# Color Revolution: A Novel Operator for Imperialist Competitive Algorithm in Solving Cloud Computing Service Composition Problem

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

**Example**

**1.**

**Example**

**2.**

#### 1.1. Literature Review

## 2. Problem and Algorithm Description

#### 2.1. Service Time-Cost Optimization in Cloud Computing Service Composition (STCOCCSC)

#### 2.2. Imperialist Competitive Algorithm (ICA)

## 3. Imperialist Competitive Algorithm with the Color Revolution Operator (ICACRO)

#### 3.1. Color Revolution Operator (CRO)

#### 3.2. ICA with CRO (ICACRO)

## 4. Experimental Design

#### 4.1. ICACRO Implementation and Execution

#### 4.2. Definitions

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

**Definition**

**4.**

**Definition**

**5.**

**Definition**

**6.**

**Definition**

**7.**

## 5. Comparison of Results and Discussion

#### 5.1. ICACRO-C or ICACRO-I?

#### 5.2. Fps or Fs?

#### 5.3. Performance Statistical Test

## 6. Conclusions and Directions for Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Country movement [20].

**Figure 5.**Pseudocode of applied CRO in imperialist competitive algorithm with color revolution operator (ICACRO).

**Figure 8.**Comparison of the total service time-costs obtained using the four algorithms for problem A: (

**a**) after 1500 iterations and (

**b**) after 6000 iterations.

**Figure 9.**Comparison of the total service time-costs obtained using the four algorithms for problem B: (

**a**) after 1500 iterations and (

**b**) after 6000 iterations.

**Figure 10.**Comparison of the total service time-costs obtained using the four algorithms for problem C: (

**a**) after 1500 iterations and (

**b**) after 6000 iterations.

**Figure 11.**Comparison of the total service time-costs obtained using the four algorithms for problem D: (

**a**) after 1500 iterations and (

**b**) after 6000 iterations.

**Figure 12.**Comparison of the total service time-costs obtained using the four algorithms for problem E: (

**a**) after 1500 iterations and (

**b**) after 6000 iterations.

**Figure 13.**Optimality values of the four algorithms based on niching particle swarm optimization (PSO) for problems A–E.

**Table 1.**Mapping description of key terms of service time-cost optimization problem in CCSC (STCOCCSC) and imperialist competitive algorithm (ICA).

STCOCCSC | ICA | Optimization |
---|---|---|

Composite Service (CS) | Country | Solution |

Merit Value (MV) | Power of Country | Objective Function |

Problem A | Problem B | Problem C | Problem D | Problem E | |
---|---|---|---|---|---|

ICACRO-C Best result after 1500 iterations (Cfps) | 34.53 | 69.63 | 103.02 | 147.96 | 190.64 |

ICACRO-C Best result after 6000 iterations (Cfs) | 34.15 | 66.94 | 98.49 | 132.70 | 165.87 |

ICACRO-C 1500-iteration execution time (CfpsT) | 6.5 s | 13.4 s | 20.2 s | 26.8 s | 34.4 s |

ICACRO-C 6000-iteration execution time (CfsT) | 25.7 s | 53.5 s | 80.4 s | 107 s | 136.6 s |

ICACRO-I Best result after 1500 iterations (Ifps) | 35.23 | 73.78 | 107.54 | 155.29 | 197.45 |

ICACRO-I Best result after 6000 iterations (Ifs) | 35.08 | 69.50 | 102.39 | 137.41 | 173.46 |

ICACRO-I 1500-iteration execution time (IfpsT) | 5.9 s | 12.2 s | 18.7 s | 24.5 s | 31.1 s |

ICACRO-I 6000-iteration execution time (IfsT) | 23.5 s | 49.1 s | 74.6 s | 97.5 s | 123.8 s |

Cfps—Cfs | 0.38 | 2.69 | 4.53 | 15.26 | 24.77 |

Ifps—Ifs | 0.15 | 4.28 | 5.15 | 17.88 | 23.99 |

CfsT—CfpsT | 19.2 s | 40.1 s | 60.2 s | 80.2 s | 102.2 s |

IfsT—IfpsT | 17.6 s | 36.9 s | 55.9 s | 73 s | 92.7 s |

df | Mean Square | F | Sig. | ||
---|---|---|---|---|---|

Problem A | Between Groups | 1.234 | 1654453.748 | 1064352.466 | <0.001 |

Error | 7400.915 | 1.554 | |||

Problem B | Between Groups | 1.079 | 9596518.233 | 258544.375 | <0.001 |

Error | 6473.570 | 37.117 | |||

Problem C | Between Groups | 1.082 | 31014381.517 | 441298.360 | <0.001 |

Error | 6493.645 | 70.280 | |||

Problem D | Between Groups | 1.052 | 46227282.898 | 199913.106 | <0.001 |

Error | 6309.354 | 231.237 | |||

Problem E | Between Groups | 1.040 | 72555514.778 | 195415.062 | <0.001 |

Error | 6239.068 | 371.289 |

(I) Algorithm | (J) Algorithm | Mean Difference (J—I) | Std. Error | Sig. | |
---|---|---|---|---|---|

Problem A | ICACRO-C | Niching PSO | −22.836 | 0.018 | <0.001 |

ICACRO-I | Niching PSO | −22.037 | 0.019 | <0.001 | |

ICA | Niching PSO | −12.575 | 0.009 | <0.001 | |

ICACRO-C | ICA | −10.261 | 0.015 | <0.001 | |

ICACRO-I | ICA | −9.462 | 0.016 | <0.001 | |

ICACRO-C | ICACRO-I | −0.798 | 0.002 | <0.001 | |

Problem B | ICACRO-C | Niching PSO | −50.116 | 0.089 | <0.001 |

ICACRO-I | Niching PSO | −47.144 | 0.088 | <0.001 | |

ICA | Niching PSO | −18.518 | 0.026 | <0.001 | |

ICACRO-C | ICA | −31.598 | 0.072 | <0.001 | |

ICACRO-I | ICA | −28.626 | 0.071 | <0.001 | |

ICACRO-C | ICACRO-I | −2.972 | 0.01 | <0.001 | |

Problem C | ICACRO-C | Niching PSO | −92.806 | 0.127 | <0.001 |

ICACRO-I | Niching PSO | −89.269 | 0.121 | <0.001 | |

ICA | Niching PSO | −51.471 | 0.044 | <0.001 | |

ICACRO-C | ICA | −41.335 | 0.098 | <0.001 | |

ICACRO-I | ICA | −37.798 | 0.091 | <0.001 | |

ICACRO-C | ICACRO-I | −3.537 | 0.009 | <0.001 | |

Problem D | ICACRO-C | Niching PSO | −111.665 | 0.221 | <0.001 |

ICACRO-I | Niching PSO | −104.956 | 0.218 | <0.001 | |

ICA | Niching PSO | −53.594 | 0.061 | <0.001 | |

ICACRO-C | ICA | −58.071 | 0.178 | <0.001 | |

ICACRO-I | ICA | −51.362 | 0.174 | <0.001 | |

ICACRO-C | ICACRO-I | −6.709 | 0.019 | <0.001 | |

Problem E | ICACRO-C | Niching PSO | −139.396 | 0.293 | <0.001 |

ICACRO-I | Niching PSO | −132.027 | 0.27 | <0.001 | |

ICA | Niching PSO | −71.467 | 0.086 | <0.001 | |

ICACRO-C | ICA | −67.928 | 0.225 | <0.001 | |

ICACRO-I | ICA | −60.56 | 0.2 | <0.001 | |

ICACRO-C | ICACRO-I | −7.369 | 0.026 | <0.001 |

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**MDPI and ACS Style**

Jula, A.; Sundararajan, E.A.; Othman, Z.; Naseri, N.K.
Color Revolution: A Novel Operator for Imperialist Competitive Algorithm in Solving Cloud Computing Service Composition Problem. *Symmetry* **2021**, *13*, 177.
https://doi.org/10.3390/sym13020177

**AMA Style**

Jula A, Sundararajan EA, Othman Z, Naseri NK.
Color Revolution: A Novel Operator for Imperialist Competitive Algorithm in Solving Cloud Computing Service Composition Problem. *Symmetry*. 2021; 13(2):177.
https://doi.org/10.3390/sym13020177

**Chicago/Turabian Style**

Jula, Amin, Elankovan A. Sundararajan, Zalinda Othman, and Narjes Khatoon Naseri.
2021. "Color Revolution: A Novel Operator for Imperialist Competitive Algorithm in Solving Cloud Computing Service Composition Problem" *Symmetry* 13, no. 2: 177.
https://doi.org/10.3390/sym13020177