Enhanced Load Balancing Based on Hybrid Artificial Bee Colony Enhanced Load Balancing Based on Hybrid Artificial Bee Colony with Enhanced β -Hill climbing in Cloud with Enhanced -Hill climbing in Cloud

This paper proposes enhanced load balancer based arti ﬁ cial bee colony and b -Hill climbing for improving the performance metrics such as response time, processing cost, and utilization to avoid overloaded or under loaded situations of virtual machines. In this study, the suggested load balancer is called enhanced load balancing based on hybrid arti ﬁ cial bee colony with enhanced b -Hill climbing (ELBABCE b HC) to improve the response time, processing cost and the resource utilization. Our proposed approach starts by ranking the task then the greedy randomized adaptive search procedure (GRASP) is used in initializing populations. Further, the binary arti ﬁ cial bee colony (BABC) enhanced with the modi ﬁ ed b -Hill climbing with the sinusoidal map strategy is applied to schedule tasks considering load balancing in cloud. The proposed approach is implemented in CloudAnalyst. The experimental results show that for different user groups all over the world. The performance of ELBABCE b HC algorithm outperforms round robin (RR), throttled load balancer (TLB), and active monitoring load balancing (AMLB) algorithms considering response time, processing cost and utilization.


Introduction
C loud is a distributed computing system con- sisting of a collection of interconnected data centers consist of high-performance hosts configured to numbers of virtual machines (VMS) on the same physical machine depending on virtualization.which deliver dynamically on-demand resources with different characteristics over the Internet based on quality of services (QoS) metrics and the servicelevel agreement (SLA) established between the service provider and the end-users.The cloud provider can offer three types of services as Infrastructure as a Service (IaaS), Platform as a Service (PaaS), or Software as a Service (SaaS).There are many companies to transfer these services from cloud such as Amazon, Yahoo, Microsoft Google etc. via Internet connection using the resources hardware and Software.The users accept services from the cloud without paying attention to the details by sending user requests and receiving responses through the Internet (Ranjan and Buyya, 2009).
There are various challenges and issues when providing services to the end-users as the load balancing problem.Load balancing mechanism is used for redistributing the workload among the nodes trying to find an efficient mapping for a set of tasks to a set of computing machines so that no single node is overloaded or underloaded (Mell and Grance, 2011;Buyya et al., 2011).
There are mainly two types of load balancing algorithms considering the current state of the system, they are static or dynamic.Round robin (RR), and threshold algorithm (TH) are static load balancing that require prior knowledge about the applications and the resources.Dynamic load balancing algorithms as throttled load balancing algorithm (TA) and active monitoring load balancing algorithm (AMLB) depend on the current state of the system not the previous state (Mishra and Majhi, 2020).
Practically, for solving load balancing, conventional methods may take a long time to find an optimal solution.Researchers are satisfied with the metaheuristics for solving such problems which do not guarantee the optimality but provide acceptable solutions in a reasonable amount of time (Talbi, 2009).
Many classifications criteria may be used for metaheuristics.The most common one are population-based vs single-based.
Single-based metaheuristics include local search as hill climbing, and a greedy randomized adaptive search procedure (GRASP).Population-based metaheuristics include swarm intelligence (SI) optimization techniques which are nature inspired metaheuristics such as artificial bee colony, ant colony, and particle swarm algorithms.These algorithms consist of simple agents trying to solve optimization problems such as load balancing by interacting with each other (Luke and Edition, 2009).
Population-based metaheuristics have the main advantage that they are able to widely scan many search space regions at the same time beginning with a number of random solutions but this may cause premature convergence.To maintain the balance between diversification and intensification over the solution space, population-based algorithms is hybridized with other techniques to overcome such problems (Houssein et al., 2021).
For solving load balancing problems, this paper tackles load balancing problem in cloud using a new hybrid load balancing algorithm called ELBAB-CEbHC.It combines artificial bee colony with an extension of hill climbing called b-Hill climbing algorithm (Al-Betar, 2017) which in turn enhanced by a chaotic sinusoidal sequence strategy (Peitgen et al., 2006) for generating random values.
We summarize in Tables 1 and 2, respectively, the various notations used in defining load balancing problem and the notations used by the proposed ELBABCEbHC algorithm.Our main contributions in this research are:

F
The multiobjective function.

Z
The objective functions number.f 1 ðyÞ; f z ðyÞ The objective functions that are counterdary to each other.

S
The decision space S ¼ fy 1 ; y 2 ; y 3 ; ……y d g: PF * The pareto front.j i The weighted coefficients set.m The virtual machines number.n The tasks number.

VMS
A list of m virtual machines VMS ¼ fvm 1 ; vm 2 ; :vm m g. vm i A virtual machine i has processing speed ðMpÞ measured in Million Instructions per Second ðMIPSÞ per processing element: The task j with the length ðMÞ in million instructions ðMIÞ P e The processors numbers for running a task T j on the virtual machinevm i t NL The network latency is the time taken by the system to respond to the user request: The processing delay which is the time taken by the router to process the data packets: The queuing delay or the waiting time which is the time data waits in the router buffer.

d pr
The propagation delay which is the time taken by data to cross the transmission medium that depends on the data speed and the geographical distance.

t TT
The data transmission delay (time) which is the time taken by data to be transported from one machine to another.
The execution time for task t j on vm i .

U kj
The bandwidth measured in Bits per Seconds (B/S).

D out kj
The transmitted data amount in Bits(B).
The arrival time of t j at vm i .

t RT
The service response time t RT for a single user request ðtaskÞ t j assigned to the virtual machine vm i Çƫ i The completion time at the virtual machine vm i : The decision variable x ij 2f0; 1g: ɱʂ The makespan ða schedule lengthÞ: Çƫ Av The average completion time:

Aȗ
The resource utilization: The cost of data processing per hour at the virtual machine vm i C d exe The total processing cost for all virtual machines: a ik The resources of vm i used by t k pp i The processing power of the virtual machine vm i .

BA
The Budget for processing tasks in $.
(1) This paper proposes an efficient load balancing algorithm in cloud called enhanced load balancing based on hybrid artificial bee colony with enhanced b-Hill climbing (ELBABCEbHC) to improve response time, processing cost and utilization.
(2) The proposed ELBABCEbHC approach is implemented in cloudAnalyst simulator (Wickremasinghe et al., 2010).( 3) The algorithm performance is evaluated for a large scale application as a Facebook considering peak hours and workloads and compared with the state of art algorithms.(4) The experiments results confirmed that the proposed ELBABCEbHC minimizes the service response time t RT and the processing cost ðC d exe Þ while maximizing the resource utilization (Aȗ) compared to round robin (RR), throttled load balancer (TLB), and active monitoring load Balancing (AMLB).
The remainder of this paper is organized as: Section II is related work.Section III defines and formulate the load balancing problem as an optimization problem.Section IV proposes in detail the new hybrid approach.Section V presents the experimental results and analysis.Finally, Section VI presents the conclusion and Section VI presents the future work.

Related work
For solving load balancing problems, some approaches are investigating.We summarize the comparison of various existing load balancing algorithms in Table 3.
Hill climbing (Yuret and De La Maza, 1993;Arram et al., 2014) is a metaheuristic local searching technique.The authors in (Al-Betar, 2017) propose an extension version called b-hill climbing(bHC) that utilizes two stochastic operators called N-operator and b-operator in hill climbing to control the balance between the exploration and exploitation during the search.The authors in (Al-Betar et al., 2019) propose an adaptive b-hill climbing (AbHC) algorithm for adapting N and b operators according to the parameter K.We try to tackle load balancing problem in cloud using the proposed ELBAB-CEbHC algorithm that combines artificial bee colony (ABC) (Karaboga and Basturk, 2007;Pham and Castellani, 2015;Kim et al., 2017) with b-Hill climbing (Al-Betar, 2017;Zahid et al., 2018) and the chaotic sinusoidal strategy (Peitgen et al., 2006).

Modeling load balancing problem
This section describes our proposed architecture of the load balancer, the load balancing model, and the proposed load balancing algorithm with the constraints.

The system model
The general steps of the resource provisioning scenario by any cloud provider are the following (Mell and Grance, 2011;Buyya et al., 2011): (i)The application submits its tasks to the scheduling service.(ii)The scheduling algorithm finds each resource that matches the task requirements.(iii) The scheduling service will ask provision service to get resources as the algorithm determined.(iv)The provision service will send the provision request to a resource pool manager which communicates with seach other to start a number of virtual machines based on the requests from the provision service.(v) A worker instance (virtual machine) will be configured and running then connect to the master machine and will register themselves.(vi)The scheduling algorithm will be acknowledged once these virtual machines registered and will start allocating tasks to the virtual machines.(vii)Once the application tasks are finished, all the resources will be released.
Due to the task and the resources heterogeneity, it is hard to maintain the performance of the task scheduling and distribute equal workload among the servers ensuring high quality of services (QoS) and the service-level agreement (SLA).Therefore, the load balancing is the main issue in the cloud.
The framework architecture of our load balancer, enhanced load balancing based on hybrid artificial bee colony with enhanced b-Hill climbing (ELBAB-CEbHC) is implemented in Fig. 1.
In our proposed framework, when the user generates task request with the specified application Identification, the service broker receives the

Notation Definition
Pu E The population of the bees.

P k
The probability assigned to the K th food source.

b-operator
The operator b2½0; 1 utilized in b-hill climbing.

N-operator
To navigate the neighboring solutions of the current one.R R ¼ fr 1 ; r 2 ; …r i …:r N g utilized as a random value.Firefly (FF) algorithm tries to minimize the search space where IMPSO technique is implemented to enhance the response by selecting the global best (Gbest) particle with a small distance of point to a line then global best (Gbest) particle candidates is elected.
Enhance response time, CPU, and memory utilization, reliability and throughput along with a make span Does not consider other QoS performance metrics as the cost, and the profit.(Balaji et al., 2021) In 2021 Balaji; K:; P: Sai Kiran; and M: Sunil Kumar: ACSO: Adaptive cat swarm optimization.
In ACSO, each cat duplicates its own position to seek memory pool.All the cat positions are compared using a fitness value which is a combination of energy, cost and memory utilization.Cats start moving from seeking mode to tracing mode, after seeing any pray.In tracing mode, cats conduct will be recreated with ACSO algorithm, and each cat follows the best position to update its velocity.
Enhance energy, cost, and memory utilization Does not consider the response time or the processing Time.(Mishra and Majhi, 2021) In 2021 Mishra; Kaushik; and Santosh Kumar Majhi: BSO-LB: A bird swarm optimization load balancing algorithm.
BSO-LB considers tasks as birds and VMs as food patches.A small position value (SPV) rule has been applied with each iteration considering the binary position of each particle.BSO-LB analyzes task mapping onto underloaded VMs, and the underloaded VMs.
Maximizing utilization with minimizing makespan and waiting time.

Hyper heuristic Honey Bee-Based Load Balancing Technique
This technique is used where the honey bee represents the cloudlet.As honey bees search for food source, cloudlets will be allocated in VMs to be executed.To achieve better performance, the load of the best solution generated by this technique is evaluated using the VM capacity.Then, the load balancing will be done based on the current virtual machine processing time and the standard deviation of the load.
Enhance Makespan, and the processing time, and reduce the degree of imbalance.
1)-It does not consider other QoS performance metrics as the cost, the profit.
(continued on next page) request.The service broker selects the best data centers based on the service brokerage policy selected.In our proposed system, we consider the broker policy called the performance optimized routing algorithm where the broker maintains a list of the latest request processing times at each data center, then it adds the processing time of the best response data center to the appropriate network delay and selects the data center that would give the least total response time.

Important definitions
We assume collections of interdependent tasks T have been modelled as the set of n tasks T ¼ ft 1 ; t 2 ; ……:t n g to be allocated to the numbers of heterogeneous virtual machines VMS ¼ fvm 1 ; vm 2 ; ……:vm m g.
Definition 1 (Tasks T): The task can be represented as t j with j represents the identifier of t j .These tasks have length M ¼ fM 0 ; M j …; M n g measured in million instructions ðMIÞ and the number of processing elements required for running tasks P e ¼ fp e 0 ; p e i ::p e n g.
Definition 2 (Virtual Machines VMS): These virtual machines with different processing cores (singlecore and multi-core), and CPUs have different cycle times (Millions of Instructions Per Second (MIPS)).The virtual machine can be described as vm i with i represents identifier, the processing speed measured in Million Instructions per Second (MIPS ) per processing element is MpfMp 0 ; Mp i …Mp m g, and P e ¼ fp e 0 ; p e i …p e m g represents the number of processing elements in the virtual machinesðvm i Þ.
Definition 3 (Network Latency t NL ): This latency describes the time measured in milliseconds ðmsÞ.It is the sum of all possible delays including processing delay d p , queuing delay (waiting time) d q and propagation delay d pr .
Definition 4 (Data Transfer Time t TT ): This time that is calculated by dividing the size of the unit of data (in bits) by the available bandwidth (in bits/ second).
Definition 5 (Response Time t RT ): The time interval between the user request sent and the provider response received.It is the sum of the execution time t ex , the network latency t NL , the request (task) arrival time t arr and data transmission delay (data transfer time) t TT after the task is assigned to the virtual machine.
Definition 6 (multi-objective optimization MOP: A multi-objective optimization problem (Talbi, 2009) with the objective functions z ðz !2Þ and feasible decision variables set S can be formulated as Equation ( 1 Such problem can be expressed either maximum or minimum functions and can be transferred to each other by Equation ( 2 When solving minimization problem, we obtain a set of solutions called a pareto-optimal or nondominated.Equation (3) and Equation ( 4) should be satisfied for Pareto dominate: for all indices b2f1; 2; ………::zg for at least one index h2f1; 2; …::zg To deal with the multi-objective problem, the weighted sum is applied using a set of weighted coefficients j i .The minimization formula for z objectives can be formulated as Equations ( 5) and ( 6): for if1; 2; 3; ……zg ð5Þ j i !0; i2f1; 2; 3; ……zg ð 6Þ

Load balancing problem modeling
The proposed mathematical model for the enhanced load balancing algorithm can be formulated considering the following assumptions for simplicity: (1) The execution of the tasks is a non-preemptive.
(2) All predecessor tasks should be completed before task execution.(3) Due to the cloud heterogeneity, there are different execution times for the summited tasks on different virtual machines.
Let x ij is defined as a binary decision variable given using Equation ( 7): We assume that task execution time t ex is constructed as m Â n matrix using m of virtual machines VMS and n of tasks T. Let t exij be the execution time for task t j corresponding to vm i calculated using Equation (8): The transfer time t TT ij is determined using Equation ( 9) The transfer time between the tasks running on the same virtual machine (vm) is 0.
The network latency t NL ðvm i ; t j Þ is determined using Equation (10) The service response time t RT is the first objective function to be minimized for a single user request (task) t j assigned to the virtual machine vm i is calculated using (11): The total completion time Çƫ i of tasks allocated onto a virtual machine ðvm i Þ is calculated using Equation ( 12): x ij ci ¼ 1; 2; ::m and j ¼ 1; 2; ::n The average completion time Çƫ Av is calculated by Equation ( 13): The makespan (ɱʂ) is calculated by Equation ( 14): The second proposed objective function to be maximized is the resource utilization (Aȗ) can be calculated considering Equations 13 and 14 using Equation ( 15): The third proposed objective function for minimization is the data processing cost ðC d exe Þ can be calculated considering the completion time Çƫ i in Equation ( 12) and C exe i as the data processing cost per hour using Equation ( 16): To solve the proposed load balancing related to task scheduling problem using weighted sum method in Equations ( 5) and ( 6), the multiobjective function ðFðyÞÞ can be formulated to minimize the service response time t RT and the data processing cost ðC d exe Þ while the resource utilization (Aȗ) is maximized as Equation ( 17) with the constraints that should be satisfied as in Equations 18e20 can be modeled as: s:t: The constraints represent the tasks requirements and the cloud resources availability.The first one in Equation ( 18) assures the summation of task t i to only one virtual machine vm i .Secondly, Equation ( 19) guarantees that the resources required for all tasks assignment to the virtual machine vm I don't exceed the processing power pp i of vm i .Thirdly, at Equation ( 20), the constraint ensures that the total processing cost must be less or equal to the dedicated budget to that application.

The proposed algorithm for load balancer based on hybrid artificial bee colony
Our proposed load balancer called enhanced load balancing approach based on hybrid artificial bee colony with enhanced b-Hill climbing (ELBAB-CEbHC) is composed of multi-phases: ranking list, population initialization and task allocation phases.
In the ranking list phase, a list of the submitted tasks is built using heterogeneous earliest finish time (HEFT) algorithm (Mazrekaj et al., 2019) based on the average execution time of each task on the virtual machines available.When initialize population, a greedy randomized adaptive search procedure (GRASP) (Resende and Ribeiro, 2019) is used.In the task allocation phase, the artificial bee colony algorithm (BABC) (Karaboga, 2005;Karaboga and Basturk, 2008) is used.The local search of the employee bees in BABC algorithm is enhanced by hybridizing BABC with the enhanced b-hill climbing algorithm (Al-Betar, 2017) that is combined with one chaotic sequence called Sinusoidal iterator (Peitgen et al., 2006;Lu et al., 2014).The local search of the onlooker bees in BABC is enhanced by using the mutation operator (Poli et al., 2008) for maintaining diversity in a population.The mutation (swap) is applied in the solution among the tasks at the virtual machine of the maximum completion time and the tasks at the virtual machine with minimum completion time to have the neighborhood solutions (food sources).

The ranking list strategy
In this phase, the tasks are ranked considering descending order suggested in (Mazrekaj et al., 2019).The ranking values ðrankðt i ÞÞ are calculated as Equation ( 21): 4.2.Initialization phase using GRASP GRASP (Resende and Ribeiro, 2019) presented in Algorithm 1 is used for initialization of the solutions (food sources) of the population.
The bee colony in ABC contains three groups of bees: employed bees assigned to each feasible solution (food source), onlooker bees watch the waggle dance of employed bees in the dance area within the hive to choose the better food sources, and scout bees search for the food sources randomly.The nectar amounts of these food sources correspond to the fitness of the associated solutions which can be calculated using the multi-objective function minðFÞ in Equations 17e20.A scout bee will search for a new solution randomly.

b-Hill climbing algorithm enhanced with sinusoidal map
The enhanced b-Hill Climbing algorithm with the sinusoidal map strategy (Peitgen et al., 2006;Karaboga and Basturk, 2008) is presented in Algorithm 3. b-Hill climbing algorithm is used to enhance the local search in ELBABCEbHC algorithm considering the load of each virtual machine ðvm i Þ calculated as the total completion time ðÇƫ i Þ. b-hill climbing algorithm iteratively generates a new solution based on two operators: N À operator and b À operator.N-operator navigates the neighboring solutions of the current one which is considered as the source of exploitation.b-operator allows moving from one region to another based on the comparison with R ¼ fr 1 ; r 2 ; …r i …:r N g as a random set of values.b-operator is utilized in hill climbing as the source of the exploration.
The random set R is generated using the sinusoidal map of the total completion time Çƫ i of tasks that assigned onto each virtual machine ðvm i Þ.
Çƫ i is generated using sinusoidal function as Equation ( 22): 4.5.The proposed ELBABCEbHC algorithm for scheduling with load balancing The proposed enhanced load balancing approach based on hybrid artificial bee colony with enhanced b-Hill climbing combined with sinusoidal map (ELBABCEbHC) algorithm is presented in Algorithm 4.

The experiments results and analysis
The overall experimental setup, performance metrics, results, and analysis are described in this section to evaluate the proposed enhanced load balancing approach based on hybrid artificial bee colony with enhanced b-Hill climbing (ELBAB-CEbHC) algorithm.

Environment setup
The experiments were carried out by the simulators CloudSim version-3.0and CloudAnalyst and using NetBeans IDE Version 8.0.2 (Wickremasinghe et al., 2010).The experimental environment running on Microsoft Windows 10 including Intel(R)-Core(TM)i7-7500U-2.70 GHz processor and 16.0 GB RAM.Our proposed simulation carries the proposed load balancing algorithm ELBABCEbHC coded in Java and evaluated by cloudAnalyst.
In cloudAnalyst framework, the environment parameters are defined in Tables 4e8.The regions definitions are defined in Table 4 where the world is divided into six regions according to the six continents.Our simulation Based on Facebook Users distribution around the world in 2021 presented in (https:// worldpopulationreview.com/country-rankings/facebook-users-by-country).Assuming the requests are in the evening within a single time zone, the userbases configuration scaled by 0.1 are suggested in Table 5. Amazon EC2 instance pricing model in (https:// aws.amazon.com/ec2/pricing/on-demand/) is used.
We also define the main characteristics of the data centers in Table 6 whereas the virtual machines configuration is described in Table 7 with other parameters such as: (1) User grouping factor as the users count in a single bundle.(2) Request Grouping Factor for a virtual machine of the requests number in a single bundle.(3) The length of the executable instruction (or request) parameter is defined in bytes.(4)A broker policy selected is the performance optimized routing algorithm.The suggested configuration for the proposed approach ELBABCEbHC is provided in Table 8.

Experimental results
To measure the effectiveness of our proposed enhanced load balancing approach based on hybrid artificial bee colony with enhanced b-Hill climbing (ELBABCEbHC) algorithm, the performance of the proposed algorithm is compared with Round Robin (RR), Throttled load Balancer (TLB), and Active Monitoring Load Balancing (AMLB).These algorithms are implemented using five UserBases (UserBase 1: UserBase 5) in CloudAnalyst simulators.Tables 9e13 show the experimental results obtained by the proposed ELBABCEbHC and the other counterparts algorithms considering various parameters.The response time by the region for the proposed approach ELBABCEbHC (ms) is shown in Table 9.The request service time(ms) of different data centers using the proposed ELBABCEbHC is shown in Table 10.Further, the overall response time in milliseconds is presented in Table 11.The data processing cost ($) obtained is presented in Table 12.The data center utilization (%) is shown in Table 13.

Performance evaluation
A statistical analysis is described by Figs.2e6.The average response times of the UserBases (UB1:UB5) using the proposed approach ELBABCEbHC are shown in Fig. 2.
It is obvious that UB1, UB4 and UB5 are processed in the closest data centers which reduce the transmission latency and in consequence the overall response time.As a result, UB1, UB4 and UB5 have better overall response time compared to UB2 and UB3.The request service times of different data centers using the proposed ELBABCEbHC are shown in Fig. 3.The data center (DC3) at region 4 (Africa) gives minimum request service time compared with DC1, DC2 because the number of userbases requests that are processed by DC3 is the minimum.The data center (DC1) at region 0(North America) has more requests to serve than DC3.The data center (DC2) at region 3(Asia) has the maximum request service time because it serves the greatest number of UserBases requests (UB3, UB4).Fig. 4 shows the overall response time obtained by RR, TLB, AMLB, and ELBABCEbHC.TLB is better than AMLB, and RR algorithms.ELBABCEbHC outperforms the three counterpart algorithms in terms of response time.Fig. 5 shows the data center processing cost obtained by RR, TLB, AMLB, and ELBABCEbHC.TLB is better than AMLB and RR but ELBABCEbHC outperforms the three   algorithms in terms of data processing cost.Fig. 6 shows that ELBABCEbHC gives the best results in terms of resource utilization considering three data centers distributed in three regions (North America, Asia, and Africa).TLB algorithm is better than AMLB algorithm and the RR algorithm.

Conclusion
Load balancing is an essential issue for enhancing the overall service response time for the users in cloud with achieving minimum processing cost and maximum utilization taking into account the quality of services (QoS) and the service level agreement (SLA).The main issue is that the increasing in the overall response time causing the services cost raise due to the searching for the least loaded virtual machine.In our proposed approach for dynamic load balancing, we use the population-based metaheuristic.First, the population is initialized using greedy randomized adaptive search procedure (GRASP).Further, the local search in the binary artificial bee colony (BABC) algorithm is enhanced using b-hill climbing algorithm combined with sinusoidal sequence considering the virtual machine vm i load.For maintaining the diversity in the population, the bit inversion mutation is used in the onlooker bees in BABC.According to the simulation results, it is obvious that the proposed algorithm ELBABCEbHC as a scheduling algorithm with load balancer gives the best results in terms of the overall response time, the data processing cost ($) and the data center utilization compared with Round Robin (RR), Throttled load Balancer (TLB), and Active Monitoring Load Balancing (AMLB) for load balancing of all the proposed five user groups requests in the globe using the data centers that are distributed in three regions (North America, Asia, and Africa).

The future work
The future work is to investigate other types of metaheuristics algorithms for solving load balancing issues related to the task scheduling problems in the cloud environment.
The corresponding author is responsible for ensuring that the descriptions are accurate and agreed by all authors.
x i Current solution in b-hill climbing.x i New solution in b-hill climbing.Uð0; 1Þ Uniform distribution of the solution space.u bi The solution space upper bound.l bi The solution space lower bound.MaxItr Maximum iteration of the b-hill climbing.Itr Number of iterations of the b-hill climbing.

Fig. 2 .
Fig. 2. The response time by region for the proposed approach ELBABCE b HC(ms).

Fig. 3 .
Fig. 3.The request service time(ms) of different data centers using the proposed ELBABCEbHC.

Table 1 .
The notations used in defining the load balancing problem.

Table 2 .
The notations used in formulating the proposed ELBABCEbHC.

Table 3 .
Comparison of previous existing load balancing algorithms.

Table 5 .
User Base configuration.

Table 6 .
Data center configuration.

Table 8 .
The configuration of the proposed ELBABCEbHC algorithm.

Table 9 .
The response time by region for the proposed approach ELBABCEbHC (ms).For each onlooker bee in the population 3.4.1.Evaluate the current solution fitness function using Equations 17e20.3.4.2.Search the neighborhood solution using Bit Mutation Operator considering machines load.3.4.3.Memorize the best solution.3.4.4.Abandon the worst solutions.3.4.5.Send scout bee to explore search area for new solutions using GRASP in Algorithm 1. 3.4.6.Relace the abandon solutions with the new solutions.3.4.7.Sorting the best-found solutions in the population.3.4.8.Select the best non-dominated solution.4. Until (stopping criteria is met.)

Table 10 .
The request service time(ms) of different data centers using the proposed ELBABCEbHC.

Table 12 .
The data center processing cost ($) obtained by RR, TLB, AMLB, and the proposed ELBABCEbHC.