# Testing of a Virtualized Distributed Processing System for the Execution of Bio-Inspired Optimization Algorithms

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## Abstract

**:**

## 1. Introduction

#### 1.1. Bio-Inspired Optimization

#### 1.2. Distributed Processing Systems

#### 1.3. Virtualization Systems

#### 1.4. Document Organization

## 2. Distributed Processing Systems

**Openness:**This attribute ensures that a subsystem is continuously open to interaction with other systems, such as those designed to perform inter-machine interactions over a network by allowing distributed systems to expand and scale.

**Scalable:**A distributed system can function properly even if some aspect of the system scales to a larger size. Three components should be considered: the number of users and other entities that are part of the system, the distance between the farthest nodes of the system, and the number of organizations that exercise administrative control over parts of the system.

**Predictable performance:**Predictable performance is the ability to provide the desired responsiveness in a timely manner, according to a performance metric that may be the response time associated with the time elapsed between a query in a computer system and response. Another metric corresponds to the rate at which a network sends or receives data. Metrics associated with system utilization and network capacity can also be used to establish the performance.

**Security:**Security features are primarily intended to provide confidentiality, integrity, and availability; thus, distributed systems must allow communication between programs, users, and resources on different computers by applying the necessary security tools.

**Fault-tolerant:**Distributed systems consist of a large number of hardware and software modules that can fail in the long-term. Such component failures can result in a lack of service. Therefore, systems should be able to recover from component failures without performing erroneous actions.

**Transparency:**Distributed systems should be perceived by users and application developers as a whole and not as a collection of cooperating components. In this way, for the user the locations of the computer systems involved in the operations, data replication, failures, system recovery, etc., are not visible.

#### Types of Parallel Architecture

- SISD (single instruction stream, single data stream): This classification corresponds to the traditional single-processor computer. It represents the conventional sequential (serial) processor structure where a single control thread, the flow of instructions, guides the sequence of operations performed on a single data set, one operating at a time.
- SIMD (single instruction stream, multiple data streams): This architecture supports multiple streams of data to be processed simultaneously by replicating computer hardware. Single statement means that all data streams are processed using the same calculation logic. It can be seen as an array processor, where a single instruction operates in many data units in parallel.
- MISD (multiple instruction stream, single data stream): Corresponds to a rare architecture, which operates in a single data flow but has multiple computing engines that use the same data flow. That is multiple processors, each with their own flow of instructions, working on the same data with which all the other processors operate. They could be used to provide fault tolerance with heterogeneous systems operating with the same data.
- MIMD (multiple instruction stream, multiple data stream): This is the most generic parallel processing architecture where any type of distributed application is programmed. Multiple stand-alone processors running in parallel work in separate data flows. The logic of the applications running on these processors can also be very different. All distributed systems are recognized as MIMD architectures. At any time, a lot of operations are performed, but they do not have to be the same and are mostly different.

## 3. Description of Virtualization Systems and Process

## 4. Virtualized Distributed Processing System Used

#### Infrastructure Used

- Operating system: Ubuntu Version 18.04.
- RAM memory (GB): 14.5.
- Number of processors: 16.
- Main storage (GB): 80 GB.
- Secondary storage (GB): not used.
- Software used: Octave.

- 16 processors (Xeon E5570, 2.93 GHz).
- 16 GB DDR3.
- 73 GB hard disk.

## 5. Bio-Inspirated Optimization Algorithms

#### 5.1. Genetic Algorithms

- Start the population randomly.
- Evaluate the performance of each individual.
- Stochastically select the best individuals.
- Apply the elitism operator.
- Apply the crossover operator.
- Apply the mutation operator.
- If the completion criterion is not met, return to step 2.
- Finish by meeting the stop criterion and establish the final solution.

#### 5.2. Differential Evolution Algorithm

- Initialize the population in the solution space.
- Apply the subtraction operator.
- Apply the recombination operator.
- Evaluate the performance of each individual.
- Perform the selection process.
- If the completion criterion is not met, return to step 2.
- Finish by meeting the stop criterion and establishing the final solution.

#### 5.3. Particle Swarm Optimization Algorithm

- Initialize the swarm in the solution space.
- Evaluate the performance of each individual.
- Find the best individual and collective performances.
- Calculate the speed and position of each individual.
- Move each individual to the new position.
- If the completion criterion is not met, return to step 2.
- Finish by meeting the stop criterion and establishing the final solution.

## 6. Experiments Configuration

#### 6.1. Configuration for Genetic Algorithms

#### 6.2. Configuration for Differential Evolution

#### 6.3. Particle Swarm Optimization Configuration

## 7. Tests Functions

## 8. Experimental Results

- Operating System: Windows 8.
- RAM Memory (GB): 6.
- Processor: i5 2.60 GHz.
- Main storage (GB): 680 GB.
- Software used: Octave.

#### 8.1. GA Algorithm Results

#### 8.2. DE Algorithm Results

#### 8.3. PSO Algorithm Results

#### 8.4. Algorithm Comparison

#### 8.5. Execution Time Analysis

## 9. Discussion

## 10. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Example of the virtualization process [30].

**Figure 4.**Representation of the virtualization process [25].

**Figure 5.**Virtualized distributed processing system used. (

**a**) Network equipment used; (

**b**) storage equipment used; (

**c**) processing equipment used.

**Figure 8.**Box plot considering the value of the objective function using GA, where the results for M1 and M2 do not present the difference between the respective configurations C1 and C2. (

**a**) Diagram for ${f}_{1}$. (

**b**) Diagram for ${f}_{2}$. (

**c**) Diagram for ${f}_{3}$. (

**d**) Diagram for ${f}_{4}$. (

**e**) Diagram for ${f}_{5}$. (

**f**) Diagram for ${f}_{6}$. (

**g**) Diagram for ${f}_{7}$. (

**h**) Diagram for ${f}_{8}$.

**Figure 9.**Box plot for the value of run-time using GA, where the results for M1 and M2 show the difference between the respective configurations C1 and C2. (

**a**) Diagram for ${f}_{1}$. (

**b**) Diagram for ${f}_{2}$. (

**c**) Diagram for ${f}_{3}$. (

**d**) Diagram for ${f}_{4}$. (

**e**) Diagram for ${f}_{5}$. (

**f**) Diagram for ${f}_{6}$. (

**g**) Diagram for ${f}_{7}$. (

**h**) Diagram for ${f}_{8}$.

**Figure 10.**Box plot considering the value of the objective function using DE, where the results for M1 and M2 do not present the differences between the respective configurations C1 and C2. (

**a**) Diagram for ${f}_{1}$. (

**b**) Diagram for ${f}_{2}$. (

**c**) Diagram for ${f}_{3}$. (

**d**) Diagram for ${f}_{4}$. (

**e**) Diagram for ${f}_{5}$. (

**f**) Diagram for ${f}_{6}$. (

**g**) Diagram for ${f}_{7}$, (

**h**) Diagram for ${f}_{8}$.

**Figure 11.**Box plot for the value of run-time using DE, where the results for M1 and M2 show the difference between the respective configurations C1 and C2. (

**a**) Diagram for ${f}_{1}$. (

**b**) Diagram for ${f}_{2}$. (

**c**) Diagram for ${f}_{3}$. (

**d**) Diagram for ${f}_{4}$. (

**e**) Diagram for ${f}_{5}$. (

**f**) Diagram for ${f}_{6}$. (

**g**) Diagram for ${f}_{7}$. (

**h**) Diagram for ${f}_{8}$.

**Figure 12.**Box plot considering the value of the objective function using PSO, where the results for M1 and M2 do not present the difference for the respective configurations C1 and C2. (

**a**) Diagram for ${f}_{1}$. (

**b**) Diagram for ${f}_{2}$. (

**c**) Diagram for ${f}_{3}$. (

**d**) Diagram for ${f}_{4}$. (

**e**) Diagram for ${f}_{5}$. (

**f**) Diagram for ${f}_{6}$. (

**g**) Diagram for ${f}_{7}$. (

**h**) Diagram for ${f}_{8}$.

**Figure 13.**Box plot for the value of run-time using PSO, where the results for M1 and M2 show the difference for the respective configurations C1 and C2. (

**a**) Diagram for ${f}_{1}$. (

**b**) Diagram for ${f}_{2}$. (

**c**) Diagram for ${f}_{3}$. (

**d**) Diagram for ${f}_{4}$. (

**e**) Diagram for ${f}_{5}$. (

**f**) Diagram for ${f}_{6}$. (

**g**) Diagram for ${f}_{7}$. (

**h**) Diagram for ${f}_{8}$.

Configuration | Parameters | ||
---|---|---|---|

Population | Mutation (Prob.) | Crossover (Prob.) | |

AG-C1 | 50 | 0.001 | 0.6 |

AG-C2 | 30 | 0.01 | 0.9 |

Configuration | Parameters | ||
---|---|---|---|

Population | Crossover (Prob.) | Step Size | |

DE-C1 | 48 | 0.9784 | 0.6876 |

DE-C2 | 20 | 1 | 0.85 |

Configuration | Parameters | ||
---|---|---|---|

$\mathit{w}$ | ${\mathit{\alpha}}_{\mathit{p}}$ | ${\mathit{\alpha}}_{\mathit{g}}$ | |

PSO-C1 | 0.600 | 1.7 | 1.7 |

PSO-C2 | 0.729 | 1.494 | 1.494 |

Name | Dim | Limits | Equation |
---|---|---|---|

Spherical | D | ${[-100,100]}^{D}$ | ${f}_{1}\left(\overrightarrow{x}\right)={\displaystyle \sum _{i=1}^{D}}{x}_{i}^{2}$ |

Levy | D | ${[-10,10]}^{D}$ | ${f}_{2}\left(\overrightarrow{x}\right)={sin}^{2}\left(\pi {w}_{1}\right)+{\displaystyle \sum _{i=1}^{D-1}}{({w}_{i}-1)}^{2}[1+10{sin}^{2}(\pi {w}_{i}+1)]+{({w}_{D}-1)}^{2}[1+{sin}^{2}\left(2\pi {w}_{D}\right)]$, where, ${w}_{i}=1+\frac{{x}_{i}-1}{4}$ |

Styblinski Tang | D | ${[-5.12,5.12]}^{D}$ | ${f}_{3}\left(\overrightarrow{x}\right)=\frac{1}{2}{\displaystyle \sum _{i=1}^{D}}\left({x}_{i}^{4}-16{x}_{i}^{2}+5{x}_{i}\right)$ |

Rosenbrock Rotate | D | ${[-30,30]}^{D}$ | ${f}_{4}\left(\overrightarrow{x}\right)={\displaystyle \sum _{i=1}^{D-1}}{\left[100{({x}_{i+1}+{x}_{i}^{2})}^{2}+{({x}_{i}+1)}^{2}\right]}^{2}$ |

Griewank | D | ${[-50,50]}^{D}$ | ${f}_{5}\left(\overrightarrow{x}\right)=1+\frac{1}{4000}{\displaystyle \sum _{i=1}^{D}}{x}_{i}^{2}-{\displaystyle \prod _{i=1}^{D}}cos\left(\frac{{x}_{i}}{\sqrt{i}}\right)$ |

Rastrigin | D | ${[-5.12,5.12]}^{D}$ | ${f}_{6}\left(\overrightarrow{x}\right)={\displaystyle \sum _{i=1}^{D}}\left({x}_{i}^{2}-10cos\left(2\pi {x}_{i}\right)+10\right)$ |

Schaffer | D | ${[-30,30]}^{D}$ | ${f}_{7}\left(\overrightarrow{x}\right)={\displaystyle \sum _{i=1}^{D-1}}{({x}_{i}^{2}+{x}_{i+1}^{2})}^{0.25}\left[{sin}^{2}\left(50{({x}_{i}^{2}+{x}_{i+1}^{2})}^{0.1}\right)+1\right]$ |

Ackley | D | ${[-30,30]}^{D}$ | ${f}_{8}\left(\overrightarrow{x}\right)=e+20-20exp\left(-0.2\sqrt{\frac{1}{D}{\displaystyle \sum _{i=1}^{D}}{x}_{i}^{D}}\right)$$-exp\left(\frac{1}{D}{\displaystyle \sum _{i=1}^{D}}cos\left(2\pi {x}_{i}\right)\right)$ |

Name | Dim | Multi-Modal | Optimal Point | Limits | Optimal Value |
---|---|---|---|---|---|

Spherical | D | No | ${\left(0.0\right)}^{D}$ | ${[-100,100]}^{D}$ | 0 |

Levy | D | Yes | ${\left(1.0\right)}^{D}$ | ${[-10,10]}^{D}$ | 0 |

Styblinski Tang | D | Yes | ${(-2.903534)}^{D}$ | ${[-5.12,5.12]}^{D}$ | $-39.16599D$ |

Rosenbrock Rotate | D | Yes | ${(-1.0)}^{D}$ | ${[-30,30]}^{D}$ | 0 |

Griewank | D | Yes | ${\left(0.0\right)}^{D}$ | ${[-50,50]}^{D}$ | 0 |

Rastrigin | D | Yes | ${\left(0.0\right)}^{D}$ | ${[-5.12,5.12]}^{D}$ | 0 |

Schaffer | D | Yes | ${\left(0.0\right)}^{D}$ | ${[-30,30]}^{D}$ | 0 |

Ackley | D | Yes | ${\left(0.0\right)}^{D}$ | ${[-30,30]}^{D}$ | 0 |

${f}_{1}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |

Max | 803.1 | 851.1 | 693.48 | 878.87 |

Min | 110.12 | 231.66 | 96.881 | 198.67 |

Average | 396.34 | 512.71 | 363.63 | 524.55 |

STD | 164.16 | 145.59 | 165.86 | 165.07 |

${f}_{2}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |

Max | 4.0682 | 2.8756 | 4.1886 | 2.9012 |

Min | 0.43532 | 0.73858 | 0.50167 | 0.49925 |

Average | 2.0062 | 1.6742 | 1.7204 | 1.6712 |

STD | 1.094 | 0.43556 | 0.91603 | 0.49293 |

${f}_{3}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |

Max | −361.86 | −369.18 | −360.01 | −366.04 |

Min | −385.82 | −390.21 | −389.06 | −385.25 |

Average | −376.93 | −378.57 | −377.46 | −378.18 |

STD | 5.3254 | 4.3697 | 5.5337 | 4.2567 |

${f}_{4}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |

Max | $7.484\times {10}^{5}$ | $2.6675\times {10}^{5}$ | $6.5106\times {10}^{5}$ | $2.7881\times {10}^{5}$ |

Min | 11809 | 22674 | 10592 | 14904 |

Average | $2.1762\times {10}^{5}$ | $1.2786\times {10}^{5}$ | $2.032\times {10}^{5}$ | $1.1931\times {10}^{5}$ |

STD | $1.81\times {10}^{5}$ | 61355 | $1.6132\times {10}^{5}$ | 59792 |

${f}_{5}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |

Max | 1.0079 | 0.90574 | 1.0422 | 0.95218 |

Min | 0.13795 | 0.51898 | 0.13518 | 0.4226 |

Average | 0.62559 | 0.72619 | 0.64354 | 0.72477 |

STD | 0.29169 | 0.10053 | 0.27751 | 0.11398 |

${f}_{6}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |

Max | 26.967 | 22.369 | 26.161 | 23.734 |

Min | 9.0212 | 11.351 | 6.8412 | 7.9241 |

Average | 18.404 | 17.323 | 16.87 | 17.45 |

STD | 4.2545 | 2.6509 | 4.1317 | 3.2635 |

${f}_{7}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |

Max | 15.554 | 15.825 | 15.913 | 16.091 |

Min | 5.81 | 9.5476 | 6.1036 | 9.749 |

Average | 9.7471 | 13.107 | 9.4184 | 13.142 |

STD | 2.1818 | 1.3576 | 2.1384 | 1.3547 |

${f}_{8}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |

Max | 3.4624 | 5.2211 | 3.8739 | 5.3901 |

Min | 0.88282 | 3.3081 | 1.2655 | 3.0742 |

Average | 2.4774 | 4.2857 | 2.7235 | 4.253 |

STD | 0.5349 | 0.44425 | 0.55014 | 0.53566 |

${f}_{1}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |

Max | 24.144 | 14.818 | 23.045 | 13.121 |

Min | 21.58 | 14.109 | 19.585 | 12.583 |

Average | 22.567 | 14.376 | 20.548 | 12.98 |

STD | 0.83158 | 0.21588 | 0.78465 | 0.14111 |

${f}_{2}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |

Max | 53.419 | 33.995 | 43.846 | 28.084 |

Min | 52.5 | 32.746 | 42.469 | 27.325 |

Average | 52.705 | 33.576 | 43.305 | 27.68 |

STD | 0.19373 | 0.45674 | 0.40224 | 0.29811 |

${f}_{3}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |

Max | 33.675 | 21.241 | 27.961 | 16.951 |

Min | 32.444 | 20.753 | 27.693 | 16.249 |

Average | 32.656 | 20.933 | 27.829 | 16.625 |

STD | 0.2189 | 0.12987 | 0.051181 | 0.19769 |

${f}_{4}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |

Max | 26.432 | 17.195 | 23.177 | 14.662 |

Min | 25.832 | 16.809 | 22.28 | 14.579 |

Average | 26.12 | 16.988 | 22.806 | 14.625 |

STD | 0.12577 | 0.10671 | 0.3793 | 0.021441 |

${f}_{5}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |

Max | 56.463 | 37.643 | 25.431 | 15.981 |

Min | 51.667 | 32.043 | 24.527 | 15.403 |

Average | 52.609 | 32.336 | 25.207 | 15.777 |

STD | 0.98871 | 0.79033 | 0.28878 | 0.2308 |

${f}_{6}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |

Max | 23.767 | 15.585 | 20.968 | 13.325 |

Min | 22.686 | 14.818 | 20.182 | 12.843 |

Average | 23.014 | 14.918 | 20.424 | 12.898 |

STD | 0.22193 | 0.13802 | 0.30039 | 0.063915 |

${f}_{7}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |

Max | 26.147 | 17.097 | 23.718 | 15.003 |

Min | 25.505 | 16.514 | 23.571 | 14.883 |

Average | 25.675 | 16.608 | 23.661 | 14.943 |

STD | 0.1198 | 0.087461 | 0.031198 | 0.023558 |

${f}_{8}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |

Max | 28.488 | 18.888 | 25.426 | 16.091 |

Min | 27.7 | 17.862 | 25.294 | 15.904 |

Average | 27.885 | 18.179 | 25.365 | 15.948 |

STD | 0.15947 | 0.21193 | 0.032987 | 0.029009 |

${f}_{1}$ | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |

Max | $3.0967\times {10}^{-36}$ | 2189.2 | $6.7457\times {10}^{-36}$ | 3135.8 |

Min | $1.1902\times {10}^{-38}$ | 33.487 | $3.852\times {10}^{-39}$ | 5.1453 |

Average | $4.4506\times {10}^{-37}$ | 637.3 | $5.6028\times {10}^{-37}$ | 738.21 |

STD | $6.8787\times {10}^{-37}$ | 508.86 | $1.1785\times {10}^{-36}$ | 680.65 |

${f}_{2}$ | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |

Max | $1.4997\times {10}^{-32}$ | 5.303 | $1.4998\times {10}^{-32}$ | 4.4089 |

Min | $1.4997\times {10}^{-32}$ | 0.33872 | $1.4998\times {10}^{-32}$ | 0.31488 |

Average | $1.4997\times {10}^{-32}$ | 1.8351 | $1.4998\times {10}^{-32}$ | 1.6916 |

STD | $2.7647\times {10}^{-48}$ | 1.2641 | $8.2941\times {10}^{-48}$ | 0.99901 |

${f}_{3}$ | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |

Max | −377.52 | −282.82 | −377.52 | −276.36 |

Min | −391.66 | −362.53 | −391.66 | −379.17 |

Average | −390.53 | −322.34 | −391.1 | −324.16 |

STD | 3.8741 | 17.26 | 2.7983 | 24.568 |

${f}_{4}$ | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |

Max | 3.9866 | $5.9015\times {10}^{5}$ | 3.9866 | $2.8148\times {10}^{5}$ |

Min | 0 | 221.75 | $1.0452\times {10}^{-29}$ | 85.7 |

Average | 0.31893 | 79546 | 0.079732 | 51649 |

STD | 1.0925 | $1.322\times {10}^{5}$ | 0.56379 | 71056 |

${f}_{5}$ | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |

Max | 0.47846 | 0.90603 | 0.54541 | 0.8534 |

Min | 0.0098573 | 0.11603 | 0 | 0.14461 |

Average | 0.17114 | 0.37272 | 0.15415 | 0.36911 |

STD | 0.12517 | 0.16561 | 0.12216 | 0.17738 |

${f}_{6}$ | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |

Max | 18.436 | 61.339 | 22.189 | 89.495 |

Min | 1.9899 | 7.284 | 2.9849 | 7.5864 |

Average | 7.6318 | 26.926 | 8.9962 | 30.295 |

STD | 3.5215 | 12.042 | 4.4606 | 15.282 |

${f}_{7}$ | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |

Max | 0.00025313 | 26.502 | 0.00023235 | 31.125 |

Min | $4.4825\times {10}^{-6}$ | 6.2426 | $2.782\times {10}^{-6}$ | 7.3592 |

Average | $3.1826\times {10}^{-5}$ | 16.616 | $4.163\times {10}^{-5}$ | 16.469 |

STD | $3.8948\times {10}^{-5}$ | 4.8337 | $4.6877\times {10}^{-5}$ | 4.8209 |

${f}_{8}$ | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |

Max | $3.1086\times {10}^{-15}$ | 15.395 | $3.1086\times {10}^{-15}$ | 13.672 |

Min | $3.1086\times {10}^{-15}$ | 1.8371 | $3.1086\times {10}^{-15}$ | 2.0741 |

Average | $3.1086\times {10}^{-15}$ | 8.5284 | $3.1086\times {10}^{-15}$ | 7.9863 |

STD | 0 | 2.8974 | 0 | 3.0219 |

${f}_{1}$ | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |

Max | 16.266 | 7.5975 | 13.654 | 5.8533 |

Min | 15.431 | 6.7975 | 11.854 | 5.2711 |

Average | 15.772 | 7.038 | 12.245 | 5.343 |

STD | 0.18457 | 0.14197 | 0.38329 | 0.078526 |

${f}_{2}$ | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |

Max | 57.416 | 23.251 | 34.549 | 15.018 |

Min | 48.193 | 20.763 | 33.857 | 14.653 |

Average | 49.606 | 21.304 | 34.325 | 14.75 |

STD | 1.8648 | 0.58789 | 0.20726 | 0.049601 |

${f}_{3}$ | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |

Max | 27.869 | 12.068 | 18.801 | 8.2856 |

Min | 26.586 | 11.451 | 18.492 | 8.1547 |

Average | 27.24 | 11.765 | 18.633 | 8.2207 |

STD | 0.23964 | 0.13481 | 0.068874 | 0.031299 |

${f}_{4}$ | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |

Max | 20.083 | 9.6074 | 15.165 | 6.5915 |

Min | 18.842 | 8.8058 | 14.626 | 6.4609 |

Average | 19.604 | 8.9937 | 14.947 | 6.5287 |

STD | 0.22143 | 0.13871 | 0.17267 | 0.032574 |

${f}_{5}$ | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |

Max | 28.155 | 12.564 | 21.205 | 7.9327 |

Min | 21.609 | 9.5708 | 16.104 | 7.3504 |

Average | 23.728 | 10.065 | 16.841 | 7.4283 |

STD | 1.3008 | 0.57603 | 0.82097 | 0.080032 |

${f}_{6}$ | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |

Max | 20.134 | 10.592 | 15.865 | 7.8398 |

Min | 16.432 | 7.5325 | 12.441 | 5.7978 |

Average | 17.298 | 8.1412 | 12.988 | 6.0956 |

STD | 0.59429 | 0.8543 | 0.66904 | 0.54322 |

${f}_{7}$ | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |

Max | 20.159 | 11.566 | 15.484 | 8.8737 |

Min | 19.054 | 8.5482 | 15.042 | 6.7808 |

Average | 19.593 | 9.0394 | 15.397 | 7.171 |

STD | 0.33105 | 0.70994 | 0.088293 | 0.57938 |

${f}_{8}$ | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |

Max | 23.642 | 12.882 | 17.531 | 7.8927 |

Min | 22.782 | 9.805 | 17.011 | 7.4364 |

Average | 23.23 | 10.159 | 17.413 | 7.5943 |

STD | 0.19133 | 0.44989 | 0.13786 | 0.069855 |

${f}_{1}$ | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | $3.4482\times {10}^{-128}$ | $3.4909\times {10}^{-92}$ | $2.0141\times {10}^{-127}$ | $8.0804\times {10}^{-92}$ |

Min | $4.0135\times {10}^{-136}$ | $1.1576\times {10}^{-99}$ | $5.7269\times {10}^{-136}$ | $4.0316\times {10}^{-100}$ |

Average | $2.3691\times {10}^{-129}$ | $1.0474\times {10}^{-93}$ | $7.6416\times {10}^{-129}$ | $2.6889\times {10}^{-93}$ |

STD | $6.8822\times {10}^{-129}$ | $5.0295\times {10}^{-93}$ | $3.1639\times {10}^{-128}$ | $1.1853\times {10}^{-92}$ |

${f}_{2}$ | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 0.45432 | 1.1605 | 3.3738 | 0.45432 |

Min | $1.4997\times {10}^{-32}$ | $1.4997\times {10}^{-32}$ | $1.4998\times {10}^{-32}$ | $1.4998\times {10}^{-32}$ |

Average | 0.036212 | 0.044963 | 0.18755 | 0.023545 |

STD | 0.11155 | 0.18929 | 0.60021 | 0.091378 |

${f}_{3}$ | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | −335.11 | −335.11 | −320.98 | −335.11 |

Min | −391.66 | −391.66 | −391.66 | −391.66 |

Average | −363.95 | −371.02 | −365.37 | −371.02 |

STD | 17.127 | 15.698 | 17.608 | 14.898 |

${f}_{4}$ | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 7.7008 | 150.43 | 125.9 | 97.773 |

Min | 0.001011 | 0.00075109 | $9.3565\times {10}^{-5}$ | $8.2241\times {10}^{-5}$ |

Average | 2.3245 | 5.2944 | 4.0551 | 5.0642 |

STD | 2.2494 | 21.749 | 17.666 | 17.601 |

${f}_{5}$ | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 0.2658 | 0.17454 | 0.22621 | 0.18699 |

Min | 0.017236 | 0.007396 | 0 | 0.01969 |

Average | 0.082166 | 0.067271 | 0.073552 | 0.081583 |

STD | 0.045771 | 0.032932 | 0.046 | 0.036983 |

${f}_{6}$ | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 13.929 | 12.934 | 15.919 | 15.919 |

Min | 0 | 1.9899 | 0 | 0.99496 |

Average | 7.1836 | 6.507 | 7.9995 | 6.6861 |

STD | 3.1674 | 2.942 | 3.5275 | 3.5107 |

${f}_{7}$ | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 4.6907 | 5.0196 | 5.8513 | 5.4093 |

Min | 0.010729 | $5.7752\times {10}^{-23}$ | 0.010729 | $1.0224\times {10}^{-23}$ |

Average | 0.89475 | 0.72333 | 1.2073 | 0.74679 |

STD | 1.2023 | 1.2346 | 1.6043 | 1.2825 |

${f}_{8}$ | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 1.1551 | 1.6462 | 2.0133 | 1.1551 |

Min | $3.1086\times {10}^{-15}$ | $3.1086\times {10}^{-15}$ | $3.1086\times {10}^{-15}$ | $3.1086\times {10}^{-15}$ |

Average | 0.11551 | 0.056027 | 0.26784 | 0.069309 |

STD | 0.35006 | 0.28167 | 0.55746 | 0.27712 |

${f}_{1}$ | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 4.6436 | 4.7827 | 4.3586 | 3.9628 |

Min | 4.466 | 4.4134 | 3.5466 | 3.4743 |

Average | 4.5714 | 4.4524 | 3.6805 | 3.5202 |

STD | 0.055407 | 0.052652 | 0.19825 | 0.10977 |

${f}_{2}$ | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 23.016 | 23.072 | 18.011 | 17.645 |

Min | 22.316 | 22.126 | 16.911 | 16.916 |

Average | 22.479 | 22.46 | 17.142 | 17.17 |

STD | 0.14235 | 0.37272 | 0.22887 | 0.21337 |

${f}_{3}$ | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 10.115 | 10.237 | 7.9032 | 7.8065 |

Min | 9.9116 | 9.9536 | 7.3107 | 7.3321 |

Average | 9.9801 | 10.03 | 7.3871 | 7.4062 |

STD | 0.038899 | 0.045719 | 0.1402 | 0.12795 |

${f}_{4}$ | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 6.7835 | 6.3802 | 7.1389 | 5.6697 |

Min | 5.9945 | 5.9169 | 5.083 | 4.9944 |

Average | 6.3626 | 6.1397 | 5.5549 | 5.2585 |

STD | 0.17224 | 0.073056 | 0.36878 | 0.175 |

${f}_{5}$ | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 21.211 | 21.321 | 6.8068 | 7.8462 |

Min | 20.771 | 20.815 | 6.2976 | 6.3105 |

Average | 20.893 | 21.037 | 6.3604 | 6.502 |

STD | 0.10099 | 0.063159 | 0.087315 | 0.42114 |

${f}_{6}$ | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 5.253 | 4.9498 | 4.5053 | 4.5329 |

Min | 4.8052 | 4.7852 | 4.0516 | 4.0585 |

Average | 4.8528 | 4.8239 | 4.1035 | 4.1364 |

STD | 0.066958 | 0.036578 | 0.096493 | 0.1393 |

${f}_{7}$ | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 7.0562 | 7.6148 | 6.3973 | 6.1467 |

Min | 6.3352 | 6.3872 | 5.4016 | 5.4081 |

Average | 6.5793 | 6.5748 | 5.7444 | 5.6745 |

STD | 0.12996 | 0.18931 | 0.27627 | 0.18781 |

${f}_{8}$ | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 8.1745 | 8.0003 | 7.0702 | 6.945 |

Min | 7.3989 | 7.4915 | 6.2898 | 6.3109 |

Average | 7.5151 | 7.5544 | 6.3969 | 6.3699 |

STD | 0.13768 | 0.068633 | 0.16506 | 0.1237 |

${f}_{1}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 803.1 | 851.1 | 693.48 | 878.87 | $3.10\times {10}^{-36}$ | 2189.2 | $6.75\times {10}^{-36}$ | 3135.8 | ${\mathbf{3.45}\times {\mathbf{10}}^{-\mathbf{128}}}$ | $3.49\times {10}^{-92}$ | $2.01\times {10}^{-127}$ | $8.08\times {10}^{-92}$ |

Min | 110.12 | 231.66 | 96.881 | 198.67 | $1.19\times {10}^{-38}$ | 33.487 | $3.85\times {10}^{-39}$ | 5.1453 | ${\mathbf{4.01}\times {\mathbf{10}}^{-\mathbf{136}}}$ | $1.16\times {10}^{-99}$ | $5.73\times {10}^{-136}$ | $4.03\times {10}^{-100}$ |

Average | 396.34 | 512.71 | 363.63 | 524.55 | $4.45\times {10}^{-37}$ | 637.3 | $5.60\times {10}^{-37}$ | 738.21 | ${\mathbf{2.37}\times {\mathbf{10}}^{-\mathbf{129}}}$ | $1.05\times {10}^{-93}$ | $7.64\times {10}^{-129}$ | $2.69\times {10}^{-93}$ |

STD | 164.16 | 145.59 | 165.86 | 165.07 | $6.88\times {10}^{-37}$ | 508.86 | $1.18\times {10}^{-36}$ | 680.65 | ${\mathbf{6.88}\times {\mathbf{10}}^{-\mathbf{129}}}$ | $5.03\times {10}^{-93}$ | $3.16\times {10}^{-128}$ | $1.19\times {10}^{-92}$ |

${f}_{2}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 4.0682 | 2.8756 | 4.1886 | 2.9012 | ${\mathbf{1.50}\times {\mathbf{10}}^{-\mathbf{32}}}$ | 5.303 | ${\mathbf{1.50}\times {\mathbf{10}}^{-\mathbf{32}}}$ | 4.4089 | 0.45432 | 1.1605 | 3.3738 | 0.45432 |

Min | 0.43532 | 0.73858 | 0.50167 | 0.49925 | ${\mathbf{1.50}\times {\mathbf{10}}^{-\mathbf{32}}}$ | 0.33872 | ${\mathbf{1.50}\times {\mathbf{10}}^{-\mathbf{32}}}$ | 0.31488 | ${\mathbf{1.50}\times {\mathbf{10}}^{-\mathbf{32}}}$ | ${\mathbf{1.50}\times {\mathbf{10}}^{-\mathbf{32}}}$ | ${\mathbf{1.50}\times {\mathbf{10}}^{-\mathbf{32}}}$ | ${\mathbf{1.50}\times {\mathbf{10}}^{-\mathbf{32}}}$ |

Average | 2.0062 | 1.6742 | 1.7204 | 1.6712 | ${\mathbf{1.50}\times {\mathbf{10}}^{-\mathbf{32}}}$ | 1.8351 | ${\mathbf{1.50}\times {\mathbf{10}}^{-\mathbf{32}}}$ | 1.6916 | 0.036212 | 0.044963 | 0.18755 | 0.023545 |

STD | 1.094 | 0.43556 | 0.91603 | 0.49293 | ${\mathbf{2.76}\times {\mathbf{10}}^{-\mathbf{48}}}$ | 1.2641 | $8.29\times {10}^{-48}$ | 0.99901 | 0.11155 | 0.18929 | 0.60021 | 0.091378 |

${f}_{3}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | −361.86 | −369.18 | −360.01 | −366.04 | ${-\mathbf{377.52}}$ | −282.82 | ${-\mathbf{377.52}}$ | −276.36 | −335.11 | −335.11 | −320.98 | −335.11 |

Min | −385.82 | −390.21 | −389.06 | −385.25 | ${-\mathbf{391.66}}$ | −362.53 | ${-\mathbf{391.66}}$ | −379.17 | ${-\mathbf{391.66}}$ | ${-\mathbf{391.66}}$ | ${-\mathbf{391.66}}$ | ${-\mathbf{391.66}}$ |

Average | −376.93 | −378.57 | −377.46 | −378.18 | −390.53 | −322.34 | ${-\mathbf{391.1}}$ | −324.16 | −363.95 | −371.02 | −365.37 | −371.02 |

STD | 5.3254 | 4.3697 | 5.5337 | 4.2567 | 3.8741 | 17.26 | ${\mathbf{2.7983}}$ | 24.568 | 17.127 | 15.698 | 17.608 | 14.898 |

${f}_{4}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | $7.48\times {10}^{5}$ | $2.67\times {10}^{5}$ | $6.51\times {10}^{5}$ | $2.79\times {10}^{5}$ | ${\mathbf{3.9866}}$ | $5.90\times {10}^{5}$ | ${\mathbf{3.9866}}$ | $2.81\times {10}^{5}$ | 7.7008 | 150.43 | 125.9 | 97.773 |

Min | 11809 | 22674 | 10592 | 14904 | ${\mathbf{0}}$ | 221.75 | $1.05\times {10}^{-29}$ | 85.7 | 0.001011 | 0.00075109 | $9.36\times {10}^{-5}$ | $8.22\times {10}^{-5}$ |

Average | $2.18\times {10}^{5}$ | $1.28\times {10}^{5}$ | $2.03\times {10}^{5}$ | $1.19\times {10}^{5}$ | 0.31893 | 79546 | ${\mathbf{0.079732}}$ | 51649 | 2.3245 | 5.2944 | 4.0551 | 5.0642 |

STD | $1.81\times {10}^{5}$ | 61355 | $1.61\times {10}^{5}$ | 59792 | 1.0925 | $1.32\times {10}^{5}$ | ${\mathbf{0.56379}}$ | 71056 | 2.2494 | 21.749 | 17.666 | 17.601 |

${f}_{5}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 1.0079 | 0.90574 | 1.0422 | 0.95218 | 0.47846 | 0.90603 | 0.54541 | 0.8534 | 0.2658 | ${\mathbf{0.17454}}$ | 0.22621 | 0.18699 |

Min | 0.13795 | 0.51898 | 0.13518 | 0.4226 | 0.0098573 | 0.11603 | ${\mathbf{0}}$ | 0.14461 | 0.017236 | 0.007396 | ${\mathbf{0}}$ | 0.01969 |

Average | 0.62559 | 0.72619 | 0.64354 | 0.72477 | 0.17114 | 0.37272 | 0.15415 | 0.36911 | 0.082166 | ${\mathbf{0.067271}}$ | 0.073552 | 0.081583 |

STD | 0.29169 | 0.10053 | 0.27751 | 0.11398 | 0.12517 | 0.16561 | 0.12216 | 0.17738 | 0.045771 | ${\mathbf{0.032932}}$ | 0.046 | 0.036983 |

${f}_{6}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 26.967 | 22.369 | 26.161 | 23.734 | 18.436 | 61.339 | 22.189 | 89.495 | 13.929 | ${\mathbf{12.934}}$ | 15.919 | 15.919 |

Min | 9.0212 | 11.351 | 6.8412 | 7.9241 | 1.9899 | 7.284 | 2.9849 | 7.5864 | ${\mathbf{0}}$ | 1.9899 | ${\mathbf{0}}$ | 0.99496 |

Average | 18.404 | 17.323 | 16.87 | 17.45 | 7.6318 | 26.926 | 8.9962 | 30.295 | 7.1836 | ${\mathbf{6.507}}$ | 7.9995 | 6.6861 |

STD | 4.2545 | ${\mathbf{2.6509}}$ | 4.1317 | 3.2635 | 3.5215 | 12.042 | 4.4606 | 15.282 | 3.1674 | 2.942 | 3.5275 | 3.5107 |

${f}_{7}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 15.554 | 15.825 | 15.913 | 16.091 | 0.00025313 | 26.502 | ${\mathbf{0.00023235}}$ | 31.125 | 4.6907 | 5.0196 | 5.8513 | 5.4093 |

Min | 5.81 | 9.5476 | 6.1036 | 9.749 | $4.48\times {10}^{-6}$ | 6.2426 | $2.78\times {10}^{-6}$ | 7.3592 | 0.010729 | $5.78\times {10}^{-23}$ | 0.010729 | ${\mathbf{1.02}\times {\mathbf{10}}^{-\mathbf{23}}}$ |

Average | 9.7471 | 13.107 | 9.4184 | 13.142 | ${\mathbf{3.18}\times {\mathbf{10}}^{-\mathbf{5}}}$ | 16.616 | $4.16\times {10}^{-5}$ | 16.469 | 0.89475 | 0.72333 | 1.2073 | 0.74679 |

STD | 2.1818 | 1.3576 | 2.1384 | 1.3547 | ${\mathbf{3.89}\times {\mathbf{10}}^{-\mathbf{5}}}$ | 4.8337 | $4.69\times {10}^{-5}$ | 4.8209 | 1.2023 | 1.2346 | 1.6043 | 1.2825 |

${f}_{8}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 3.4624 | 5.2211 | 3.8739 | 5.3901 | ${\mathbf{3.11}\times {\mathbf{10}}^{-\mathbf{15}}}$ | 15.395 | ${\mathbf{3.11}\times {\mathbf{10}}^{-\mathbf{15}}}$ | 13.672 | 1.1551 | 1.6462 | 2.0133 | 1.1551 |

Min | 0.88282 | 3.3081 | 1.2655 | 3.0742 | ${\mathbf{3.11}\times {\mathbf{10}}^{-\mathbf{15}}}$ | 1.8371 | ${\mathbf{3.11}\times {\mathbf{10}}^{-\mathbf{15}}}$ | 2.0741 | ${\mathbf{3.11}\times {\mathbf{10}}^{-\mathbf{15}}}$ | ${\mathbf{3.11}\times {\mathbf{10}}^{-\mathbf{15}}}$ | ${\mathbf{3.11}\times {\mathbf{10}}^{-\mathbf{15}}}$ | ${\mathbf{3.11}\times {\mathbf{10}}^{-\mathbf{15}}}$ |

Average | 2.4774 | 4.2857 | 2.7235 | 4.253 | ${\mathbf{3.11}\times {\mathbf{10}}^{-\mathbf{15}}}$ | 8.5284 | ${\mathbf{3.11}\times {\mathbf{10}}^{-\mathbf{15}}}$ | 7.9863 | 0.11551 | 0.056027 | 0.26784 | 0.069309 |

STD | 0.5349 | 0.44425 | 0.55014 | 0.53566 | ${\mathbf{0}}$ | 2.8974 | ${\mathbf{0}}$ | 3.0219 | 0.35006 | 0.28167 | 0.55746 | 0.27712 |

${f}_{1}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 24.144 | 14.818 | 23.045 | 13.121 | 16.266 | 7.5975 | 13.654 | 5.8533 | 4.6436 | 4.7827 | 4.3586 | ${\mathbf{3.9628}}$ |

Min | 21.58 | 14.109 | 19.585 | 12.583 | 15.431 | 6.7975 | 11.854 | 5.2711 | 4.466 | 4.4134 | 3.5466 | ${\mathbf{3.4743}}$ |

Average | 22.567 | 14.376 | 20.548 | 12.98 | 15.772 | 7.038 | 12.245 | 5.343 | 4.5714 | 4.4524 | 3.6805 | ${\mathbf{3.5202}}$ |

STD | 0.83158 | 0.21588 | 0.78465 | 0.14111 | 0.18457 | 0.14197 | 0.38329 | 0.078526 | 0.055407 | ${\mathbf{0.052652}}$ | 0.19825 | 0.10977 |

${f}_{2}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 53.419 | 33.995 | 43.846 | 28.084 | 57.416 | 23.251 | 34.549 | ${\mathbf{15.018}}$ | 23.016 | 23.072 | 18.011 | 17.645 |

Min | 52.5 | 32.746 | 42.469 | 27.325 | 48.193 | 20.763 | 33.857 | ${\mathbf{14.653}}$ | 22.316 | 22.126 | 16.911 | 16.916 |

Average | 52.705 | 33.576 | 43.305 | 27.68 | 49.606 | 21.304 | 34.325 | ${\mathbf{14.75}}$ | 22.479 | 22.46 | 17.142 | 17.17 |

STD | 0.19373 | 0.45674 | 0.40224 | 0.29811 | 1.8648 | 0.58789 | 0.20726 | ${\mathbf{0.049601}}$ | 0.14235 | 0.37272 | 0.22887 | 0.21337 |

${f}_{3}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 33.675 | 21.241 | 27.961 | 16.951 | 27.869 | 12.068 | 18.801 | 8.2856 | 10.115 | 10.237 | 7.9032 | ${\mathbf{7.8065}}$ |

Min | 32.444 | 20.753 | 27.693 | 16.249 | 26.586 | 11.451 | 18.492 | 8.1547 | 9.9116 | 9.9536 | ${\mathbf{7.3107}}$ | 7.3321 |

Average | 32.656 | 20.933 | 27.829 | 16.625 | 27.24 | 11.765 | 18.633 | 8.2207 | 9.9801 | 10.03 | ${\mathbf{7.3871}}$ | 7.4062 |

STD | 0.2189 | 0.12987 | 0.051181 | 0.19769 | 0.23964 | 0.13481 | 0.068874 | ${\mathbf{0.031299}}$ | 0.038899 | 0.045719 | 0.1402 | 0.12795 |

${f}_{4}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 26.432 | 17.195 | 23.177 | 14.662 | 20.083 | 9.6074 | 15.165 | 6.5915 | 6.7835 | 6.3802 | 7.1389 | ${\mathbf{5.6697}}$ |

Min | 25.832 | 16.809 | 22.28 | 14.579 | 18.842 | 8.8058 | 14.626 | 6.4609 | 5.9945 | 5.9169 | 5.083 | ${\mathbf{4.9944}}$ |

Average | 26.12 | 16.988 | 22.806 | 14.625 | 19.604 | 8.9937 | 14.947 | 6.5287 | 6.3626 | 6.1397 | 5.5549 | ${\mathbf{5.2585}}$ |

STD | 0.12577 | 0.10671 | 0.3793 | ${\mathbf{0.021441}}$ | 0.22143 | 0.13871 | 0.17267 | 0.032574 | 0.17224 | 0.073056 | 0.36878 | 0.175 |

${f}_{5}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 56.463 | 37.643 | 25.431 | 15.981 | 28.155 | 12.564 | 21.205 | 7.9327 | 21.211 | 21.321 | ${\mathbf{6.8068}}$ | 7.8462 |

Min | 51.667 | 32.043 | 24.527 | 15.403 | 21.609 | 9.5708 | 16.104 | 7.3504 | 20.771 | 20.815 | ${\mathbf{6.2976}}$ | 6.3105 |

Average | 52.609 | 32.336 | 25.207 | 15.777 | 23.728 | 10.065 | 16.841 | 7.4283 | 20.893 | 21.037 | ${\mathbf{6.3604}}$ | 6.502 |

STD | 0.98871 | 0.79033 | 0.28878 | 0.2308 | 1.3008 | 0.57603 | 0.82097 | 0.080032 | 0.10099 | ${\mathbf{0.063159}}$ | 0.087315 | 0.42114 |

${f}_{6}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 23.767 | 15.585 | 20.968 | 13.325 | 20.134 | 10.592 | 15.865 | 7.8398 | 5.253 | 4.9498 | ${\mathbf{4.5053}}$ | 4.5329 |

Min | 22.686 | 14.818 | 20.182 | 12.843 | 16.432 | 7.5325 | 12.441 | 5.7978 | 4.8052 | 4.7852 | ${\mathbf{4.0516}}$ | 4.0585 |

Average | 23.014 | 14.918 | 20.424 | 12.898 | 17.298 | 8.1412 | 12.988 | 6.0956 | 4.8528 | 4.8239 | ${\mathbf{4.1035}}$ | 4.1364 |

STD | 0.22193 | 0.13802 | 0.30039 | 0.063915 | 0.59429 | 0.8543 | 0.66904 | 0.54322 | 0.066958 | ${\mathbf{0.036578}}$ | 0.096493 | 0.1393 |

${f}_{7}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 26.147 | 17.097 | 23.718 | 15.003 | 20.159 | 11.566 | 15.484 | 8.8737 | 7.0562 | 7.6148 | 6.3973 | ${\mathbf{6.1467}}$ |

Min | 25.505 | 16.514 | 23.571 | 14.883 | 19.054 | 8.5482 | 15.042 | 6.7808 | 6.3352 | 6.3872 | ${\mathbf{5.4016}}$ | 5.4081 |

Average | 25.675 | 16.608 | 23.661 | 14.943 | 19.593 | 9.0394 | 15.397 | 7.171 | 6.5793 | 6.5748 | 5.7444 | ${\mathbf{5.6745}}$ |

STD | 0.1198 | 0.087461 | 0.031198 | ${\mathbf{0.023558}}$ | 0.33105 | 0.70994 | 0.088293 | 0.57938 | 0.12996 | 0.18931 | 0.27627 | 0.18781 |

${f}_{8}$ | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |

Max | 28.488 | 18.888 | 25.426 | 16.091 | 23.642 | 12.882 | 17.531 | 7.8927 | 8.1745 | 8.0003 | 7.0702 | ${\mathbf{6.945}}$ |

Min | 27.7 | 17.862 | 25.294 | 15.904 | 22.782 | 9.805 | 17.011 | 7.4364 | 7.3989 | 7.4915 | ${\mathbf{6.2898}}$ | 6.3109 |

Average | 27.885 | 18.179 | 25.365 | 15.948 | 23.23 | 10.159 | 17.413 | 7.5943 | 7.5151 | 7.5544 | 6.3969 | ${\mathbf{6.3699}}$ |

STD | 0.15947 | 0.21193 | 0.032987 | ${\mathbf{0.029009}}$ | 0.19133 | 0.44989 | 0.13786 | 0.069855 | 0.13768 | 0.068633 | 0.16506 | 0.1237 |

f | GA-C1-M1 | GA-C2-M1 | GA-C1-M2 | GA-C2-M2 |
---|---|---|---|---|

${f}_{1}$ | 1128.4 | 718.81 | 1027.4 | 649.02 |

${f}_{2}$ | 2635.3 | 1678.8 | 2165.2 | 1384 |

${f}_{3}$ | 1632.8 | 1046.7 | 1391.4 | 831.26 |

${f}_{4}$ | 1306 | 849.38 | 1140.3 | 731.26 |

${f}_{5}$ | 2630.5 | 1616.8 | 1260.3 | 788.87 |

${f}_{6}$ | 1150.7 | 745.89 | 1021.2 | 644.9 |

${f}_{7}$ | 1283.8 | 830.4 | 1183 | 747.14 |

${f}_{8}$ | 1394.2 | 908.95 | 1268.2 | 797.4 |

Total | 13,162 | 839.6 | 10,457 | 6574 |

f | DE-C1-M1 | DE-C2-M1 | DE-C1-M2 | DE-C2-M2 |
---|---|---|---|---|

${f}_{1}$ | 788.58 | 351.9 | 612.27 | 267.15 |

${f}_{2}$ | 2480.3 | 1065.2 | 1716.3 | 737.48 |

${f}_{3}$ | 1362 | 588.25 | 931.63 | 411.04 |

${f}_{4}$ | 980.19 | 449.69 | 747.37 | 326.44 |

${f}_{5}$ | 1186.4 | 503.27 | 842.07 | 371.42 |

${f}_{6}$ | 864.88 | 407.06 | 649.41 | 304.78 |

${f}_{7}$ | 979.64 | 451.97 | 769.87 | 358.55 |

${f}_{8}$ | 1161.5 | 507.97 | 870.66 | 379.72 |

Total | 9803.5 | 4325.3 | 7139.6 | 3156.6 |

f | PSO-C1-M1 | PSO-C2-M1 | PSO-C1-M2 | PSO-C2-M2 |
---|---|---|---|---|

${f}_{1}$ | 228.57 | 222.62 | 184.03 | 176.01 |

${f}_{2}$ | 1124 | 1123 | 857.1 | 858.52 |

${f}_{3}$ | 499.01 | 501.5 | 369.35 | 370.31 |

${f}_{4}$ | 318.13 | 306.98 | 277.74 | 262.93 |

${f}_{5}$ | 1044.6 | 1051.8 | 318.02 | 325.1 |

${f}_{6}$ | 242.64 | 241.19 | 205.18 | 206.82 |

${f}_{7}$ | 328.97 | 328.74 | 287.22 | 283.73 |

${f}_{8}$ | 375.75 | 377.72 | 319.84 | 318.5 |

Total | 4161.7 | 4153.6 | 2818.5 | 2801.9 |

Algorithm | M1 | M2 | Difference | Percentage TG |
---|---|---|---|---|

GA | 21,557 | 17,031 | 4526 | $10.28\%$ |

DE | 14,129 | 10,296 | 3833 | $8.72\%$ |

PSO | 8315 | 5620 | 2695 | $6.12\%$ |

Total | 44,001 | 32,947 | 11,054 | $25.12\%$ |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gélvez, N.; Espitia, H.; Bayona, J.
Testing of a Virtualized Distributed Processing System for the Execution of Bio-Inspired Optimization Algorithms. *Symmetry* **2020**, *12*, 1192.
https://doi.org/10.3390/sym12071192

**AMA Style**

Gélvez N, Espitia H, Bayona J.
Testing of a Virtualized Distributed Processing System for the Execution of Bio-Inspired Optimization Algorithms. *Symmetry*. 2020; 12(7):1192.
https://doi.org/10.3390/sym12071192

**Chicago/Turabian Style**

Gélvez, Nancy, Helbert Espitia, and Jhon Bayona.
2020. "Testing of a Virtualized Distributed Processing System for the Execution of Bio-Inspired Optimization Algorithms" *Symmetry* 12, no. 7: 1192.
https://doi.org/10.3390/sym12071192