 9600 MIPS. The contrast between the two rows is what the rest of the paper turns on: an active host draws 300 W before it does any work and 600 W at full load, so the dominant term in fleet energy is how many hosts are awake and for how long, which the reservation row sets, rather than how much computing they did, which is the time-shared row. Bar heights in (b) are illustrative proportions chosen for legibility, not measured values from any run.

Fig. 1 shows the resulting structure: the host fleet, the virtual machines resident on each host, the cloudlets they carry, and the two decision points at which an allocation policy acts. 3.2 Power and energy Energy follows from utilisation through the host power model. A powered host draws a fixed amount regardless of load, plus an amount that rises with processor utilisation, and it is the size of the fixed term that makes emptying and deactivating a host worthwhile. The standard linear form [12] is

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P(u) = k Pmax + (1 − k) Pmax u,

(2)

with k the idle fraction. This study uses k = 0.5, following the convention that an idle powered server draws 50 to 70 per cent of peak [3,12]. For the Dell PowerEdge R740, with Pmax = 600 W, Eq. (2) gives P(u) = 300 + 3.00u watts with u in per cent. Energy is the time integral of Eq. (2) summed over active hosts, accumulated at every scheduling tick and reported in kilojoules. The tick accumulation matters because the alternative, evaluating Eq. (2) once at a host’s mean utilisation and multiplying by its uptime, is unbiased only if that mean is itself time-weighted. In the simulator used here a busy host contributes a utilisation sample at most once per second while an idle host contributes one at every tick, so idle readings are over-represented and the resulting mean understates true utilisation by an amount that grows with the idle-but-powered time a policy produces. Since that quantity is exactly what the arms differ in, the two estimators disagree by −16% to +6% depending on arm, and the tick integral is used throughout. Both quantities are present in the deposited data [21]. Absolute energies by arm are given in Fig. S1. 3.3 Decomposition of the energy saving The energy saving a policy achieves relative to the baseline is the sum of two contributions, one from the placement it applies at admission and one from the search it runs above that placement. Resolving that sum into its terms requires a third energy measurement, taken under the same placement rule with the search disabled. Writing EB for baseline energy, EK for the control and EX for a policy X, all within the same fleet and load regime, placement effect = 100 (EB − EK )/EB ,

(3)

search effect = 100 (EK − EX )/EB . Both are expressed in percentage points of baseline energy, so they sum to the policy’s total saving. A negative search effect records that the metaheuristic consumed more energy than the same placement rule with the search disabled. 3.4 Energy per unit of delivered work Policies complete different numbers of cloudlets, so an energy comparison alone weighs arms that performed different amounts of work. Delivered work w is the fraction of submitted millions of instructions that were executed, counted as the instruction volume completed across all cloudlets whether or not the cloudlet itself reached completion, and energy per unit of delivered work is E/w. Instruction volume and cloudlet count are reported separately, since a run can lose a larger share of one than of the other. How strongly to charge for undelivered work is itself an assumption, so the family

E/wγ

(4)

is reported at γ = 0 (raw energy), γ = 0.5, and γ = 1 (undelivered work charged at the policy’s own average rate). For each positive search effect, the flip exponent is the value of γ at which the gain reverses, and it measures how strong a charge for undelivered work that gain withstands.

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4. Controlled Experimental Framework 4.1 Separating admission from search The placement and search effects defined in Section 3 are differences between three energies measured on one workload. Obtaining them requires arms that differ from one another by one component at a time, and the components have to be identified before they can be separated. An allocation policy in this setting performs two functions. On admission it chooses a host for each arriving virtual machine. Thereafter, at each scheduling interval, it decides whether resident virtual machines move and where they move to. A metaheuristic policy supplies both: the search it performs operates on an allocation that the policy’s own admission rule produced, and the two arrive together as one software component. A comparison between such a policy and a framework default therefore varies the admission rule and the search at the same time, and the energy difference it yields is the sum of two contributions in unknown proportion. The arms used here are organised as three levels of a single stack. The lowest level admits virtual machines by a rule that spreads them across the fleet and keeps every host powered. The middle level replaces that rule with one that packs virtual machines onto as few hosts as capacity allows and powers down the hosts it empties. The upper level adds a migration search above the packing. Adjacent levels differ by one component, so each contrast between them attributes an energy difference to that component alone. 4.2 Policy arms Five of the six arms occupy the middle and upper levels of the stack and therefore share one admission rule. Among hosts with sufficient free memory, storage and bandwidth for the arriving virtual machine, the rule prefers hosts that are already active, and among those selects the host with the fewest free processing elements. Hosts whose last virtual machine departs are powered down, in every arm but artificial bee colony, whose behaviour in this respect is given in Section 4.5. The fleet is consolidated at admission, before any search has run, onto as few active hosts as the capacity constraints permit. Migration search is the second stage, and it operates on the result of the first. At each scheduling interval the simulator requests a migration plan from the allocation policy and applies the virtual-machine-to-host moves the policy returns. A policy that returns an empty plan leaves the admission-time placement in force for that interval. The control arm, PackOnly, is the shared admission rule with the plan held empty at every interval. It occupies the middle level of the stack on its own, and it measures what admission-time packing and host deactivation contribute together, because the baseline spreads virtual machines and keeps the fleet powered, so moving to the control introduces both at once. The baseline occupies the lowest level. It is CloudSim Plus’s default allocation policy [22], which selects, among suitable hosts, the one with the greatest free capacity. That rule distributes virtual machines across the fleet rather than concentrating them, and the policy leaves every host powered for the duration of the run. Table 2 sets out the six arms by the two properties that distinguish them. 4.3 The search stage Ant colony optimisation, particle swarm optimisation and the modified genetic algorithm are standard implementations of their respective metaheuristics, differing from one another only in how the migration plan

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Table 2. The six policy arms, by admission rule, search stage and host-deactivation behaviour. Arm

Admission rule

Search

Deactivates hosts

Baseline PackOnly ACO PSO MGA ABC

VmAllocationPolicySimple (spreads) active-first best-fit, shared same best-fit rule same best-fit rule same best-fit rule same best-fit rule

none disabled ant colony particle swarm modified genetic artificial bee colony

no yes yes yes yes, once per simulation no

Note. The baseline is CloudSim Plus’s default allocation policy [22], which selects the suitable host with the greatest free capacity and therefore spreads virtual machines across the fleet. Bold marks the properties that distinguish the control and the ABC arm from the other four.

is constructed. Shared initial placement: active-first best-fit

active

VM queue

(a) PackOnly (control)

(b) ACO

deactivated

(c) PSO

(d) MGA crossover

plan = ∅

VM v

inertia

parent 1

h2

h5

h1

h4

h3

parent 2

h6

h6

h3

h1

h5

child

h2

h5

h3

h1

h5

mutated

h2

h5

h3

h7

h5

gBest pull source s1

target t1

source s1

target t1

source s2

target t2

source s2

target t2

source s3

target t3

source s3

target t3

pBest pull

gBest

pBest

h2

edge width ∝ pheromone τ

h5

roulette selection

h1

h5

particle position

h3

mutation

Fig. 2. The search stage, and what precedes it. Every arm begins at the band across the top: virtual machines are placed by one rule, which among hosts suitable for the VM prefers those already active and then takes the one with the fewest free processing elements, consolidating the fleet onto as few active hosts as it can and deactivating the rest. This rule is the defaultFindHostForVm override carried, character for character, by all four metaheuristic policy classes, so the arms below branch from an identical starting placement. (a) The control returns an empty migration plan at every scheduling interval, drawn as the same source-to-target question the searches are asked with no edge proposed: the initial placement stands, no VM is migrated and no host is reactivated. (b) Ant colony optimisation treats re-placement as a bipartite graph from source hosts to target hosts, with edge weight proportional to deposited pheromone τ; 5 ants × 10 iterations = 50 fitness evaluations per invocation, τ0 = 1.0, ρ = 0.1, α = 1.0, β = 2.0, q0 = 0.7, minimising the number of hosts left awake with a tie-break on residual free capacity. (c) Particle swarm optimisation encodes a whole VM-to-host assignment as one particle position, an integer vector over the target-host list, and moves it under inertia and pulls towards the particle’s own best and the swarm’s best; 10 particles × 10 iterations = 100 evaluations, w = 0.5, c1 = c2 = 2.0, velocity unclamped. (d) The modified genetic algorithm encodes an assignment as a chromosome, selects parents by fitness-proportionate selection, and applies single-point crossover then mutation; population 10 over 100 generations = 1010 evaluations, mutation rate 0.1, fitness 1/(1 + 0.5nunder + 0.5nover ) against thresholds it derives itself from a control chart over current host utilisations rather than from the SLA contract.

Fig. 2 sets out the placement stage that every arm shares, together with the migration plan each of the three searches computes above it. Ant colony optimisation represents re-placement as a bipartite graph from source hosts to target hosts, with

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edge weights proportional to deposited pheromone (τ0 = 1.0, ρ = 0.1, α = 1.0, β = 2.0, q0 = 0.7), and minimises the number of hosts left awake with a tie-break on residual free capacity. Particle swarm optimisation encodes a complete virtual-machine-to-host assignment as a single particle position and moves it under inertia with attraction towards the particle’s own best position and the swarm’s best (w = 0.5, c1 = c2 = 2.0, velocity unclamped). The modified genetic algorithm encodes an assignment as a chromosome, selects parents by fitness-proportionate selection, and applies single-point crossover followed by mutation at rate 0.1, with fitness 1/(1 + 0.5 nunder + 0.5 nover ) evaluated against thresholds the algorithm derives from a control chart over current host utilisations. Search effort is conventionally reported per invocation, and on that measure the budgets are 50 evaluations for ant colony optimisation (5 ants over 10 iterations), 100 for particle swarm optimisation (10 particles over 10 iterations), 1010 for the modified genetic algorithm (an initial population of 10 followed by 100 generations) and 500 for artificial bee colony. Invocation counts differ by more than three orders of magnitude between those same policies, which makes effort per run the comparable unit. Ant colony and particle swarm search at each of approximately 4130 scheduling intervals in a run, artificial bee colony searches about nine times under a throttle of one search per 500 simulated seconds, and the modified genetic algorithm searches once. Section 7 reports effort per run alongside measured search time. Convergence of a particle swarm depends on the relation between the inertia weight and the acceleration coefficients, and the Clerc-Kennedy analysis [6] gives the parameter region within which particle trajectories contract towards an attractor. With w = 0.5, c1 + c2 = 4.0 and velocity unclamped, the configuration measured here sits outside that region, so particle positions remain free to grow across iterations. 4.4 Verification of the design premises Two premises carry the design, that the five packing arms share one admission rule and that every arm receives the same workload, and both are established by direct inspection of the code. All four metaheuristic classes override defaultFindHostForVm. Normalising whitespace and hashing each implementation returns the same digest, so the rule described in Section 4.2 is carried character for character by all four, and it is this rule, rather than the framework’s power-aware parent rule, that executes, and the control arm reproduces the same routine. The metaheuristics therefore inherit a hand-written best-fit rule rather than the framework’s power-aware placement, which is what the arrangement of the code suggests. Workload identity is established by a SHA-256 fingerprint computed over the broker’s created-virtual-machine list and the complete cloudlet-to-virtual-machine assignment. Across 93 fingerprinted runs spanning all six arms, both fleets, all four load regimes and many seeds, exactly one fingerprint pair occurs per load regime, and all 272 runs created 100% of their submitted virtual machines. Every arm therefore receives an identical virtual machine set in identical submission order with an identical cloudlet mapping. Submission order is fixed by construction, so the fingerprint is reproducible across runs and across machines. 4.5 Operating characteristics of the search policies Three characteristics of the policies in this configuration bear on the results reported in Section 6. Ant colony, particle swarm and artificial bee colony choose migration sources by classifying each active host as overloaded or underloaded against a pair of utilisation thresholds taken from the service-level contract. The contract in CustomerSLA.json stores those thresholds as percentages, 20 and 80, and 9

SlaMetricDimension.getValue() returns them on that scale, while the host utilisation they are compared against is returned by getCpuPercentUtilization() as a fraction in [0, 1]. Under that comparison every active host is classified as underloaded, and the classification returns the same verdict at every interval. All three policies therefore treat the entire active fleet as a candidate migration source for the whole run, and migration is driven entirely by the underload path. The modified genetic algorithm derives its thresholds from a control chart over current host utilisations and is unaffected. The simulator requests a migration plan from each policy at every scheduling interval, and the modified genetic algorithm answers that request once. A guard in its allocation routine returns an empty map on every invocation after the first, so the search runs a single time per simulation and the placement it produces then stands for the remainder of the run. In seven of its eight cells the algorithm performs zero migrations, and its energy in those cells is bit-identical to the control arm across ten seeds per cell, 70 runs in total. Consolidation reduces energy only when the hosts a policy empties are powered down. Ant colony, particle swarm and the modified genetic algorithm each invoke shutdownEmptyHosts to do so. Artificial bee colony holds every host powered and reaches its results through migration alone. Its mean active-host count is 19.98 of 20 in every cell, matching the baseline to within 10−5 of a host.

5. Experimental Design 5.1 Configuration The implementation measured here is a research implementation of the algorithm descriptions cited in Section 2, written for this programme of work and deposited in full with this paper [21]. The comparison therefore targets those descriptions as realised in one codebase, rather than any particular set of previously reported figures. Table 3 summarises the testbed. Fig. 3 shows the pipeline: the workload model, broker, host pool, power model and migration loop are common to every arm, and the allocation policy is the only component that varies across the six. Two properties of the configuration carry more weight than the rest. Memory is identical across the two fleets at 5120 GB, so any difference between them is attributable to the distribution of processing capacity and power ratings rather than to a change in the constraint that determines whether a host can accept a virtual machine at all. The simulated horizon is effectively common to every run. Completion is governed by stragglers on single-element LIGHT virtual machines, whose processing allocation is the same under every host fleet and every allocation policy. Every arm therefore accumulates energy over the same interval, and the percentage comparisons reported in Section 6 are percentages of a common quantity. Replication follows the behaviour of each arm. The baseline and the control carry no stochastic element and produce bit-identical output in every recorded column under different seeds at the cells where this was checked, so each is run once per cell, while the three search policies are run ten times per cell against recorded seeds. The design therefore comprises eight fleet-and-load conditions, and repetition within a condition estimates the variation the search seeds contribute on a fixed workload rather than sampling further workloads. Recording completion alongside energy separates an energy reduction obtained by leaving work unfinished from one obtained by consolidating efficiently, which is the second of the two properties Section 2 identifies as absent from the surveyed designs.

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Workload model 160–1010 VMs 300–2000 cloudlets 4 load regimes

Host pool

Datacenter Broker

VmAllocationPolicy Power model

Baseline

Greatest free capacity

search: none

placement VM submission order, cloudlet-to-VM map, SHA-256 fingerprint

PackOnly search: off

ACO

Recorded metrics

search: on

Active-first best-fit

20 hosts, 256 GB, 48 / 56 / 24 PEs, 2 fleet mixes

per active host, P(u) = 300 + 3.00 u W

PSO search: on

MGA search: on

search

energy (kJ), active hosts, work delivered, migrations, search time

ABC search: on

Migration loop: every scheduling interval (1 s) sample host CPU / RAM

classify over- and under-loaded hosts

migrate VMs to realise the plan

Fig. 3. The testbed and the two reported contrasts. The workload model, broker, host pool, power model and migration loop are identical for every arm, and the allocation policy is the only component that changes. The broker submits the same VM set in the same order with the same cloudlet-to-VM mapping to every arm, verified per run by SHA-256 fingerprints of both: across 93 fingerprinted runs spanning all six arms, both fleets, all four load regimes and many seeds there is exactly one fingerprint pair per load regime, and all 272 runs created 100% of their submitted VMs. The policy slot holds six arms over two placement rules. The spreading baseline uses CloudSim Plus’s default placement, which selects the suitable host with the greatest free capacity; the other five share the active-first best-fit rule shown in Fig. 2. PackOnly is that rule with the search switched off, its getOptimizedAllocationMap returning an empty map on every interval. The placement contrast is the baseline against PackOnly and the search contrast is PackOnly against each of the four search policies, both reported in Fig. 4. The fleets are 20 hosts of 256 GB each, homogeneous as 20 × 48 processing elements at 3.0 GHz and heterogeneous as 8 × 48 at 3.0 GHz, 6 × 56 at 2.7 GHz and 6 × 24 at 2.4 GHz; the scheduling interval is 1 s; the power model is P(u) = 300 + 3.00 u W per active host, with start-up at 400/450/300 W for 5 s and shut-down at 50 W for 3 s.

Table 3. Fleet composition, workload, replication and instrumentation. Element

Configuration

Platform Homogeneous fleet

CloudSim Plus 8.5.5, OpenJDK 21; scheduling interval 1 s 20 × Dell PowerEdge R740 (48 cores at 3.0 GHz, 256 GB, 300 W idle / 600 W peak) 8 × R740; 6 × HPE ProLiant DL380 Gen10 (56 cores at 2.7 GHz, 350/700 W); 6 × Supermicro 1029U-TR4 (24 cores at 2.4 GHz, 200/400 W) 256 GB per host, 5120 GB per fleet in both configurations start-up 5 s at 400/450/300 W; shut-down 3 s at 50 W three classes on 1/2/4 cores, reserving 2/4/8 GB against 1000/4000/9600 MIPS S1–S4: 160, 380, 760 and 1010 VMs against 300, 750, 1500 and 2000 cloudlets ten per stochastic cell for ACO, PSO and MGA, each with a recorded seed; baseline and PackOnly deterministic; ABC at one to three replications; 272 runs in total makespan spans 0.02% across all 272 runs (4105.3–4106.2 s) energy, mean active hosts, processor and memory utilisation, cloudlets submitted and completed, delivered million-instructions, makespan, migrations started, algorithm wall-clock time

Heterogeneous fleet Fleet memory Host transitions VM classes Load regimes Replication

Simulated horizon Recorded per run

11

5.2 Verification and validation Alongside the two design premises verified in Section 4.4, four properties of the testbed on which the results of Section 6 depend were established by direct check rather than assumed. Determinism in the two reference arms was confirmed directly, repeated runs of the baseline and the control under different seeds returning bit-identical output in every recorded column at the cells where this was checked, which is what allows each to be run once per cell and treated as a constant in the tests of Section 5.3. The structural identities reported in Section 6.1 are exact rather than approximate, since in its seven zero-migration cells the modified genetic algorithm returns an energy bit-identical to the control across ten seeds per cell, 70 runs in total, which also confirms that the control’s energy is reproducible from an independent code path. The energy measure is physically consistent, in that host power is linear in utilisation and dynamic energy must therefore be proportional to delivered work at a ratio independent of the policy. Measured across the homogeneous runs the tick integral of Eq. (2) satisfies this to within 1.3%, whereas evaluating Eq. (2) at each host’s mean sampled utilisation gives a ratio varying by two orders of magnitude, which is the sampling asymmetry set out in Section 3.2. The capacity floor is reproducible from the configuration, the per-regime floors of 3, 7, 14 and 16 hosts in the homogeneous fleet and 3, 7, 13 and 18 in the heterogeneous fleet following from the declared host capacities and the virtual machine mix. Nine of the 272 runs sit below their floor, and each of those nine delivered less than the full workload, which is the signature of lost residency rather than of denser packing. 5.3 Statistical protocol The control arm is the comparator in every search contrast, and it is deterministic. Its energy in a given cell is therefore a constant, and the sampling distribution belongs entirely to the policy arm. Each contrast is a one-sample t test of the policy’s ten per-seed energies against that constant, with nine degrees of freedom. The comparison is paired on the workload as well, since the fingerprinting described in Section 4.4 establishes that every arm within a load regime receives the same virtual machines in the same order with the same cloudlets attached. Seven of the 24 comparisons are structural identities. The modified genetic algorithm in its seven zero-migration cells returns an energy bit-identical to the control across all ten seeds, and those cells are recorded as p = 1. Restricting the family to the 17 testable comparisons raises particle swarm optimisation at heterogeneous Scenario 4 to significance, so the family used here reports one benefit fewer than the narrower alternative would. Table 4 gives the remaining choices.

6. Results 6.1 Decomposition of the energy saving Table 5 separates each policy’s saving into a placement component, which is a property of the cell, and a search component, which is a property of the policy within that cell. The placement component is the control arm’s saving against the spreading baseline, and it runs from 0.82% at heterogeneous Scenario 4 to 81.40% at homogeneous Scenario 1, obtained with zero migrations and every submitted cloudlet completed. The component is therefore strongly load-dependent: under light load the packing rule captures most of the energy a consolidation policy can reach, and under the heaviest load tested it captures almost none, because the fleet 12

Table 4. Statistical procedure. Element

Choice

Test Family Correction

one-sample t against the deterministic control, nine degrees of freedom 24 pre-specified comparisons: {ACO, PSO, MGA} × 2 fleets × 4 load regimes Holm–Bonferroni primary; Benjamini–Hochberg q-values alongside; simultaneous Bonferroni intervals at 99.79% two one-sided tests against a ±2 percentage point margin Friedman over the eight blocks with Nemenyi post hoc [23], on raw energy and on energy per unit of delivered work, over the five arms excluding ABC and again over the four sharing the packing rule ABC, reported descriptively

Equivalence Cross-arm

Outside the family

at that point admits almost no consolidation at all. Table 5. Decomposition of the energy saving into placement and search components, in percentage points of baseline energy. Fleet

Load

Homogeneous

S1 S2 S3 S4 S1 S2 S3 S4

Heterogeneous

Placement

ACO

PSO

MGA

81.40 58.60 24.65 11.88 67.62 43.57 13.91 0.82

−0.12∗∗∗ −0.09 +0.82 −2.41∗∗∗ +3.22∗∗∗ +2.51∗∗∗ −3.55∗∗∗ +11.76∗∗∗

−37.03∗∗∗ −44.32∗∗∗ −18.04∗∗∗ −8.06∗∗∗ −31.08∗∗∗ −41.70∗∗∗ +5.90∗∗∗ +6.61∗∗∗

−71.62∗∗∗ 0.00 0.00 0.00 0.00 0.00 0.00 0.00

∗∗∗ significant at Holm-corrected α = 0.05 across the 24-comparison family. Bold marks the placement component in every cell, the

largest positive search effect, and the one positive search effect that holds after normalisation by delivered work.

Of the 24 search effects, eleven are negative, seven are exactly zero and six are positive. Fifteen are significant after Holm correction, ten of them increases in energy and five reductions. Equivalence testing at a ±2 percentage point margin places nine of the 24 within that band of zero, though seven of those nine are the structural identities described below rather than statistical equivalences established against dispersion. Fig. 4 presents the decomposition. The seven exact zeros are the modified genetic algorithm’s zero-migration cells, where its energy is bit-identical to the control across all ten seeds, so those cells record an identity rather than a test outcome. In the single cell where that algorithm’s search does fire, homogeneous Scenario 1, it costs 71.62 percentage points, because a mean of 142 migrations takes a 3.01-host placement back up to 17.98 hosts. 6.2 Workload completion and energy normalisation The control completes every submitted cloudlet in all eight cells, while the search policies deliver between 81.9% and 100% of theirs, which bears directly on the six positive effects. Table 6 places each against the work its arm delivered and against the flip exponent γ defined in Section 3.4, the correction strength at which the gain reverses. Five of the six reverse at γ between 0.356 and 0.834, so each is erased by a charge for undelivered work weaker than full, and at full charging they stand at losses of 0.3 to 12.6 percentage points. The sixth, ant colony optimisation at heterogeneous Scenario 1, reverses only at γ = 27.7 and therefore holds under any plausible accounting of unfinished work.

13

PackOnly

Placement effect (%)

(a)

ACO

PSO

MGA

Homogeneous fleet

Heterogeneous fleet

75 50 25 0

(b)

Search effect (pp)

0 −20 −40 −60

S1

S2

S3

S4

S1

S2

Load regime

S3

S4

Load regime

Fig. 4. Decomposition of the energy saving into a placement effect and a search effect, by host fleet and load regime. (a) Placement effect: the saving of the PackOnly control against the spreading baseline, that is, the saving obtained by the metaheuristics’ own placement rule with the search switched off. It is 81.4, 58.6, 24.6 and 11.9% at homogeneous S1–S4 and 67.6, 43.6, 13.9 and 0.8% at heterogeneous S1–S4, and it is obtained with zero migrations and 100% of cloudlets completed in every cell. (b) Search effect: the saving of each policy minus the placement effect, in percentage points added to it. Bars above the zero rule are cells where the search improved on the placement it was handed; bars below are cells where it reduced part of it. The search effect is negative in 11 of these 24 cells, exactly zero in 7 and positive in 6. The seven zeros are MGA cells in which the search returned no plan at all: MGA runs its search once per simulation and then returns an empty map, so in those cells it reproduces PackOnly. The largest single effect is MGA at homogeneous S1, −71.6 pp, the one cell where its search fires, with a mean of 142 migrations, 138 to 146 across the ten runs, taking a 3.01-host placement back up to 17.98 hosts. PSO reduces the placement saving in six of its eight cells (−37.0, −44.3, −18.0, −8.1, −31.1 and −41.7 pp). ACO lies between −3.6 and +11.8 pp and is not separable from zero after Holm correction in two of its eight cells. Error bars are 95% t intervals on the mean of ten independent replications. No interval is drawn on the placement bars in (a) or on MGA outside homogeneous S1: PackOnly and the baseline are deterministic, verified bit-identical across seeds and run once per cell, so they have no dispersion to show rather than dispersion too small to see; MGA’s ten runs are likewise bit-identical in the seven cells where its search produces no plan. ABC appears in Figs. 6 and S1. Table 6. The six positive search effects against delivered work. Fleet

Load

Policy

Search (pp)

Work delivered

Flip γ

Heterogeneous Heterogeneous Heterogeneous Heterogeneous Heterogeneous Homogeneous

S4 S4 S3 S1 S2 S3

ACO PSO PSO ACO ACO ACO

+11.76 +6.61 +5.90 +3.22 +2.51 +0.82

85.95% 82.83% 81.91% 99.65% 91.28% 98.49%

0.834 0.366 0.356 27.7 0.496 0.720

Note. Bold marks the one effect whose flip exponent lies beyond any plausible charge for undelivered work.

The loss of work tracks migration rather than load, which identifies where it comes from. All 86 runs that performed no migrations delivered 100% of their submitted instructions, and every run that fell short of complete delivery had migrated at least one virtual machine. Across the sixteen ant colony and particle swarm cells the correlation between search effect and work lost is r = 0.536 (p = 0.032), which points to an arithmetic mechanism rather than an algorithmic one: a host that stays powered draws its idle term either way, so a policy that leaves cloudlets unfinished records a lower mean processor utilisation and therefore a lower energy. Fig. 5 plots every search effect against the work its arm delivered.

14

8

Search effect (pp)

4 0 −4 ACO PSO

−8

MGA PackOnly

−20 −40 −60 80

85

90

95

100

Cloudlets completed (% of submitted)

Fig. 5. Search effect against delivered work, one point per policy and cell. The control sits at (100%, 0 pp) by construction, PackOnly being the origin of this plane, and completes 100% of submitted cloudlets in all eight cells with zero migrations. Five of the six positive search effects sit to its left, between 81.9% and 98.5% of work delivered: heterogeneous ACO S4 at +11.8 pp with 86.0% delivered, heterogeneous PSO S4 at +6.6 pp with 82.8%, heterogeneous PSO S3 at +5.9 pp with 81.9%, heterogeneous ACO S2 at +2.5 pp with 91.3% and homogeneous ACO S3 at +0.8 pp with 98.5%. Across the sixteen ACO and PSO cells the correlation between search effect and work lost is r = 0.536 (p = 0.032). The mechanism is arithmetic rather than algorithmic: the host stays powered either way, so a policy that drops 9–18% of its cloudlets records lower mean processor utilisation and therefore lower energy. The single exception, and the only clean positive result in the matrix, is ACO at heterogeneous S1: +3.22 pp (95% CI +2.96 to +3.47) with 0.35% of work lost. Open markers are the homogeneous fleet, filled markers the heterogeneous fleet; marker shape identifies the policy. MGA’s seven zero-search cells coincide exactly with the control and are drawn inside its open diamond. The ordinate is broken: the search effect spans −71.6 to +11.8 pp and seventeen of the twenty-four cells fall within ±9 pp. No point is clipped. Error bars are 95% t intervals on both cell means, n = 10.

6.3 Active hosts and the capacity floor The placement effect reported in Section 6.1 follows directly from how many hosts each rule leaves powered, since an active host draws 300 W before it performs any work. The baseline holds 19.98 of 20 hosts active in every cell regardless of load, while the shared best-fit rule packs virtual machines onto as few hosts as the capacity constraints allow. Fig. 6 shows the resulting counts against the resource-derived lower bound. That lower bound is set by whichever resource runs out first. Each virtual machine reserves memory and requests processing elements, so the fewest hosts that could accommodate a load regime can be computed separately for each resource, and the larger of the two values is the one that binds. Memory gives a floor of 2, 5, 9 and 12 hosts across the four regimes, the same in both fleets because every host carries 256 GB, while processing gives 3, 7, 14 and 16 hosts in the homogeneous fleet and 3, 7, 13 and 18 in the heterogeneous fleet. Processing is therefore the binding constraint in all eight cells. The control reaches the homogeneous floor exactly at the first three load levels, placing virtual machines on 3.01, 7.00 and 13.99 hosts against floors of 3, 7 and 14, so the placement already achieves the lowest host count available and a search can at best match it. In the heterogeneous fleet the control settles two to four hosts above the floor, because the placement rule ranks candidate hosts by the number of free processing elements and takes no account of how fast those elements run, filling the slower Supermicro hosts as readily as the faster Dell ones.

15

Baseline

PackOnly

ACO

PSO

MGA

ABC

Capacity floor

Mean active hosts (of 20)

20

15

10

5

0 S1

S2

S3

S4

S1

Homogeneous fleet

S2

S3

S4

Heterogeneous fleet

Fig. 6. Time-weighted mean active hosts, by arm, host fleet and load regime, against the capacity floor. The floor is the fewest hosts that could hold the regime’s requested resources, taking the largest-capacity hosts first: 3, 7, 14 and 16 hosts for the homogeneous fleet and 3, 7, 13 and 18 for the heterogeneous fleet. Processing capacity binds in all eight cells and memory does not, the memory-only floor being 2, 5, 9 and 12 hosts in both fleets since every host carries 256 GB, so the bound drawn is the processor bound and it is a lower bound on a relaxation rather than an achievable packing. PackOnly reaches it exactly at homogeneous S1, S2 and S3 (3.01, 7.00 and 13.99 hosts against 3, 7 and 14) and sits one host above it at S4. In the heterogeneous fleet it stays two to four hosts above the floor throughout, because the placement rule ranks hosts by free processing elements and is blind to how fast those elements run; this gap is where the one clean positive search effect lies, ACO reaching 6.12 hosts against PackOnly’s 7.00 at heterogeneous S1. ABC’s line lies on the baseline’s in all eight cells, the two agreeing to within 10−5 of a host, because it holds every host powered. Its energy reduction on the tick integral is correspondingly small, from −0.35% to +2.55%, while continuous migration drops delivered work to 85.6–98.4% and raises time spent above the 80% processor threshold above the baseline’s in every cell where the baseline registers any. The two reference conditions are drawn as pale ribbons and the four algorithm arms as thin lines over them. Error bars are 95% t intervals on the mean of ten replications and are drawn only where dispersion exists; PSO at homogeneous S1 (10.73 ± 1.38 hosts) is the widest.

6.4 Search gain under heterogeneous light load One positive search effect remains significant after correction and after work normalisation. Ant colony optimisation in the heterogeneous fleet under light load gains 3.217 percentage points, with a 95% confidence interval of 2.962 to 3.472 and a simultaneous Bonferroni-24 interval of 2.735 to 3.699. The test gives t(9) = 28.50 and a Holm-corrected p of 8.2 × 10−9 . The arm delivers 99.65% of its work, and the gain stands at 3.11 percentage points after full normalisation, with a 95% confidence interval of 2.82 to 3.41. The mechanism is the gap identified in Section 6.3 between the control’s placement and the capacity floor. The control sits four hosts above the floor in that cell, at 7.00 against a floor of 3, and ant colony optimisation closes part of that gap by reaching 6.12 active hosts. The condition under which search helps is therefore specific: it helps where the packing rule has left room, and the homogeneous fleet leaves none. The size of the result against the rest of the matrix is set by two further figures. The gain amounts to 4.8% of the placement effect in the same cell, and the same algorithm consumes significantly more energy than the control in two other cells, so one significant positive among 24 pre-specified comparisons supports a claim that search helps under a particular condition rather than a claim of general advantage. 6.5 Friedman rank comparison across arms Comparing all five arms simultaneously confirms the placement result and locates where the differences lie. A Friedman test over the eight blocks, ranking by raw energy, gives χ 2 (4) = 18.93 and p = 8.1 × 10−4 , against

16

a Nemenyi critical difference of 2.156 rank units. The baseline ranks last at 5.00 and separates from ant colony optimisation at 2.00, from the control at 2.19 and from the modified genetic algorithm at 2.56. No other pair separates, and the three best-ranked arms lie within 0.56 rank units of one another. Under energy per unit of delivered work the same comparison gives χ 2 (4) = 23.43 and p = 1.0 × 10−4 , the control ranks best at 1.56, and it separates from particle swarm optimisation at 4.00 and from the baseline at 4.75. Removing the baseline puts the paper’s own question to the same test. Across the four arms that share the packing rule, raw energy gives χ 2 (3) = 4.39 and p = 0.223 against a critical difference of 1.658, so the test does not separate any arm from any other. Under energy per unit of delivered work the test is significant at χ 2 (3) = 14.89 and p = 0.0019, the control ranks best at 1.56, followed by the modified genetic algorithm at 1.94 and ant colony at 2.62, and particle swarm at 3.88 is the one arm from which the control separates. Fig. 7 shows both rankings. (a)

(b) CD = 2.16

1

2

CD = 2.16 3

4

ACO 2.00 PackOnly 2.19 MGA 2.56

5

1

2

3

4

5

PackOnly 1.56 MGA 1.94 ACO 2.75

5.00 Baseline 3.25 PSO

4.75 Baseline 4.00 PSO

Fig. 7. Friedman average ranks with Nemenyi critical difference, over the eight fleet × load-regime blocks, ranked within block with 1 = lowest energy. (a) Ranked by raw energy: χ 2 (4) = 18.93, p = 8.1 × 10−4 ; CD(.05) = 2.156 rank units. The baseline separates from ACO (∆ = 3.00), PackOnly (2.81) and MGA (2.44), and no other pair separates. (b) Ranked by energy per unit of delivered work: χ 2 (4) = 23.43, p = 1.0 × 10−4 , and the control at 1.56 separates from PSO at 4.00 and from the baseline at 4.75. Horizontal bars join arms the test cannot separate. With the baseline dropped, which is the paper’s own question, the raw-energy test is not significant at all, χ 2 (3) = 4.39, p = 0.223, CD(.05) = 1.658, while under energy per unit of delivered work the test is significant, χ 2 (3) = 14.89, p = 0.0019, and PSO is the one arm the control separates from. Eight blocks is below the ten Derrac et al. [23] suggest, and the blocks are two fleets crossed with four monotone load levels rather than independent draws from a population of problems, so the critical difference is correspondingly wide; these tests corroborate the per-cell comparisons of Fig. 4. ABC is excluded; a six-arm sensitivity places it between PSO and the baseline and changes nothing else.

Once delivered work enters the comparison, the best average rank in both the five-arm and the four-arm test belongs to an arm that performs no search, and the arm ranked second performs no migrations. These omnibus tests run over eight blocks formed by two fleets crossed with four monotone load levels rather than over independent draws from a population of problems, and eight blocks is below the ten Derrac et al. [23] recommend, so the critical difference is correspondingly wide and the tests corroborate the per-cell comparisons of Section 6.1 rather than carrying the argument on their own. 6.6 Migration without consolidation, and an energy measure that concealed it The artificial bee colony arm migrates continuously and consolidates nothing, which makes it the clearest case in the matrix of a policy whose behaviour and whose reported saving come apart. Its mean active-host count is 19.98 in every cell, identical to the baseline, because the class holds every host powered. Measured on the tick integral its saving against the baseline runs from −0.35% to +2.55%, which is what a policy that never empties a host should achieve. The behaviour shows as migration churn in three measurements that agree. Delivered work falls to between 85.6% and 98.4%, while migration intensity is highest exactly where the saving is smallest, reaching 7.67 migrations per virtual machine at homogeneous Scenario 1. Time spent above the 80% utilisation threshold rises above the baseline’s, at 11,125 against 8,315 host-seconds at homogeneous Scenario 4, so a lower mean 17

Baseline

PackOnly

ACO

PSO

MGA

ABC

Total host energy (MJ)

30

20

10

0 S1

S2

S3

S4

S1

Homogeneous fleet

S2

S3

S4

Heterogeneous fleet

Fig. S1. Absolute total host energy by arm, host fleet and load regime, on the tick integral of Eq. (2). The same measurements underlie the percentage decompositions of Figs. 4 and 6, and are given here so that the percentages can be read against the quantities they are taken from. Energy rises with load for every arm and spans 4.77 to 31.02 MJ across the matrix. The spreading baseline sits between 24.49 and 31.02 MJ and varies least with load, because it holds 19.98 of 20 hosts powered in every cell. The control spans 4.77 to 30.43 MJ, the width of that range being the placement effect expressed in joules rather than percentage points. ABC tracks the baseline in all eight cells, within 0.6 MJ, which is the absolute form of the result reported in Section 6.6. Bars are means over ten replications for the stochastic arms and single deterministic runs for the baseline and the control; error bars are 95% t intervals and are drawn only where dispersion exists. The simulated horizon is common to every run, 4105.3–4106.2 s across all 272 runs, so these totals are accumulated over the same interval and are directly comparable.

utilisation combined with more time above threshold marks work being moved rather than concentrated. Producing that pattern occupies up to 1618 s of search per run. The same arm supplies a direct demonstration of why the energy measure in Section 3.2 was chosen. Evaluating host power once at each host’s mean sampled utilisation, rather than integrating it over the run, credits this arm with savings of 1.1% to 24.1% against the baseline. That estimator reports a quarter of the fleet’s energy saved by a policy that holds all twenty hosts powered for the whole run, and it does so because continuous migration depresses the sampled mean utilisation of hosts that remain active throughout, which places the saving in the measurement rather than in the policy. This arm carries one to three replications per cell, so the observations reported for it are structural properties of its behaviour rather than distributional estimates. 6.7 Validation against corrected utilisation thresholds The threshold scale described in Section 4.5 raises a question the decomposition cannot answer on its own, namely whether the search effects reported above are properties of migration search or of a classification step that never fires. A separate arm settles it. The two policies that consult the service-level thresholds, ant colony and particle swarm optimisation, were re-run with those thresholds expressed on the same scale as the utilisation they are compared against, ten seeds per cell, at the two light-load cells and at the heaviest heterogeneous cell. The original behaviour is retained as the default and reproduces the published runs bit-identically, so the two sets of figures are directly comparable. Expressing the thresholds on the corrected scale moves the search effect further from zero rather than closer to it, so the decomposition reported above is conservative with respect to this design choice. In the three cells that continue to deliver the full workload, ant colony falls from −0.12 to −49.27 percentage points at 18

homogeneous Scenario 1 and from +3.22 to −37.76 at heterogeneous Scenario 1, while particle swarm falls to −81.40 at homogeneous Scenario 1, a figure equal to the placement effect in that cell and therefore one that returns the fleet to baseline energy exactly. The mechanism is visible in the classification: under the original scale every active host counted as under-utilised at every interval, so the searches drained hosts continuously and reached three to six active hosts, whereas a host on the corrected scale ceases to be a drain candidate once it passes 20 per cent utilisation and consolidation stalls above thirteen. The three remaining cells deliver between 0.4 and 5.1 per cent of their workload under the corrected scale, so the comparison there rests on the three work-conserving cells reported above.

7. Discussion 7.1 Principal findings The packing rule accounts for the whole of the measured consolidation saving. Against the spreading baseline it delivers between 0.82% and 81.40% of baseline energy across the eight cells, obtained with zero migrations and every submitted cloudlet completed. The amount available is set by load: under light load the rule captures most of what consolidation can reach, and at the heaviest load tested the fleet admits almost no consolidation and the rule captures almost nothing. Enabling migration search above that placement moves energy in both directions, and more often upward. Across the 24 controlled comparisons it increases energy in eleven cells, leaves it unchanged in seven and reduces it in six, with ten increases and five reductions significant after Holm correction. The search effect lies statistically within ±2 percentage points of zero in nine of the 24, though seven of those nine are structural identities rather than equivalences established against dispersion. Normalising by delivered work removes five of the six reductions. Those five coincide with between 1.5% and 18.1% of the workload left unfinished, and they reverse at γ between 0.356 and 0.834, each erased by a charge for undelivered work weaker than full. The one reduction that holds under every correction applied is ant colony optimisation under light heterogeneous load, at 3.22 percentage points with 99.65% of work delivered. 7.2 The capacity floor and unfinished work as mechanisms The findings above raise two questions: why a search operating on an already-packed fleet so seldom improves on it, and why five of the six reductions disappear once delivered work is taken into account. The first is answered by how close the packing rule comes to the fleet’s capacity limit, and the second by how a powered host accumulates energy whether or not its work completes. Energy in this model is governed largely by the number of powered hosts, and the packing rule drives that number close to the lowest value the resources permit. It reaches the processor-derived floor exactly in three of the four homogeneous regimes, at 3.01, 7.00 and 13.99 hosts against floors of 3, 7 and 14. A placement already on the floor offers a search no better arrangement to find, so the search can only move work between hosts whose number is already minimal. In the heterogeneous fleet the same rule settles two to four hosts above the floor, because it ranks candidate hosts by their number of free processing elements and takes no account of how fast those elements run. That gap is where the one positive effect that holds under normalisation occurs, and its size, 4.8% of the placement effect in that cell, is of the order of the gap available to it. Energy accumulates on a powered host whether or not the cloudlets assigned to it complete, which is the

19

second mechanism. A policy that leaves work unfinished therefore records a lower mean utilisation and a lower energy without having improved the allocation, and this accounts both for the five reductions that reverse under normalisation and for the positive correlation of r = 0.536 between search effect and work lost across the ant colony and particle swarm cells. 7.3 Implications for data centre operation The operational content of these results is that a packing heuristic combined with deactivation of emptied hosts captured, in these experiments, essentially all of the available consolidation energy, while requiring no search, completing all submitted work and performing no migrations. Both components are configuration choices available in existing allocators rather than research outputs, which places the saving within reach of an operator specifying a platform rather than only of one running an optimisation study. The cost of obtaining those outcomes supports the same reading. Mean search time per run ranges from 0.4 s for the modified genetic algorithm on the heterogeneous fleet under light load to 202 s for ant colony optimisation on the heterogeneous fleet under heavy load, and reaches 1618 s for artificial bee colony, to arrive at outcomes that in aggregate matched what the control achieved without searching. Individual runs range more widely still, the longest search occupying 1126 s. Where search did reduce energy without reducing delivered work, the margin was 3.22 percentage points in one cell of eight. Section 1 described a build-out in which 5.9 GW of contracted demand stands against 405 MW drawn, most of it still at the design stage, which is the window in which a placement-policy result can be acted on. The consolidation energy available in these experiments comes from a packing heuristic and a host-deactivation policy, both configuration decisions, so the lever is available at the point where a platform is specified rather than only where an optimisation study is run. Existing guidance addresses the facility layer, with the National Investment Council recommending a power usage effectiveness at or below 1.4 for hyperscale projects [4]. A criterion at the information technology layer, requiring host deactivation and a packing rather than spreading admission policy, would address a lever that these simulations show to be strongly load-dependent and, under light load, large. Measurement on production fleets would establish what it is worth at deployment scale. 7.4 Implications for comparative evaluation A consolidation result obtained by comparing a metaheuristic against a spreading or first-fit policy, with no matched initial-placement control, measures the joint effect of the placement change and the search. It identifies the contribution of the search only where the two arms share an admission rule, and in the implementations examined here that contribution was negative more often than positive. The three operating characteristics reported in Section 4.5 bear on the same point. A policy whose thresholds are evaluated against values on a different scale, a policy that searches once and returns an empty plan thereafter, and a policy that holds every host powered would each be visible immediately against a matched control, and each records a plausible saving against a spreading baseline alone. Four reporting elements follow for comparative placement studies: a matched initial-placement control arm, delivered work reported alongside energy, the simulated horizon, and the search budget actually consumed. Each is available from instrumentation that a simulation study already produces, and together they cost one additional arm and three additional recorded quantities.

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7.5 Extensions The decomposition reported here was carried out under one set of conditions, and the same design extends past them in three directions. The fleet in these experiments is twenty hosts, and repeating the decomposition at rack and multi-rack scale would establish whether the placement and search components hold their relative sizes once network topology, thermal coupling and failure domains begin to bear on allocation. The stochastic arms carry ten replications, set by the computation available; thirty would narrow the intervals reported here and bring the non-parametric tests within reach of a plain Bonferroni threshold. Energy is accounted at the server, and incorporating cooling and distribution as further parameters would express the saving on a facility rather than an information technology basis, a difference of 54% per joule at a power usage effectiveness of 1.54.

8. Conclusion This study separated the energy saving obtained by admission-time VM packing and host deactivation from the additional effect of migration search. In CloudSim Plus, a matched control retained the reproduced policies’ own placement and host-deactivation behaviour while disabling search. Across two fleet configurations and four load regimes, with workload completion recorded in all 272 runs, this design identified which savings persisted when placement and delivered work were accounted for. Packing and host deactivation reduced energy by 0.8–81.4% relative to the spreading baseline, without migrations and with every submitted cloudlet completed, the saving available falling sharply as load rises. Adding migration search changed the saving by −71.6 to +11.8 percentage points of baseline energy: energy increased in eleven of the 24 comparisons, remained identical in seven, and decreased in six. Five of the six reductions coincided with unfinished work and reversed after normalisation by delivered computational work. Only ACO under light heterogeneous load retained an advantage: 3.22 percentage points in raw energy (95% confidence interval 2.96–3.47), or 3.11 points after full work normalisation (95% confidence interval 2.82–3.41), with 99.65% of work delivered. The active-host measurements help explain these outcomes. Packing reached the processor-derived host-count floor in three homogeneous regimes, leaving little scope for further consolidation; the surviving ACO benefit partly closed a gap above that floor in the heterogeneous fleet. The ABC arm illustrated the complementary risk: it kept the same number of hosts active as the baseline and left work unfinished, and under an energy estimator based on mean sampled utilisation it would have been credited with savings of up to 24.1%. These findings concern the implementations and configuration examined, whose threshold handling and search invocation behaviour materially shaped the results. They establish the need to isolate search contributions rather than a general absence of value in metaheuristic consolidation. The practical finding is that packing and host deactivation captured the dominant energy saving in these experiments without search or lost work. The methodological implication is equally direct: comparative consolidation studies should include the proposed policy’s own placement with search disabled and report delivered work alongside energy, together with the simulated horizon and actual search effort. These additions make the incremental contribution of search visible and prevent reduced workload delivery from being credited as improved energy efficiency.

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CRediT authorship contribution statement Aun Yichiet: Conceptualization, Methodology, Formal analysis, Writing – original draft, Writing – review & editing, Supervision, Project administration. Woo Yu Hang: Software, Investigation, Data curation, Validation, Writing – review & editing.

Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability The simulation source, configuration, seeds, per-run records, workload fingerprints and the scripts that regenerate every table and figure are deposited at Zenodo under doi:10.5281/zenodo.23632346 [21], released under CC BY 4.0.

Declaration of generative AI and AI-assisted technologies in the manuscript preparation process During the preparation of this work, the authors used Claude (Anthropic) in order to draft and edit the text of the manuscript. The tool was used under continuous author supervision, sentence by sentence, for language, structure and exposition. No generative AI tool was used in the design of the experiments, the configuration or execution of the simulations, the generation or analysis of the results, or the derivation of the conclusions reported here; all simulation runs, data and findings are the authors’ own. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of the published article.

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