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A multi‐objective method for virtual machines allocation in cloud data centres using an improved grey wolf optimization algorithm

2021; Institution of Engineering and Technology; Volume: 15; Issue: 18 Linguagem: Inglês

10.1049/cmu2.12274

1751-8636

Masoud Reza Hashemi, Danial Javaheri, Parisa Sabbagh, Behdad Arandian, Karlo Abnoosian,

Software-Defined Networks and 5G

IET CommunicationsVolume 15, Issue 18 p. 2342-2353 ORIGINAL RESEARCH PAPEROpen Access A multi-objective method for virtual machines allocation in cloud data centres using an improved grey wolf optimization algorithm Masoud Hashemi, Corresponding Author Masoudhashemi60@yahoo.com Zabol University, Zabol, Iran Correspondence Masoud Hashemi, Zabol University, Zabol, Iran. Email: Masoudhashemi60@yahoo.com Karlo Abnoosian, Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran. Email: karlo.abnoosian@srbiau.ac.irSearch for more papers by this authorDanial Javaheri, orcid.org/0000-0002-7275-2370 Department of Computer Engineering, Science and Research Branch, Islamic Azad University, Tehran, IranSearch for more papers by this authorParisa Sabbagh, orcid.org/0000-0001-5342-6994 DISA-MIS Department, University of Salerno, Fisciano, ItalySearch for more papers by this authorBehdad Arandian, orcid.org/0000-0002-4984-7224 Department of Electrical Engineering, Dolatabad Branch, Islamic Azad University, Isfahan, IranSearch for more papers by this authorKarlo Abnoosian, Corresponding Author karlo.abnoosian@srbiau.ac.ir orcid.org/0000-0002-6080-9202 Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran Correspondence Masoud Hashemi, Zabol University, Zabol, Iran. Email: Masoudhashemi60@yahoo.com Karlo Abnoosian, Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran. Email: karlo.abnoosian@srbiau.ac.irSearch for more papers by this author Masoud Hashemi, Corresponding Author Masoudhashemi60@yahoo.com Zabol University, Zabol, Iran Correspondence Masoud Hashemi, Zabol University, Zabol, Iran. Email: Masoudhashemi60@yahoo.com Karlo Abnoosian, Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran. Email: karlo.abnoosian@srbiau.ac.irSearch for more papers by this authorDanial Javaheri, orcid.org/0000-0002-7275-2370 Department of Computer Engineering, Science and Research Branch, Islamic Azad University, Tehran, IranSearch for more papers by this authorParisa Sabbagh, orcid.org/0000-0001-5342-6994 DISA-MIS Department, University of Salerno, Fisciano, ItalySearch for more papers by this authorBehdad Arandian, orcid.org/0000-0002-4984-7224 Department of Electrical Engineering, Dolatabad Branch, Islamic Azad University, Isfahan, IranSearch for more papers by this authorKarlo Abnoosian, Corresponding Author karlo.abnoosian@srbiau.ac.ir orcid.org/0000-0002-6080-9202 Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran Correspondence Masoud Hashemi, Zabol University, Zabol, Iran. Email: Masoudhashemi60@yahoo.com Karlo Abnoosian, Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran. Email: karlo.abnoosian@srbiau.ac.irSearch for more papers by this author First published: 14 September 2021 https://doi.org/10.1049/cmu2.12274AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Abstract Cloud computing is a rapidly evolving computational technology. It is a distributed computational system that offers dynamically scaled computational resources, such as processing power, storage, and applications, delivered as a service through the Internet. Virtual machines (VMs) allocation is known as one of the most significant problems in cloud computing. It aims to find a suitable location for VMs on physical machines (PMs) to attain predefined aims. So, the main purpose is to reduce energy consumption and improve resource utilization. Because the VM allocation issue is NP-hard, meta-heuristic and heuristic methods are frequently utilized to address it. This paper presents an energy-aware VM allocation method using the improved grey wolf optimization (IGWO) algorithm. Our key goals are to decrease both energy consumption and allocation time. The simulation outcomes from the MATLAB simulator approve the excellence of the algorithm compared to previous works. 1 INTRODUCTION Cloud computing has become a popular service because of the rapid advancement of information and communication technology [1, 2]. Cloud computing and data-storage systems use several technologies to link and manage required resources across several devices [3, 4]. It is a concept for supplying and distributing on-demand network accessibility to a public pool of computing resources with little administrative effort and/or service provider interaction [5]. Cloud computing has developed as a modern paradigm to offer clients a service through the Internet to fulfil many objectives, such as controlling the robots and classification [6-9]. It is a location-independent, virtualized, and on-demand pay-per-use pricing model to increase productivity and maximize resource usage [10]. Cloud computing has significantly altered the conventional ownership structure (where computational powers were owned in the past) to the present subscription model [11]. It offers pay-as-you-go accessibility to elastic resources in the shape of services, with a pay-as-you-go model based on actual resource use [12]. So far, the deployment of clouds has been fuelled by three primary service models: platform, software, and infrastructure as a service (PaaS, SaaS, and IaaS) [13]. The greatest degree of abstraction is SaaS, which allows customers to reach applications hosted in cloud data centres (CDC) through the Internet. For example, it has enabled enterprises to have more flexible access to the software by allowing unrestricted and on-demand access to various ready-to-use apps. Corporations may also reduce direct or internal expenditures like license fees and IT infrastructure preservation by using SaaS. PaaS is designed for consumers that want more control over their IT resources, and it provides a basis for building and deploying cloud apps, including auto-scaling and programming models. For instance, it has made it simple for designers to construct apps that utilize the cloud's elastic resource paradigm. Eventually, IaaS provides access to computational resources, such as virtual machines (VMs) and storage space, by leasing them [14]. This layer has served as the cornerstone of cloud computing and the base for PaaS and SaaS. It has performed this work by allowing subscribers to utilize the information technology (IT) infrastructure only when they require it to alter the number of resources utilized on a flexible basis and spend only for what is utilized, all while totally controlling the resources [15]. Virtualization is known as a fundamental cloud computing technology and offers an efficient way to manage dynamic resources in cloud data centres using some well-known methods, such as clustering [16, 17]. The VMs are separated from each other, and they can act as a whole system to execute users' applications [18]. Also, the physical machine (PM) as a server or host of VMs provides all required VM resources, including network bandwidth, storage, memory, and CPU [19]. Therefore, the power utilization of cloud data centres is increasing as cloud computing becomes more prevalent. Surprisingly, data centre power is squandered for various reasons, including server use, network equipment, and inefficient data centre cooling systems [20, 21]. As a result, energy efficiency has gained significance in wireless and cloud data centres [22]. Lately, different works have been proposed on energy efficiency, which is categorized into three main groups, including task scheduling, migration, and resource allocation [23, 24]. Consolidation of VMs is a method of making intelligent and effective utilization of cloud resources. The VM allocation issue is one of the most difficult aspects of VM consolidation. It is defined as finding the appropriate PM for a VM that reduces the running PMs or hosts in the cloud data centres [25]. Academic investigators have focused on VM allocation as an NP-hard issue that has been addressed using various meta-heuristic and heuristic approaches [26]. Therefore, different objectives have been considered to improve load balance, reduce cost and network consumption, mitigate SLA violations, increase energy efficiency, and maximize resource utilization [27]. There are many nature-inspired algorithms which have been commonly used recently in many domains, such as Harris hawks [28, 29], moth flame [30-32], fruit fly [33, 34], whale [35, 36], bacterial foraging [37], grasshopper [38] and ant colony [39, 40] optimization algorithms. In the present investigation, the improved grey wolf optimization algorithm (IGWO) was used to tackle the issue of VM allocation. This improved algorithm is based on changes in wolf populations and the effect of each wolf's fitness level. It has solved optimization problems in many different fields effectively. The main goals are to reduce energy consumption and VMs allocation time in the cloud using the IGWO algorithm. Also, the key contributions to the present article are as follows: Offering an improved algorithm to address the virtual machine allocation issue at cloud data centres; Improving the VM's energy consumption in an environment of cloud; Improving the VM's allocation time in an environment of the cloud. The remainder of the present article is arranged as follows: The second section examines the relevant literature. The suggested method is explained in Section 3. In Section4, the simulation outcomes are reported. Eventually, Section 5 brings the study to a conclusion. 2 RELATED WORK Cloud computing has emerged as the latest technology in the computation domain [41]. Cloud service providers (CSPs) have access to high-performance computing resources known as data centres (DCs). Users are served by CSPs using VMs [42]. VMs with a high memory has been popular lately [43]. A host has deployed several heterogeneous VMs on a parallel computing platform termed a data centre in the cloud computing platform [44]. Virtualization technology grants VM subscribers administrative access within the guest operating system, allowing them to adjust their runtime resources to meet their individual requirements [45]. The latest literature on VM migration has concentrated chiefly on the choice of destination data centres or destination servers based on migration time optimization and application quality of service (QoS) [46, 47]. The following are some studies on clouds and VMs that have been published in the literature. Yadav et al. [48] introduced GradCent for managing overloaded hosts in cloud data centres. Utilizing an actual CPU workload, this approach is employed to generate an upper CPU usage threshold to discover overloaded hosts. Furthermore, they presented the minimum size utilization (MSU) dynamic VM selection technique for picking VMs from an overloaded host for VM consolidation. Finally, they combined real-world workload measurements from numerous PlanetLab VMs with CloudSim simulations. Compared to baseline methods, the suggested algorithms reduced energy usage and SLA violations by 23 percent and 27.5 percent on average, respectively. Yadav et al. [49] introduced adaptive heuristic techniques for overloaded host identification and VM choosing, including least medial square regression and minimal usage prognostication. The suggested VM selection technique takes into account the sorts of applications being executed and their CPU use at various time intervals across the VMs. The suggested methods are validated by utilizing the CloudSim simulator and a PlanetLab workload trace. Compared to earlier techniques for overloaded host detection and VM selection, the findings indicated that these techniques significantly reduce the CDC's electric energy usage. Satpathy et al. [50] introduced the VRMap model, which discovered an optimum remapping strategy that balances remapping costs and migration overheads without sacrificing service quality. To find the best solution, VRMap used a genetic-metaheuristic. The findings indicated that while VRMap performs similarly in remapping costs, it outperforms other competitions in downtime and migration time. In cloud data centres, Naik et al. [51] suggested effective VM scheduling using the multi-objective krill herd optimization selection method. For the VMs, targets like power usage, load volume, and resource waste are assessed, and the entropy is computed for the determined objectives. Then, prioritized tasks are assigned to the VMs based on the entropy value. According to the findings, the suggested entropy-based scheduling outperformed some algorithms. Another energy-efficient VM allocation method was proposed in [52] using an improved ant colony optimization (ACO) algorithm. Reducing the energy consumption and communication cost over traffic-aware data centre networks are the main aims of this work. Nevertheless, it just checks out CPU power usage, which is the most prevalent utilization. Moreover, it does not evaluate VM algorithms with accurate trace data of the cloud platform. Also, considering optimizing the CPU utilization while decreasing energy consumption, the researchers in [53] addressed the VM placement problem. They examined the performance of four common multi-objective evolutionary algorithms utilizing the Planet Lab dataset and Cloudsim in this regard. According to simulation outcomes, the non-dominated sorting genetic algorithm II (NSGA-II) exhibits improved performance regarding SLA violation, SLA, and energy usage. Furthermore, in terms of an arithmetic mean of CPU usage, NSGAII performs better. Furthermore, eMOEA outperforms the competition in terms of CPU utilization standard deviation. Satpathy et al. [54] suggested a resource-aware solution based on a metaheuristic crow search algorithm (CSA) to integrate a large number of VMs onto minimum DCs while maximizing data centre usage to match the service level agreement (SLA) and desired QoS. To achieve the required results, they presented two separate techniques: (i) greedy crow search (GCS) and (ii) traveling salesman problem-based hybrid crow search (TSPCS). They compared their suggested technique to the conventional first fit (FF) methodology to assess its performance, and their new approaches greatly outperformed the classical technique. A multi-objective VM placement technique is offered in [55], considering the different necessities of cloud suppliers and clients. It aims to minimize load variance and energy consumption, improve the robustness of PMs, and maximize resource utilization. An energy-efficient knee point-driven evolutionary algorithm (EEKPDEA) is proposed to handle the multi-objective optimization issue presented in this paper. In addition, to enhance population initialization in EEKPDEA, an energy-efficient-oriented population initialization strategy (EEPIS) was suggested. The simulation outcomes indicated that the suggested model offers good performance in load balancing, energy consumption, and robustness. However, it ignores the abnormal loads on PMs, such as overhead. To increase a CSP's profit, Addya et al. [56] suggested a strategy termed maximum VM placement (MVMP) with low energy consumption. It is a bi-objective optimization issue that is tackled with the simulated annealing (SA) method. In the field of strategic VM placement, their MVMP method is compared against five modern algorithms: Hybrid GA (HGA), Marotta and Avallone (MA) method, first-fit decreasing (FFD), modified best-fit decreasing (MBFD), and random deployment. MVMP outperforms the Marotta and Avallone (MA) technique, MBFD, HGA, FFD, and random placement regarding the number of servers utilized, profit, energy consumption, and execution time. Furthermore, the MVMP's scalability is tested by utilizing two scenarios: (i) a fixed number of VMs and (ii) a fixed number of servers. An optimized resource allocation algorithm at data centres is proposed by Sharma and Reddy [57], in which GA and dynamic voltage frequency scaling (DVFS) techniques are combined. The frequency of PMs is modified in DVFS depending on the workload, and GA is utilized to allocate VMs in an energy-efficient way. The suggested work aimed to decrease the power utilization of data centres, increase the convergence of the solutions, and utilize resources. The simulation outcomes have shown that the proposed model consumes 22.4% less energy than the compared method. However, notwithstanding the advancements in the proposed algorithm, the power consumption of data centres has not been reduced since the DVFS method is restricted to just the CPU. Moreover, an energy-efficient VM placement using the biogeography-based optimization (BBO) algorithm is suggested in [58]. The suggested model is simulated using the MATLAB simulator and compared to GA. In terms of energy usage, the findings demonstrate that the suggested model outperforms the GA. Nevertheless, it does not study the QoS, particularly the SLA violation. In addition, it only concentrates on the new VM allocation. The grouping GA independently does not obtain an efficient solution for the VM allocation issue. So, in the suggested model in [59], the researchers improved this algorithm by presenting an effective method to encode and produce novel solving methods. The vector-packing problem has been used to model the VM placement issue to improve resource usage, decrease the number of used servers, and reduce energy usage. In addition, the suggested crossover process has improved operational efficiency, reduced resource wastage and power consumption, and managed the various collections of the VMs. Table 1 compares the existing techniques for allocating the virtual machines at data centres and shows the advantages and disadvantages of each method. For solving these problems, virtual machine allocation is suggested at data centres using the improved grey wolf optimization algorithm, which will be followed by the minimum energy consumption and the minimum virtual machine allocation time. TABLE 1. Comparison of available methods Article Method Main features Yadav et al. [48] Using a GradCent algorithm to identify overloaded hosts utilizing a real CPU workload Proposing MSU algorithm Minimizing energy consumption Minimizing SLA violation Yadav et al. [49] Proposing adaptive heuristic algorithms, including least medial square regression Improving overloaded host detection Enhancing usage prognostication for VM selection from overloaded hosts Satpathy et al. [50] Proposing a VRMap model that found an optimal remapping plan Balancing the remapping expenses and migration overheads with no compromising service quality Naik et al. [51] Proposing effective scheduling (entropy-based krill herd optimization) with multi-objective VM selection in cloud data centers Minimizing completion cloud Improving cloud task partitioning scheduling Improving round-robin techniques Wei et al. [52] VM allocation using an improved ACO algorithm Reducing communication cost over traffic-aware data center networks Not evaluating VM algorithms with real trace data of the cloud platform López-Pires and Barán [53] Using NSGA-II for VM placement problem Optimizing the CPU utilization Decreasing energy consumption Satpathy et al. [54] Proposing a resource-aware method based on a met heuristic GCS Improving QoS with maximum data centre utilization Consolidating a large number of VMs on minimal DCs to meet the SLA Ye et al. [55] Using EEKPDEA for multi-objective VM placement technique Minimizing load variance Minimizing energy consumption Improving the robustness of PMs Maximize the resource utilization Addya et al. [56] proposing the MVMP technique to enhance the profit attained by a CSP Improving energy consumption Improving profit Improving execution time Sharma and Reddy [57] Combining GA and DVFS technique for resource allocation at data centres Decreasing the power usage of data centres Increasing the convergence of the solutions Improving resource utilization Ali and Lee [58] Using the BBO algorithm for VM placement Reducing energy consumption Only focusing on the fresh VM allocation Jamali and Malektaji [59] Using the vector packing issue to model the problem of VM placement Improving the operational efficiency Reducing the resource wastage Reducing power consumption 3 PROPOSED METHOD The present section initially explains the issue and then describes the energy and time models. Next, Section 3.3 discusses the proposed algorithm. Finally, in Sections 3–4, 3–4, the suggested algorithm is presented. 3.1 Problem description The placement and diagnosis problems are very popular in many intelligent systems [60-62]. In this paper, we considered that several PMs are linked through a network in cloud data centres. They are assigned to several VMs running a diversity of apps. Figure 1 shows the diagram of the VM allocation problem. In this problem, n VMs with the diverse requested resources are allocated to suitable m PMs to obtain the objectives, including robustness, maximizing resource utilization, and minimizing power consumption. Each PM offers several resource types, namely, CPU, network bandwidth, and memory. The resource capabilities of PMs and the VMs resource requests are generally dissimilar. As shown in Figure 2, a VM allocation outline can be denoted as a vector in which the elements indicate the PMs and the element's value indicates the VMs. FIGURE 1Open in figure viewerPowerPoint Diagram of VM allocation problem FIGURE 2Open in figure viewerPowerPoint An array of VM allocation solution 3.2 Energy consumption model A linear connection between CPU use and energy utilization defines server energy consumption [63]. Therefore, the CPU utilization of the VMs is calculated by Equation (1). CP U Vm , i = V M mips , i Hos t mips , j (1) In Equation (1), V M mips , i indicates the required mips for VM i, and Hos t mips , j is the whole capacity of PM j. Also, CP U Vm , i indicates the CPU usage of VM i. The CPU utilization of PM j is calculated by Equation (2). Moreover, the energy consumption of PM j as a function of the CPU utilization is calculated using Equation (3). Pj is the current energy consumption of PM j, P j idle indicates the energy consumption (Watt) of PM j in idle, and P j busy is the maximum energy consumption (Watt) of the PM j at 100% CPU utilization. CP U Host , j = ∑ i ∈ r j CP U V m , j (2) P j = P j busy − P j idle ∗ CP U host , j + P j idle ; CP U host , j > 0 P j idle ; O t h e r w i s e (3) To calculate the system's overall energy consumption during VMs allocation, the energy consumption of all involved hosts in the problem should be considered. Therefore, the main aim of the suggested method in this paper is to decrease the energy consumption of PM that is calculated by Equation (4). Energy = ∑ j = 1 M P j = ∑ j = 1 M P j busy − P j idle ∗ CP U host , j + P j idle (4) In Equation (4), the condition of Equation (5) should be considered. The binary variable xij indicates if VM i can be allocated to Pm j. If the VM i is allocated to the PM j then the variable xij will be 1; otherwise, it will be 0. Generally, VM i is allocated to PM j when the available resources of PM j are greater than the minimum resource requirements of VM i. ∑ j = 1 M x i j = 1 ∀ i ∈ N (5) 3.3 Allocation time model Another goal is to optimize the required time to allocate VMs to the appropriate hosts. The time required to perform the allocation operation depends on the capacity of the hosts. Therefore, the data set required for the time parameter is randomly generated numerically between 0.1 and 10 ms for each source. Then, to calculate the total allocation time, the time associated with the involved hosts in the process must be summed together according to Equation (6). Time = ∑ i = 1 n T i (6) In this study, there are two goals for optimization, both of which must be minimized. However, these two parameters have different units and cannot be combined. Therefore, to calculate the value of fitness, these values must be normalized and added together using the user's priority coefficients. The coefficients must be defined in such a way that their sum is equal to 1 ( ∑ i = 1 2 w i = 1 ) . The final value of Equation (7) is obtained. In this equation, the two parameters of time and energy are obtained from the equations described earlier and then normalized and summed together by the mentioned coefficients ( w 1 & w 2 ), which results in final fitness at the end: Fitness = w 1 × Energy + w 2 × Time (7) = Energ y max − Energy Energ y max − Energ y min (8) Time = Tim e max − Time Tim e max − Tim e min (9) 4 GREY WOLF ALGORITHM Inspired by the social life and hunting of grey wolves, the GWO algorithm uses four types of wolves to simulate leadership hierarchies [64, 65]. Grey wolves have a well-defined social hierarchy [66]. The group's leaders are Alpha, a male and female duo. Alpha is primarily in charge of deciding about hunting, sleeping locations, and waking times, among other things. The group is dictated to by Alpha's choices [67]. On the other hand, Alpha has been shown to follow the other wolves in the group in a democratic manner. The whole group acknowledges the Alpha by holding its tail down in group aggregation. The group must follow Alpha's commands. Only the group's Alpha wolves are able to pick their partners. Surprisingly, Alpha is not always the group's most vital member, but it is the greatest at managing the group. It demonstrates that a group's structure and order are more essential than its power [68]. The second level of the grey wolf hierarchy is beta. Beta wolf is Alpha's consultant and organizer of the group. Beta implements Alpha's orders across the group and reports back to Alpha. Omega is the grey wolf with the lowest rank. Omega takes on the character of the helpless victim. They were the final wolf group to be killed. It is termed subordinate or Delta if the wolf is not Omega, Beta, or Alpha. The Delta wolf must provide reports to Alpha and Beta but dominates Omega. Besides the social hierarchy, hunting of grey wolves has three phases: tracking, chasing, and approaching the bait [69]. To simulate the wolves' social hierarchy, we assume Alpha to be the best option and Beta and Delta to be the second and third-best alternatives. The remaining candidate solutions are categorized as Omega. Thus, Alpha, Beta, and Delta are the three groups that drive the optimization, and the fourth group follows them. Wolf siege behaviour modelling uses Equations (10) and (11): D ⃗ = C ⃗ . X ⃗ p t − X ⃗ t (10) X ⃗ t + 1 = X ⃗ p t − A ⃗ . D ⃗ (11)where t is the number of current iterations, A and C are the coefficient vectors, Xp is the hunting position vector, and X is the position vector of a wolf. Equations (12) and (13) are used to calculate the vectors A and C [70]: A ⃗ = 2 a . r 1 ⃗ − a ⃗ (12) c ⃗ = 2 r ⃗ 2 (13) The vector a is reduced linearly from 2 to 0 within the exploitation and exploration phases iteration. r is a random vector between 0 and 1. Due to the randomness of vectors r1 and r2, wolves can randomly change their position inside the bait-enclosed space using Equations (14) and (15). An n-dimensional search space may be used to apply the same approach. In this situation, the grey wolves circle the best solution found in dimensions greater than the cube's dimensions. Alpha often leads grey wolf hunting. Sometimes Delta and Beta wolves also hunt. To replicate this behaviour, the three best answers are kept, and the other search agents are compelled to update their positions in accordance with the best search agents' positions using Equation (16): D ⃗ δ = C ⃗ 3 . X ⃗ δ − X ⃗ D ⃗ β = C ⃗ 2 . X ⃗ β − X ⃗ D ⃗ α = C ⃗ 1 − X ⃗ α − X ⃗ (14) X ⃗ 1 = X ⃗ α − A ⃗ 1 . D ⃗ α X ⃗ 2 = X ⃗ β − A ⃗ 2 . D ⃗ β X ⃗ 3 = X ⃗ δ − A ⃗ δ . D ⃗ δ (15) X ⃗ t + 1 = X ⃗ 1 + X ⃗ 2 + X ⃗ 3 3 (16) The implementation of the exploitation or attack phase [71], which occurs if the bait stops, is done by reducing the variable a value from 2 to 1. The value of A is also dependent on a, so it decreases. As the value of A drops, wolves are forced to attack the bait. An exploration phase is also provided to prevent getting stuck in the local minimum. Wolves distance themselves from each other in search of bait and approach and work together to attack. A is used with random values above 1 or below −1 [72]. Figure 3 illustrates this point. FIGURE 3Open in figure viewerPowerPoint Exploration vs. exploitation phase Another influential component of the process is the value of C. The value of this vector is a random number among [0, 2]. This random value affects the position of the bait in determining distance, intensity (C > 1), or weakness