# An Enhanced Multi-Objective Gray Wolf Optimization for Virtual Machine Placement in Cloud Data Centers

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## Abstract

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## 1. Introduction

#### 1.1. Limitations of Research and Contributions

- An enhanced levy based MOGWO is proposed to solve the VM placement problem.
- An archive is attached to save the history of VMs.
- Leader selection mechanism is used to select the best three leaders(VMs), i.e., alpha, beta and delta to fulfill the requirements of users.
- Levy flight is used to generate a long jump towards the optimal solution. The position of GWs is then updated using step size of levy flight.
- Bin packing is used to pack the VMs in minimum number of physical servers.
- Best fit strategy is used to optimally pack the number of VMs in physical servers without wasting resources.
- The proposed algorithm efficiently minimized the utilization rate of PMs.

#### 1.2. Implementation Practice Guidelines

- Initialize a population of GWs.
- Calculate the objective value of each particle.
- Find the non-dominated solutions.
- Select three leaders (alpha, beta and delta) from an archive.
- Calculate step length using levy flight.
- Update the positions of the leaders using gray wolf optimization plus step size.
- Update an archive.
- Select the leaders from an archive.

## 2. Related Work

## 3. Proposed Scheme

#### 3.1. Multi Objective Gray Wolf Optimization Algorithm (MOGWO)

- Searching
- Encircling
- Attacking

#### 3.1.1. Searching (Exploration)

#### 3.1.2. Encircling (Exploration)

#### 3.1.3. Attacking (Exploitation)

- The new value should have a better solution than the existing ones in the archive. Otherwise, it is not allowed for a new value to be inserted in the archive.
- If the new wolf has better value, then the solutions in the archive have to leave the archive and allow a new solution to come inside it.
- If the value of both solutions is same, the new solution is allowed to be moved into the archive.
- If the archive is full, the grid mechanism finds the most crowded segment to omit its solutions. Then, the new solutions should enter the least crowded segment.

Algorithm 1 Pseudocode of the MOGWO algorithm. |

#### 3.2. Levy Flight Distribution

- Select the random direction.
- Generate a new step.

#### 3.3. Simple Levy Distribution

#### Fourier Transform

#### 3.4. Levy Based Multi-Objective Gray Wolf Optimization Algorithm (LMOGWO)

Algorithm 2 Pseudocode of the LMOGWO algorithm. |

## 4. Problem Formulation

## 5. Results and Discussion

#### 5.1. Parameters Setting (Scenario 1)

- $\alpha $ = 0.1: grid inflation parameter;
- $\beta $ = 4: leader selection parameter; and
- nGrid = 10: number of grids per dimension.

- $\alpha $ = 0.1: grid inflation parameter;
- $\beta $ = 4: leader selection parameter;
- nGrid = 10: number of grids per dimension;
- c1 = 1: personal learning co-efficient;
- c2 = 2: global learning co-efficient; and
- $\omega $ = 0.5.

#### 5.2. Comparison of Algorithms

#### 5.3. Discussion of Results

#### 5.4. Parameters Setting, Comparison of Algorithms and Discussion of Results (Scenario 2)

- $\alpha $ = 1.0: grid inflation parameter;
- $\beta $ = 1.5: leader selection parameter; and
- nGrid = 20: number of grids per dimension.

- $\alpha $ = 1.5: grid inflation parameter;
- $\beta $ = 3: leader selection parameter;
- nGrid = 10: number of grids per dimension;
- c1 = 1: personal learning co-efficient;
- c2 = 2: global learning co-efficient; and
- $\omega $ = 0.5.

#### 5.5. Bin Packing

## 6. Conclusions

#### Future Studies

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Techniques | Objectives | Achievements | Limitations |
---|---|---|---|

Multi-objective based genetic algorithm [1] | Efficient VM placement | Reduce the usage of running servers | VM placement problem is an NP-hard problem |

Shadow routing-based approach [2] | Auto scaling of VMs and intelligent packing of VMs in minimum number of PMs | Reduced energy consumption and cost | Provides approach for only private clouds |

Layered VM migration [3] | Congestion and delay of network | Balanced network resources and minimized delay | Migration cost is increased |

MOGWO [4] | For mechanism to solve multi-objective problems | Achieved an optimal solution to solve multi-objective problems | Can not handle more than four objectives |

Levy based particle swarm optimization algorithm [5] | Provide an efficient mechanism to solve premature convergence problem | Enhanced global optimization, avoided trapping and optimized premature convergence | Performs well for single objective problems |

Modified transactive control system [6] | Mitigate challenges of irregular wind power | Provided robust, optimal and flexible solutions | The cost of energy is increased |

A novel framework to deploy cloud computing platform [7] | Load balancing | Used time-series forecasting to balance the load efficiently | Discontinuous network |

Cloud based energy storage pool [8] | High cost for energy storage devices | Developed cost-efficient energy storage pool for users | Great power loss for implementation purpose |

VM placement based on genetic algorithm [9] | Network congestion in network, wastage of energy resources | Balanced transmission load and reduced energy consumption | VM placement problem is an NP-hard problem |

Eco-system [10] | Management of real time smart grid data | Handle big data of smart grid | There may be a chance of congestion |

Identity based encryption with bilinear pairing [11] | Minimize wastage of time | Efficient performance of cloud in terms of cost | There is an extra energy consumption |

Multi-objective non-dominated sorting genetic algorithm [12] | VM allocation and VM template selection | Reduced power consumption and minimized wastage of resources | VM allocation is not efficient for rapidly growing users |

Improved grouping genetic algorithm [13] | Dynamic VM consolidation problem | Minimized migration cost and reduced energy consumption | Further enhancement is required to solve VM consolidation problem |

Cost-oriented optimization mechanism for smart grid user [14] | User comfort in terms of minimum cost | Efficient pricing schemes for users | Upfront payment for long-term users |

Hybrid genetic-wind driven [15] | Efficient mechanism to balance the load of smart grid | The cost is minimized | During scheduling, user comfort is compromised |

Hybrid artificial bee ant colony optimization [16] | Cloud resource management | Optimized response time and processing time | Load balancing algorithms can not handle complex cloud data centers |

An evolutionary accretive-comfort algorithm [17] | Control load of smart homes | Minimized energy consumption | During scheduling, user comfort is compromised |

Scheduling algorithm for electric vehicles charging and discharging [18] | Power supply station at public places | Balanced the load of electric vehicles during on-peak and off-peak hours | Disposal of batteries pollute the environment |

5G home energy management controller [19] | Balanced load of smart grid | Optimally balanced the load and provided communication architecture between smart homes and fog | Load balancing algorithms can not balance load of dramatically increasing smart users |

Name | Mathematical Formulation |
---|---|

UF1 | ${f}_{1}={x}_{1}+\frac{2}{{J}_{1}}{\sum}_{j\u03f5{J}_{1}}{[{x}_{j}-sin(6\pi {x}_{1}+\frac{j\pi}{n})]}^{2},{f}_{2}=1-\sqrt{x}+\frac{2}{|{J}_{2}|}{\sum}_{j\u03f5{J}_{2}}{[{x}_{j}-sin(6\pi {x}_{1}+\frac{j\pi}{n})]}^{2}$ ${J}_{1}$ = {j|j is odd and $2\le j\le n\}$, ${J}_{2}$ = {j|j is an even and $2\le j\le n\}$ |

UF2 | ${f}_{1}={x}_{1}+\frac{2}{|{J}_{1}|}{\sum}_{j\u03f5{J}_{1}}{y}_{j}^{2},{f}_{2}=1-\sqrt{x}+\frac{2}{|{J}_{2}|}{\sum}_{j\u03f5{J}_{2}}{y}_{j}^{2}$ ${J}_{1}$ = {j|j is odd and $2\le j\le n\}$, ${J}_{2}$ = {j|j is an even and $2\le j\le n\}$ ${y}_{j}=\{{x}_{j}-[0.3{x}_{1}^{2}cos(24\pi {x}_{1}+\frac{4j\pi}{n})+0.6{x}_{i}]cos(6\pi {x}_{1}+\frac{j\pi}{n})ifj\u03f5{J}_{1}\phantom{\rule{0ex}{0ex}}{x}_{j}-[0.3{x}_{1}^{2}cos(24\pi {x}_{1}+\frac{4j\pi}{n})+0.6{x}_{i}]sin(6\pi {x}_{1}+\frac{j\pi}{n})ifj\u03f5{J}_{2}\}$ |

UF3 | ${f}_{1}={x}_{1}+\frac{2}{|{J}_{1}|}{\sum}_{j\u03f5{J}_{1}}h({y}_{j}),{f}_{2}=1-{x}^{2}+\frac{2}{|{J}_{2}|}{\sum}_{j\u03f5J2}h({y}_{j})$ ${J}_{1}$ and ${J}_{2}$ are the same as those of UF1, ${y}_{j}={x}_{j}-sin(6\pi {x}_{1}+\frac{j\pi}{n}),j=2,3,\dots ,n,h(t)=\frac{|t|}{1+{e}^{2|t|}}$ |

UF4 | ${f}_{1}={x}_{1}+(\frac{1}{2N}+\u03f5)|sin(2N\pi {x}_{1})|+\frac{2}{|{J}_{1}|}{\sum}_{j\u03f5J1}h({y}_{i}),\phantom{\rule{0ex}{0ex}}{f}_{2}=1-{x}_{1}+(\frac{1}{2N}+\u03f5)|sin(2N\pi {x}_{1})|+\frac{2}{|{J}_{2}|}{\sum}_{j\u03f5J2}h({y}_{i})$ ${J}_{1}$ and ${J}_{2}$ are the identical to those of UF1, $\u03f5>0,{y}_{j}={x}_{j}-sin(6\pi {x}_{1}+\frac{j\pi}{n}),j=2,3,\dots ,n$ $h(t)=2{t}^{2}-cos(4\pi t)+1$ |

UF5 | ${f}_{1}={x}_{1}+max\{0,2(\frac{1}{2N}+\u03f5)sin(2N\pi {x}_{1})\}\frac{2}{|{J}_{1}|}(4{\sum}_{j\u03f5{J}_{1}}{{y}_{j}}^{2}-2{\prod}_{j\u03f5{J}_{1}}cos(\frac{{20}_{j\pi}}{\sqrt{j}}+1))\phantom{\rule{0ex}{0ex}}{f}_{2}=1-{x}_{1}+max\{0,2(\frac{1}{2N}+\u03f5)sin(2N\pi {x}_{1})\}\frac{2}{|{J}_{2}|}(4{\sum}_{j\u03f5{J}_{2}}{{y}_{j}}^{2}-2{\prod}_{j\u03f5{J}_{2}}cos(\frac{{20}_{j\pi}}{\sqrt{j}}+1))$ ${J}_{1}$ and ${J}_{2}$ are the identical to those of UF1, $\u03f5>0,{y}_{j}={x}_{j}-sin(6\pi {x}_{1}+\frac{j\pi}{n}),j=2,3,\dots ,n$ |

UF6 | ${f}_{1}=5\sqrt{{x}_{1}}+\frac{2}{|{J}_{1}|}{\sum}_{j\u03f5{J}_{1}}{{y}_{j}}^{2},{f}_{2}=1-5\sqrt{{x}_{1}}+\frac{2}{|{J}_{2}|}{\sum}_{j\u03f5{J}_{2}}{{y}_{j}}^{2}$ ${J}_{1}$ and ${J}_{2}$ are the identical to those of UF1, $\u03f5>0,{y}_{j}={x}_{j}-sin(6\pi {x}_{1}+\frac{j\pi}{n}),j=2,3,\dots ,n$ |

Name | Mathematical Formulation |
---|---|

UF7 | ${f}_{1}=cos(0.5{x}_{1}\pi )cos(0.5{x}_{2}\pi )+\frac{2}{|{J}_{1}|}{\sum}_{j\u03f5{J}_{1}}({x}_{j}-2{x}_{2}sin{(2\pi {x}_{1}+\frac{j\pi}{n})}^{2})$ ${f}_{2}=cos(0.5{x}_{1}\pi )sin(0.5{x}_{2}\pi )+\frac{2}{|{J}_{2}|}{\sum}_{j\u03f5{J}_{2}}({x}_{j}-2{x}_{2}sin{(2\pi {x}_{1}+\frac{j\pi}{n})}^{2})$ ${f}_{3}=sin(0.5{x}_{2}\pi )+\frac{2}{|{J}_{2}|}{\sum}_{j\u03f5{J}_{3}}({x}_{j}-2{x}_{2}sin{(2\pi {x}_{1}+\frac{j\pi}{n})}^{2})$ ${J}_{1}=\{j|3\le j\le n,$ and j-1 is a multiplication of 3}, ${J}_{2}=\{j|3\le j\le n,$ and j-2 is a multiplication of 3}, ${J}_{3}=\{j|3\le j\le n,$ and j is a multiplication of 3} |

UF8 | ${f}_{1}=0.5[max\{0,(1+\u03f5)(1-4{(2{x}_{1}-1)}^{2})\}+2{x}_{1}]{x}_{2}+\frac{2}{|{J}_{1}|}{\sum}_{j\u03f5{J}_{1}}({x}_{j}-2{x}_{2}sin{(2\pi {x}_{1}+\frac{j\pi}{n})}^{2})$ ${f}_{2}=0.5[max\{0,(1+\u03f5)(1-4{(2{x}_{1}-1)}^{2})\}+2{x}_{1}]{x}_{2}+\frac{2}{|{J}_{2}|}{\sum}_{j\u03f5{J}_{2}}({x}_{j}-2{x}_{2}sin{(2\pi {x}_{1}+\frac{j\pi}{n})}^{2})$ ${f}_{3}=1-{x}_{2}+\frac{2}{|{J}_{3}|}{\sum}_{j\u03f5{J}_{3}}({x}_{j}-2{x}_{2}sin{(2\pi {x}_{1}+\frac{j\pi}{n})}^{2})$ ${J}_{1}=\{j|3\le j\le n,$ and j-1 is a multiplication of 3}, ${J}_{2}=\{j|3\le j\le n,$ and j-2 is a multiplication of 3}, ${J}_{3}=\{j|3\le j\le n,$ and j is a multiplication of 3}, $\u03f5=0.1$ |

UF9 | ${f}_{1}=cos(0.5{x}_{1}\pi )cos(0.5{x}_{2}\pi )+\frac{2}{|{J}_{1}|}{\sum}_{j\u03f5{J}_{1}}[4{y}_{j}^{2}-cos(8\pi {y}_{j})+1]$ ${f}_{2}=cos(0.5{x}_{1}\pi )sin(0.5{x}_{2}\pi )+\frac{2}{|{J}_{2}|}{\sum}_{j\u03f5{J}_{2}}[4{y}_{j}^{2}-cos(8\pi {y}_{j})+1]$ ${f}_{3}=sin(0.5{x}_{2}\pi )+\frac{2}{|{J}_{3}|}{\sum}_{j\u03f5{J}_{3}}[4{y}_{j}^{2}-cos(8\pi {y}_{j})+1]$ ${J}_{1}=\{j|3\le j\le n,$ and j-1 is a multiplication of 3}, ${J}_{2}=\{j|3\le j\le n,$ and j-2 is a multiplication of 3}, ${J}_{3}=\{j|3\le j\le n,$ and j is a multiplication of 3}, |

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## Share and Cite

**MDPI and ACS Style**

Fatima, A.; Javaid, N.; Anjum Butt, A.; Sultana, T.; Hussain, W.; Bilal, M.; Hashmi, M.A.u.R.; Akbar, M.; Ilahi, M. An Enhanced Multi-Objective Gray Wolf Optimization for Virtual Machine Placement in Cloud Data Centers. *Electronics* **2019**, *8*, 218.
https://doi.org/10.3390/electronics8020218

**AMA Style**

Fatima A, Javaid N, Anjum Butt A, Sultana T, Hussain W, Bilal M, Hashmi MAuR, Akbar M, Ilahi M. An Enhanced Multi-Objective Gray Wolf Optimization for Virtual Machine Placement in Cloud Data Centers. *Electronics*. 2019; 8(2):218.
https://doi.org/10.3390/electronics8020218

**Chicago/Turabian Style**

Fatima, Aisha, Nadeem Javaid, Ayesha Anjum Butt, Tanzeela Sultana, Waqar Hussain, Muhammad Bilal, Muhammad Aqeel ur Rehman Hashmi, Mariam Akbar, and Manzoor Ilahi. 2019. "An Enhanced Multi-Objective Gray Wolf Optimization for Virtual Machine Placement in Cloud Data Centers" *Electronics* 8, no. 2: 218.
https://doi.org/10.3390/electronics8020218