Nature/bio inspired methods

The Salp Swarm Algorithm and the sine-cosine algorithm were combined to create a hybrid multiobjective VM placement technique [6]. The proposed technique aimed to reduce the mean time before host shutdown (MTBHS), the number of SLA violations and power consumption. The proposed method was compared to several meta-heuristics, and the findings showed that it was superior. When discussing VMs and PMs, the bandwidth has not been fully considered. Furthermore, the balanced use of multidimensional resources in physical hosts remains uncertain.

A bandwidth-aware VMP algorithm, developed on the enhanced Whale Optimisation Algorithm (WOA) and a novel bandwidth allocation methodology, was proposed in [7]. The outcomes reveal that the suggested method outperforms several meta-heuristics and heuristics. I suggested approach focuses solely on bandwidth optimisation, neglecting to consider other critical resources like memory and CPU use. Also, the study did not focus on the problem of optimising power consumption.

The authors in [8] proposed an energy-aware VM placement technique using Binary Particle Swarm Optimisation (BPSO) algorithm. The work is based on the modification of local optimum placement and global optimal placement, to get optimal VM placement with the lowest energy usage.

To minimise energy consumption and fulfil uers’ experience, an enhanced ant colony algorithm is used to propose an energy-saving VMP approach which attains a balance between user experience and energy consumption in data centres [9]. The original ant colony algorithm’s pheromone and heuristic parameters were modified, ensuring that the improved algorithm may transition from a local to a globally optimal solution, avoiding the algorithm’s early maturity. Dolphin Partner Optimisation along with optimised security for resource allocation, has been presented in [10]. Memory-aware Optimisation and Energy-based Prioritisation are utilised to pick memory and energy-established VMs for safety, and this work has also incorporated hypervisor safety into the two groups of VMs acquired. The Dolphin Partner Optimisation then enhances the two sets of virtual machines to provide the best capable VM for each set. Finally, streamlining security is applied to boost security, and the chosen virtual machine is essentially the most secure.

Authors in [11] proposed a research model that uses VM consolidation to minimise data centre power consumption while maintaining stable operation. An adaptive harmony search approach is created to achieve the best solution for the suggested VM consolidation model, which requires less effort to establish the model’s parameters than current harmony search methods.

The authors in [12] presented an energy-efficient container placement using the WOA technique. Two stages of placement, that is placing containers on suitable VMs and mapping VMs to suitable PMs are solved as one optimisation problem. The proposed method is evaluated in a heterogeneous environment and results show, it minimises the power consumption, reduces the number of PMs used and maximises the resource utilisation but increases the number of migration increasing the cost.

Authors [13] developed a hybrid approach using PSO and Flower Pollination Optimisation techniques to reduce power consumption, placement time, and resource wastage and increase server utilisation. Placements of the virtual machines onto physical machines are accomplished based on the fitness values derived from the above objectives.

Adlin Sheeba et al. proposed a VM placement technique using the Firefly Optimisation Technique [14]. In this work, the authors used the K-Means clustering technique to minimise the migration time of VMs. An enhanced Firefly Optimisation Algorithm was used to design the VMP model. To decide the optimal cluster for VMP, a combination of PSO and coyote algorithm was used.

In [15], the authors proposed a Water Wave Optimisation technique to handle virtual machine consolidation problems in the cloud. The proposed method is employed to find the proper migration plan to minimise the load on the overloaded hosts and maximise resource utilisation. In [16], a Flower Pollination-Based Nondominated Sorting Optimisation (FP-NSO) algorithm is presented to handle VM placement to minimise energy consumption and maximise resource utilisation. The method that aids in identifying the most suitable PMs for deploying VMs in a cloud environment is linked to many resource-constraint parameters.

In a recent work [17], the author has proposed a modified ant colony-based load balancing algorithm for cloud resource optimisation to improve makespan and resource utilisation in the cloud. Similar work using self-adaptive PSO (Particle Swarm Optimisation) [18] is proposed to improve cost using a combination of machine learning to predict the cost model and PSO for finding the best resource over the cloud. The work aims to improve the cost of the resources and execution time. In [19], a resource allocation algorithm is proposed using The Flower Pollination Algorithm to improve power efficiency as compared to a genetic algorithm in the cloud. This work also tried to reduce the number of migrations to improve resource utilisation (CPU and RAM utilisation). From the nature-inspired algorithms, the krill herd model has been proposed to improve SLA violation and energy efficiency in the cloud [20]. The work shows an improvement in SLA and power efficiency as compared to the genetic algorithm and the MBFD (Modified Best Fit Decreasing) algorithm. Authors in [21] proposed a hybrid approach for multi objective virtual machine placement in cloud. Ant lion optimization and sine cosine algorithm were used to optimally place VMs over suitable physical machines. Performance metrics like power consumption, resource wastage, reosuce utilization, number of active PMs, VM migrations and SLA were considered.

In [22], authors presented a Variable Neighborhood Search-Based Symbiotic Organisms Search Algorithm to enhance energy efficiency in cloud. Authors aimed to minimize energy consumption and maximize resource utilization. A minimum of active hosts and the energy-saving turnoff of inactive servers allowed for the best VM allocation. Esha Barlaskar et al., [23] proposed an enhanced cuckko search algorithm to obtain optimal solution for virtual machine placement in cloud. This work aims to reduce energy consumption, VM migrations and SLA violation. Hetergeonous hosts were used for experimentation work. In [24] authors has proposed an nature inspired squirel search optimization algorithm for resource scheduling is cloud. the work is compared with genetic algorithm, PSO and ACO using energy, cost and SLA as performance parametrs. In [25] a clonal optimization model is proposed for resource allocation for cloud infrastructure to improve power efficiency in cloud. In recent years many other work are been proposed using nature inspired algorithms like work inspired from BAT algorithm [26], jelly fish [27], wild horse [28], FOX inspired model [29], Elephant herd [30], Whale Optimization Algorithm (WOA) [31], Ant Lion [32], Butterfly Optimization Algorithm (BOA) [33] and Gray Wolf Optimization (GWO) [34].

Metaheuristic approaches

A VM allocation policy has been proposed that assigns VMs to hosts proportionally based on their RAM and CPU use. It employs the idea of skewness to assess the unevenness in host resource utilisation and assigns VMs to the host machine with the lowest skew value [35].

In [36], a combination of a mixed integer linear program and a heuristic approach was proposed for virtual machine placements in edge-cloud computing. The objective is to meet the varied latency requirements of applications while minimising the consumption of IT infrastructures for the placement of VMs in cooperative edge-cloud computing. To defend against co-location assaults in IaaS (Infrastructure As A Service) cloud providers, the authors in [37] presented a VM allocation strategy which considers 3 different types of incoming virtual machines. The proposed algorithm focuses on the secure placement of VMs over physical machines. This work aims to minimise energy consumption.

In [38], the authors presented an open-source development model algorithm to address dynamic virtual machines’ placement in the cloud. ODMA(Open Source Development Model Algorithm) is one of the meta-heuristic approaches that is used in this work to consolidate several VMs into a reduced number of hosts. The objectives of this work are to minimise the number of active hosts, achieve load balancing and improve performance. In [39], the author has proposed a multi-agent-based resource optimisation algorithm is proposed which aims to solve the optimisation problem using parallel scheduling and a multi-agent system. The work proposes a mathematical model to find an optimal solution in parallel resources. Canosa-Reyes et al., [40] proposed energy tradeoff consolidation with contention-aware resource provisioning, here authors used containers to optimally place the jobs. Cloudsim was used for experimention purpose. The proposed method reduces resource contention and makes job placement more efficient with the energy-utilization tradeoff.

Machine learning technquies

Ashawa et al. proposed the LSTM technique for load balancing to enhance cloud efficiency via resource allocation [41]. LSTM provided a dynamic resource allocation mechanism that evaluates the resource usage of an application using heuristics to determine the optimal additional resources to make available for that application. Based on the result, the proposed model shows the accuracy rate is enhanced by approximately 10–15%.

Ali Aghasi et al. employed the Q Learning technique to address virtual machine placement [42]. Reinforcement learning along with state action representation is utilised. The objectives of this work were to minimise energy consumption and reduce CPU temperature. In this generation of machine learning, various hybrid approaches have been proposed using machine learning and deep learning, like the Double Deep Q-network to improve network performance in cloud radio access networks [43]. This work [43] aims to improve performance by managing and optimising the load on network paths using Q-Network approaches. The result showcases an improvement in power consumption (Kwh) and network delay. Another work using deep learning was proposed in [44] to optimise energy efficiency and resource optimisation. This model tries to predict the best resource of a VM based on the prior performance in terms of CPU utilisation and power consumption. The work uses a deep reinforcement learning model for training and model prediction. The proposed model is compared with a greedy algorithm using power consumption and average waiting time as performance parameters.

Work has also been carried out in job scheduling. For example, Ibrahim Attiya et al. presented a hybrid job scheduling approach in cloud computing using a modified Harris Hawk Optimisation and simulated annealing algorithm [45]. This work aims to minimise the makespan and improve the convergence speed. Both standard and synthetic workloads were employed to analyze the performance of the this work.

Authors in [46] proposed a multi-objective task scheduling technique, based on Gaussian Cloud Whale Optimisation Algorithm (GCWOAS2) in cloud computing. A three-layer scheduling model was presented in this work. The goal is to reduce the operating cost of the system by minimising task completion time by effectively utilising virtual machine resources and maintaining the load balancing of each virtual machine. To develop the best scheduling scheme in the GCWOAS2 approach, an opposition-based learning mechanism is initially employed to establish the scheduling strategy. Then, to dynamically widen the search range, an adaptive mobility factor is provided. To improve the unpredictability of the search, a Whale Optimisation technique based on the Gaussian cloud model is presented.

To summarise, prior research shows that the meta-heuristic approaches listed above can identify an appropriate solution for VM scheduling in cloud computing. However, experiments were carried out using randomly generated data in some works and most of the work focused on two to three objectives without taking into account load balancing, SLA violation and execution time concurrently. The proposed work in this article focuses on multi-objective VM placement along with load balancing which was not addressed in the existing approaches.

Motivation

The motivation of this work is to develop a new meta-heuristic algorithm to achieve better performance in the field of cloud computing. Where existing work as shown in the literature work uses traditional algorithms, this work proposes the Harris Hawk Optimisation (HHO) model to improve the performance of the cloud environment in terms of power consumption and utilisation of the system. The existing models are being compared with our proposed model to study the performance.

Problem formulation

The cloud data centre in this work consists of N VM and K PMs. The resource requirements of VMs are CPU and RAM. The requirements of CPU and memory of VM_i are represented as . and respectively. The CPU and memory capacity of PMj are represented as and respectively. Table 2 depicts the terminologies used in this work.

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Table 2. Key terminologies.

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Each PM has enough capacity in this cloud data centre to allocate a set of VMs. Let r = (r_pm,pm ∈ PM) denote the VM placement approach satisfying the resource allocation policy is feasible i.e. resources allocated to every VM are fewer than the overall capacity of the PM as represented in Eq 1.

(1)

Where W_pm represents the se’ver’s willingness to offer resources or performance weight. Considering the proposed VMP method, let γ_pm be the fairness among the association of PMs. Once γ_pm = 1, the utility function of the pm is represented as UT_pm(r_pm(t)) = W_pmlog r_pm(t). Next, maximising the cumulative utilities of all PMs in the data centre is expressed as: (2)

Virtual machine placement problem statement

Let L_vp(t) symbolise the load of VM i which is hosted on physical machine pm and L_pm(t) denote the aggregate load of PM, the following condition (3) must be satisfied: (3)

Here L_vp(t) is the VM’s load requirements as the d dimensional vector, where d = 2 when CPU and memory are considered, L(t) is given by (4)

Further, Capacity_pm is defined as the available server capacity on PM j ∈ PM regarding its CPU and RAM. The following formula must hold true to confirm that the overall load on any PM is not more than its capacity.

(5)

Typically, optimal placement of virtual machines on servers and turning off other servers leads to maximisation of utilisation and minimising server power consumption. To reflect this, in our analysis, the following equation is utilized: (6)

Subject to (7) (8)

Based on the constraints below, a single PM can host a set of VMs: (9) (10)

The above equation ensures that the total resources used by a group of VMs should not surpass the CPU and memory capacities of PM.

When only CPU and RAM are considered, the PM resource utilisation problem (Y₁) will be equivalent to: (11)

Subject to (12) (13)

To facilitate the subsequent derivation of the formula, let r_pm(t) = L_pm(t) To maximise the data ce’tre’s’ overall aggregate utilities and find the best solution, a Lagrange function is defined as: (14)

Where γ = (γ_pm, pm ∈ PM) and β = (β_pm, pm ∈ PM) are Lagrange multiplier vectors,

is the relaxation factor vector. Let γ_vm denote the load requirement of the virtual machine vm. Let β_pm be the available capacity of the physical machine pm. Let the resource occupied by all VMs on physical machine pm be expressed as and represents the enduring resources present on the physical machine pm.

According to Eq (7), we obtain: (15)

Where represents the occupied resource of physical machine pm. To increase the PM utilisation and minimise server energy consumption, optimal packing is performed to place virtual machines then can be considered as the gains of PM from packing.

To save energy any PMs that are not’ in use should be turned off. The power consumption of active PMs is formulated as follows: (16) where P_idle is the idle-state power of PM_j , P_Max is the maximum power of PM_j , and P_cpuj is the percentage value ∈ [0, 1] that denotes the CPU utilisation.

Harris Hawk Optimisation for virtual machine placement

Heidari and Mirjalili et al. developed the Harris Hawks Optimisation Technique (HHO), a novel optimisation algorithm [47]. The algorithm mimics the natural behaviour and hunting strategy of Harris Hawks known as surprise pounce. The hawks collaborate to attack from many directions to startle the victim. Harris Hawks reveal a variety of pursuit methods dependent on the nature of the schemes and the victim’s’ evasive patterns. Exploration and exploitation tactics are proposed by the conventional HHO algorithm which is driven by exploring prey, surprise pounce, and Harris Haw’s’ particular attacking approach. The Harris Hawks are the candidate solutions and the targeted prey in each phase is the best candidate solution (nearly the optimal one). The exploration phase, transition from exploration to exploitation phase, and exploitation phase are the three phases of the HHO algorithm and are described below.

i) Exploration phase.

All Harris Hawks are considered solutions during this phase denoted as a solution matrix H; is a 2 × N matrix, where N is the number of VMs. Fig 2 depicts 4 feasible solutions where four hawk agents’ solutions assign 5 VMs to 3 PMs. The four solutions are represented by the set H = H₁, H₂, H₃, and H₄. According to the number of VMs, all solutions are reviewed and ranked in ascending order of PMs that are utilised in this solution [12]. The order of sorting is H₃, H₁, H₄, and H₂. The best solution is H3 because it has the minimum number of PMs, which consumes less power.

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Fig 2. Example of four feasible applicable solutions.

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The solution matrix of a single hawk H is defined in Eq 17. If there are N VMs to be allocated to J PMs, the value of the component of H of the matrix represents the PM index to host the VM number n.

(17)

The corresponding variable is the value j, ∀ j ∈ [1, J], if the virtual machine VM_i is assigned to PM_j ∈ PM. Variable denotes the virtual machine VM_i ∈ VM.

The fitness value is determined for all these feasible solutions created on the desired prey in each iteration. To replicate Harris Hawk’s’ exploring abilities in the search space chosen and updating the solution matrix is according to two techniques as specified in Eq 18.

(18)

Where H(t + 1) is the hawk’s candidate solution/position in the second iteration t, H_ρ(t) represents the best solution matrix/prey position and H_rand(t) is the random solution selected in the present population.H(t) represents the position vector of hawks in the present iteration t. r₁, r₂, r₃, r₄ and p are the random scaled factor within the range [0,1]. UB and LB are the upper bound and lower bounds of the variables, H_s(t) denotes the average number of solutions. The index of the first row is updated according to the hawk agent solutions of the best and random solution as per Eq 18.

Hawk placements are generated because of this method inside UB and LB depending on 2 rules 1) Build solutions using a randomly chosen hawk from the present population as well as other hawks. 2) Construct solutions depending on the location of the prey, the average hawk position, and random scaled variables. While r3 is a scaling factor, if the value of r4 approaches 1 it will aid in increasing the rule’s’ unpredictability. An arbitrarily scaled measure length is added to LB in this rule. More diversification strategies to investigate other sections of the feature space are examined using a random scaled component. The average hawk position (solutions) is formulated as follows: (19)

Where, H_s(t) is the current iteration’s’ average number of solutions. M denotes all possible solutions. H_i(t) indicates the location of every solution in iteration t.

The updated indexes in the hawk solutions should be in the range of [1,J]. If the updated index is outside of the range then the algorithm recalculates it as follows: (20)

ii) The transition from exploration to exploitation.

Based on the energy of the prey, this phase shows how HHO moves from exploration to exploitation. HHO posits that the energy of the prey is gradually depleted as a result of the fleeing activities. R₀ is the initial energy range between [–1,1] as expressed in Eq 21.

(21)

Where t is the current iteration and T represents the maximum number of iterations.

iii) Exploitation phase.

The exploitation phase is marked completed by utilising 4 methods/ways at parameter sets. These methods are created on the position that was discovered during the exploration phase. The prey, on the other hand, tries to flee often despite the hawk’s ‘efforts to track it down and trap it. HHO exploitation uses four different techniques to imitate the hawks’ attacking style. Hard besiege, Soft besiege, soft besiege with progressive rapid dives, and hard besiege with progressive rapid dives are the four methods. These methods depend on 2 factors r and |R|. Where R represents the prey” fleeing energy and r is the likelihood of escaping with r < 0.5 indicating a better chance of the prey escaping successfully and r ≥ 0.5 indicating an unsuccessful escape. The following is a summary of these approaches:

In the soft besiege approach, where r ≥ 0.5 and |R| ≥ 0.5, while the hawks gently round on the victim causing it to lose extra energy before completing the surprise pounce the prey still has some energy to flee. Soft besiege is mathematically formulated in Eq 22.

(22)

Where ΔH(t) is the difference between the prey” position vector and the current location in iteration t, J is the ‘ prey” jump strength, and r₅ is a random variable.

In the hard besiege, where r ≥ 0.5 and |R| < 0.5, the prey is exhausted and has a slight chance of escaping. In this situation, the hawk barely encompasses the target before launching the ultimate surprise pounce. Accordingly, the solution is updated using Eq 23.

(23)

In soft besiege with progressive rapid dives method with r < 0.5 and |R| ≥ 0.5, the prey has enough energy to flee. The hawk manoeuvres deftly around the victim and descends tolerantly before the attack. This is referred to as a clever soft besiege, in which the hawk’s ‘location is updated in two phases. In t^he 1^st stage, the hawks approach the prey by calculating the prey” next move as in Eq 24.

(24)

C represents the jump power of prey. The hawk then determines whether to dive in the second stage depending on a comparison of the prior dive and the likely outcome. If it is not,’ the hawks will produce an uneven dive based on the Levy Flight (LF) notion as expressed in (25) (25)

Where d is the dimension of solutions, Q is the random vector of size 1*d. LF is the Levy Flight function designed using Eq 26 (26)

Where β is the default constant and y, z are the random variables between [0, 1]. As a result, a method for updating the Harris Hawk’s ‘locations with advanced quick dives may be devised as (27)

Here, K and L are performed using Eqs 24 and 25.

In the last approach, hard besiege with progressive rapid dives where r < 0.5 and |R| < 0.5, the prey has no energy to flee, therefore the Harris Hawks try to approach the prey by diving quickly before making a surprise pounce to grab it. The hawk movement’ in the situation is stated in Eq 27

Where K and L are as follows (28) (29)

The parameters used in this work are presented in Table 3.

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Table 3. Parameters of HHO.

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Objective function.

After the hawk agents’ solutions have been updated the solutions are evaluated to choose the best one H_ρ. Only one HW (Hawk) solution is chosen as the best where HW denotes the number of hawk agents. The algorithm compares the solutions based on criteria e₁ in Eq 30, this shows the amount of energy consumed by this solution. The best solution is the H_ρ solution with the least power consumption and the fewest number of PMs used [12]. The objective function is formulated as: (30)

Pseudocode 1: Harris Hawk Optimisation

Input: Set of virtual machines N and physical machines J

Output: 2 × N allotment matrix mapping N virtual machines to J physical machines as H_ρ

1. Initialisation: HW: = 50, ItrE: = 100, it: = 0, LB: = 1, UB: = 800
2. while it<ItrE do
3.  Produce HW × 2 × N hawk solution matrices
4.  Assess the solutions and assign the best solution using the best solution: = H_ρ
5.  initialise a: = 1 for each iteration of the search
6.  if the solution ≠ H_ρ then
7.   Update the present solution Ha using Eq (18)
8.  if the number of hawks a < HW then
9.   set a: = a+1 and go to step 6
10.  Assess the fitness of the HW solutions using Eq 30 and assign the best solution to H_ρ
11. Return 2 × N allotment matrix H_ρ the best solution.

The pseudocode of HHO is depicted in Pseudocode 1 and the workflow process of the HHO is represented in Fig 3. The hawk agents start with randomly distributed indexes and then analyze their solution to determine the best H_ρ . The hawk agents then update their solutions based on the best option that has been chosen thus far. The optimal solution is then presented as matrix indices which map the VMs to the minimum number of PMs at the end of each iteration. The HHO algorithm has the advantages of simple operation, fewer adjustment parameters, ease of implementation and use of communication between hawks to improve the global search capability. But for higher dimensional problems it may have low converge performance.

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Fig 3. Workflow process of HHO algorithm.

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Load balancing

To perform the load balancing in the data centre, host overload and host underload detection mechanisms are incorporated.

Complexity analysis of the proposed method

In further discussion V and P denote the number of VMs and PMs respectively. Each iteration consists of two steps. The first step is to update the solution. The first step includes applying Eq 19 to each column of all solution matrices. As a result of modifying the VM’s resource utilisation the PM’s CPU and RAM utilisation may rise or decrease. Thus, the time complexity of this step is O(V).

Second, to balance the load across the data centre, overloaded PMs are collected as discussed in the load balancing section. In the worst case when the PM is overloaded, selected VMs are migrated to other PMs. If the underloaded PM is found the PM is switched to sleep mode by migrating the VMs to some other PM. The time complexity of this task is O(V × P). The PM’s CPU and RAM usage increases and decreases with each VM migration from one PM to another according to Eq 30. Thus, the fitness function can be computed by summing up the power consumption of each PM in the time complexity of O(P).

So, the worst-case total time complexity of the 2 steps and the fitness computation of each iteration is O(V + (V × P) + P) . As algorithm 1 has ItrE iterations, the worst time complexity is O(HW × ItrE × V × P) for HW hawks.

Experimental setup

To test the proposed method we used the CloudSim 3.0 toolkit simulator. Cloudsim offers a variety of virtual machine provisioning methodologies and Virtualised resources. We used real workload traces from PlanetLab to conduct the experiment. PlanetLab is a component of the CoMon project, which collects CPU utilisation from over 1000 virtual computers running on various hosts in over 500 locations across the world. We employed four distinct types of virtual computers in our test setup: Micro, Small, Medium, and Extra-Large instances. A total of 600 HP ProLiant G4 and HP ProLiant G5 heterogeneous hosts have been deployed. Table 4 lists the characteristics of these servers.

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Table 4. Characteristics of servers.

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Performance natrix and results

To assess the proposed approach against other algorithms the workloads depicted in Table 5 were used. It shows the workload number and the number of VMs in each of the workloads. Each of the workload files contains CPU utilisation values measured every 5 minutes in PlanetLab’s VMs [49]. These trace files contain traces of CoDeeN, the Coral Content Distribution Network, and Open DHT. The experiment was carried out using the workloads specified and the average result of these workloads was used to evaluate different algorithms based on the five metrics described below.

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Table 5. Traces of workload from PlanetLab.

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Experiments were carried out in two scenarios. Firstly, simulation is carried out using the workloads specified and the average result of these workloads is used to evaluate different algorithms based on the metrics under various workloads and task utilisation. For the second scenario, the performance of the proposed algorithm is done with scaling resources to study the performance in underloaded and overloaded conditions.

a) Energy consumption.

Energy Consumption represents the total amount of energy/power consumed by all the data centre’s PMs. Fig 4 depicts the energy consumption of the algorithms using scenario 1. As the instance size grows, the power consumption gradually increases. The result shows that HHO decreases average power consumption by 9% and 27% compared to PSO (Particle Swarm Optimisation) and PABFD (Best Fit Decreasing) respectively. Fig 5 shows the study with scaling resources using scenario 2 where the proposed algorithm shows the least energy consumption. The simulation is supported by two machines HP ProLiant ML110 G4 (Intel Xeon 3,040, 2 cores, 1,860 MHz, 4 GB) and HP ProLiant ML110 G5 (Intel Xeon 3,075, (2 cores, 2,660 MHz, 4 GB) [49] as defined in Cloudsim3.0. Table 6 shows the power consumption by a machine under different utilisation levels.

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Fig 4. Energy consumption of data centre using different techniques using Scenario 1.

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Fig 5. Energy consumption of data centre using different algorithms using Scenario 2.

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Table 6. Energy and utilisation of machine power model.

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b) Resource utilisation.

Figs 6 and 7 shows the resource utilisation of CPU and memory for the PMs to host VMs using scenario 1. It is observed from the result that the average CPU utilisation of HHO is higher by 3% and 12% compared to PSO and PABFD respectively. Similarly, the memory utilisation of HHO is 4% and 17% higher than PSO and PABFD. Figs 8 and 9 shows the performance study of CPU and RAM utilisation with increasing virtual machines using scenario 2, where the proposed algorithm improves the CPU and RAM utilisation as compared to existing models.

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Fig 6. CPU utilisation in the heterogeneous environment using Scenario 1.

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Fig 7. RAM utilisation in the heterogeneous environment using Scenario 1.

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Fig 8. CPU utilisation using Scenario 2.

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Fig 9. RAM utilisation using Scenario 2.

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c) Number of VM migrations.

The number of VM migrations is another evaluation metric. As the number of requests increases, some of the PMs get overloaded, to balance the load across PMs some of the virtual machines are selected and migrated to other physical machines of the data centre as discussed in the load balancing section. According to Fig 10, the number of VM migrations in HHO is less compared to other algorithms using scenario 1, since HHO places the VMs on an apt and lesser number of PMs which reduces the chance of migrating VMs between PMs. Fig 11 shows a decrease in the number of VM migrations as compared to existing algorithms using scenario 2.

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Fig 10. Number of VM migrations in the data centre using scenario 1.

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Fig 11. Number of VM migrations in the data centre using scenario 2.

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d) SLA violation.

The average SLA violation of different algorithms using scenario 1 is depicted in Fig 12. As shown. the average SLA violation of the HHO algorithm is less by 8% and 16% compared to PSO and PABFD respectively. Fig 13 shows an improvement in SLA violation with increasing resources as compared to existing algorithms using scenario 2.

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Fig 12. Average SLA violation (%) through different algorithms using scenario 1.

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Fig 13. Average SLA violation (%) through different algorithms using scenario 2.

https://doi.org/10.1371/journal.pone.0289156.g013

e) Execution time- VM reallocation.

Fig 14 shows the mean execution time required for VM reallocation using scenario 1. As shown in the result, the mean reallocation time of HHO is less compared to PSO and PABFD. Since the number of VM migrations is less in HHO, as a result, the mean execution time for VM reallocation is also less. It is observed that HHO execution time is reduced by 3.2% and 4% compared to PSO and PABFD respectively. Fig 15 shows the lower mean reallocation time of HHO using scenario 2.

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Fig 14. VM reallocation mean (sec) using scenario 1.

https://doi.org/10.1371/journal.pone.0289156.g014

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Fig 15. VM reallocation mean (sec) using scenario 2.

https://doi.org/10.1371/journal.pone.0289156.g015