# Multi-Objective Task Scheduling Optimization in Spatial Crowdsourcing

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. Task Matching in SC

#### 2.2. Task Scheduling Problem in SC

#### 2.3. The Binary-Objective Optimization Problem in SC

## 3. The MOTSO Model in SC

#### 3.1. The Ranking Strategy Algorithm

Algorithm 1. Pseudo code for algorithm pre-computation. |

// Pre-computation |

Input: set of tasks T and set of workers W |

Output: |

Initialize TE, TC, TED, RTED, RTE, Ranked with size [|T|][|W|] |

Foreach task do |

Foreach worker do |

= computeTC(t,w) // compute travel duration using (1). |

= computeTED (t,w) // compute task execution duration using (2). |

= computeTE(t,w) // compute task entropy using (3). |

End Foreach |

End Foreach |

RTED = Rank(TED); // sort ascending and rank each worker for each task. |

RTE = Rank(TE); // sort ascending and rank each task for each worker |

Foreach task do |

Foreach worker do |

= + |

End Foreach |

End Foreach |

= Rank () //sort ascending and rank |

Return |

#### 3.1.1. Task Execution Duration (TED) and Ranked Task Execution Duration (RTED)

#### 3.1.2. Task Entropy (TE) and Ranked Task Entropy (RTE)

_{t}set, while $\left|{O}_{w,t}\right|$ indicates the number of visits of the same worker to a task location in the O

_{w,t}set.

#### 3.1.3. The Ranked Tables

#### 3.2. Multi-Objective Particle Swarm Optimization

## 4. Performance Evaluation

- N is the inertia weight;
- P is population number;
- I is iteration number;
- D is duration max;
- C1 and C2 are acceleration coefficients;
- r1 and r2 are random numbers;
- S is the speed of workers;
- No.w is the number of workers;
- No.t is the number of tasks.

#### 4.1. The Performance of the Ranking Strategy Algorithm

- Initializing the position of a particle randomly (the percentage of randomness is 100%);
- Initializing the position of a hybrid particle, both randomly and from the ranked table (the percentage of randomness is 50%);
- Initializing the positions of all particles from the ranked table (the percentage of randomness is 0%).

- Initializing the positions of all particles randomly;
- Initializing the positions of all particles using the output of the ranking strategy stage.

#### 4.2. Performance of the MOTSO Model

#### 4.2.1. Maximizing the Number of Completed Tasks

#### 4.2.2. Minimizing the Total Travel Costs (TTCs)

#### 4.2.3. Minimizing the Standard Deviation of the Workload Balance

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Symbol | Name of Algorithm |

A&S | Baseline algorithm |

GALS | Global assignment and local scheduling algorithm |

NLALA-L | Naïve local assignment local scheduling based on location |

NLALS-T | Naïve local assignment local scheduling based on task-oriented partitioning |

BLALS-K | Bisection-based local assignment and local scheduling based on K-means |

BLALS-T | Bisection-based local assignment and local scheduling—task-oriented partitioning |

BLA | Baseline algorithm |

LBA | Load-balancing algorithm |

DCA | Divide-and-conquer algorithm |

MOTSO | Multi-objective task scheduling optimization |

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**Figure 1.**A classification of spatial crowdsourcing. Reward = reward-based worker; voluntary = voluntary-based worker; SAT = server-assigned task; WST = worker-selected task; single = single worker; multiple = multiple workers.

**Figure 2.**A spatial crowdsourcing (SC) scenario of the multi-objective task scheduling optimization (MOTSO) model.

**Figure 3.**The procedure of the multi-objective task scheduling optimization (MOTSO) model. TED = task execution duration table; TE = task entropy table; RTED = ranked TED; RTE = ranked TE; w1 = first worker; w2 = second worker; w3 = third worker; t1 = first task; t2 = second task.

**Figure 4.**Flowchart of the multi-objective particle swarm optimization (MOPSO) [19].

**Figure 6.**The percentages of completed tasks using the proposed MOTSO model for case 1 (

**a**), case 2 (

**b**), and Gowalla (

**c**).

**Figure 7.**The percentage of completed tasks using different algorithms. A&S = baseline algorithm; GALS = global assignment and local scheduling algorithm; NLALA-L = naïve local assignment local scheduling based on location; NLALS-T = naïve local assignment local scheduling based on task-oriented partitioning; BLALS-K = bisection-based local assignment and local scheduling based on K-means; BLALS-T = bisection-based local assignment and local scheduling; BLA = baseline algorithm; LBA = load-balancing algorithm; DCA = divide-and-conquer algorithm.

References | Task Assignment Problem | Optimization | ||
---|---|---|---|---|

Matching | Scheduling | Single Objective | Binary Objective | |

[6] | √ | √ | ||

[9] | √ | √ | ||

[31] | √ | √ | ||

[8] | √ | √ | ||

[3] | √ | √ | ||

[12] | √ | √ | ||

[4] | √ | √ | ||

[32] | √ | √ | ||

[33] | √ | √ | ||

[11] | √ | √ | ||

[7] | √ | √ | ||

[10] | √ | √ | √ | |

[2] | √ | √ | ||

[34] | √ | √ | ||

[35] | √ | √ |

w1 | w2 | w3 | w4 | w5 | |
---|---|---|---|---|---|

t1 | 137.5286391016494 | 140.77934794265565 | 140.83953070394318 | 132.77599556103092 | 156.88627234146358 |

t2 | 47.12959736369906 | 85.88725867729572 | 75.65173447900676 | 77.63439324242962 | 66.8175097791553 |

t3 | 92.55306850854014 | 130.09070678927753 | 92.66485742716874 | 101.97479734391655 | 88.3209190565524 |

w1 | w2 | w3 | w4 | w5 | |
---|---|---|---|---|---|

t1 | 2 | 3 | 4 | 1 | 5 |

t2 | 1 | 5 | 3 | 4 | 2 |

t3 | 2 | 5 | 3 | 4 | 1 |

t4 | 1 | 2 | 3 | 5 | 4 |

w1 | w2 | w3 | w4 | w5 | |
---|---|---|---|---|---|

t1 | 0.6931471805599453 | 0.6931471805599453 | 0.6931471805599453 | 0.6931471805599453 | 0.6931471805599453 |

t2 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |

t3 | 1.386943611198906 | 1.386943611198906 | 1.386943611198906 | 1.386943611198906 | 1.386943611198906 |

t4 | 0.6931471805599453 | 0.6931471805599453 | 0.6931471805599453 | 0.6931471805599453 | 0.6931471805599453 |

w1 | w2 | w3 | w4 | w5 | |
---|---|---|---|---|---|

t1 | 2 | 2 | 2 | 2 | 2 |

t2 | 1 | 1 | 1 | 1 | 1 |

t3 | 4 | 4 | 4 | 4 | 4 |

t4 | 3 | 3 | 3 | 3 | 3 |

w1 | w2 | w3 | w4 | w5 | The Optimal Worker | |
---|---|---|---|---|---|---|

t1 | 2 + 2 = 4 | 3 + 2 = 5 | 4 + 2 = 6 | 1 + 2 = 3 | 5 + 2 = 7 | w4 |

t2 | 1 + 1 = 2 | 5 + 1 = 6 | 3 + 1 = 4 | 4 + 1 = 5 | 2 + 1 = 3 | w1 |

t3 | 2 + 4 = 6 | 5 + 4 = 9 | 3 + 4 = 7 | 4 + 4 = 8 | 1 + 4 = 5 | w5 |

t4 | 1 + 3 = 4 | 2 + 3 = 5 | 3 + 3 = 6 | 5 + 3 = 8 | 4 + 3 = 7 | w1 |

Parameter | Parameter Value | |
---|---|---|

MOPSOconfiguration | P | 50 |

I | 80 | |

N | [0,1] | |

C1, C2 | 2.00, 2.00 | |

r1, r2 | [0,1] | |

SCconfiguration | No.w | Case1 = 600 Case2 = 1200 Gowalla = 2400 |

No.t | Case1 = 600 Case2 = 1200 Gowalla = 2400 | |

S | 80 | |

D | 90 |

Dataset | Fitness Function Value | ||
---|---|---|---|

100% (Randomly) | 50% (Hybrid) | 0%(Ranked table) | |

Case 1 | 0.540143 | 0.092286 | 0.096544 |

Case 2 | 0.537479 | 0.073181 | 0.071633 |

Gowalla | 0.535224 | 0.060976 | 0.056781 |

**Table 9.**Normalization values of the objectives in terms of minimization when varying the initialization mechanisms.

Normalization Values for Each Objective in Terms of Minimization | |||||||||
---|---|---|---|---|---|---|---|---|---|

$1-\mathit{N}\mathit{V}$ | NWLB | NTTC | |||||||

100% | 50% | 0% | 100% | 50% | 0% | 100% | 50% | 0% | |

Case 1 | 0.34853 | 0.026923 | 0.034188 | 0.039943 | 0.048828 | 0.051251 | 0.15167 | 0.016535 | 0.011105 |

Case 2 | 0.35715 | 0.026961 | 0.027024 | 0.028998 | 0.034157 | 0.036681 | 0.151331 | 0.012063 | 0.007929 |

Gowalla | 0.365401 | 0.026474 | 0.024522 | 0.020456 | 0.024455 | 0.026705 | 0.149367 | 0.010047 | 0.005554 |

Dataset | Total Travel Cost Using MOTSO |
---|---|

TTCs | |

Case 1 | 637.2025 |

Case 2 | 917.3457 |

Gowalla | 1292.929 |

Using Gowalla | |
---|---|

Name of algorithm | ATC value |

A&S | 8.30 |

GALS | 5.87 |

NLALA-L | 6.02 |

NLALS-T | 5.80 |

BLALS-K | 5.86 |

BLALS-T | 5.86 |

BLA | 7.8 |

LBA | 5.5 |

DCA | 6.1 |

MOTSO (our model) | 0.5527457 |

**Table 12.**The results of the standard deviation of the workload balance (WLB) using the MOTSO model.

Dataset | Workload Balancing Using MOTSO |
---|---|

WLB | |

Case 1 | 55.58566 |

Case 2 | 56.42424 |

Gowalla | 58.01609 |

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**MDPI and ACS Style**

Alabbadi, A.A.; Abulkhair, M.F. Multi-Objective Task Scheduling Optimization in Spatial Crowdsourcing. *Algorithms* **2021**, *14*, 77.
https://doi.org/10.3390/a14030077

**AMA Style**

Alabbadi AA, Abulkhair MF. Multi-Objective Task Scheduling Optimization in Spatial Crowdsourcing. *Algorithms*. 2021; 14(3):77.
https://doi.org/10.3390/a14030077

**Chicago/Turabian Style**

Alabbadi, Afra A., and Maysoon F. Abulkhair. 2021. "Multi-Objective Task Scheduling Optimization in Spatial Crowdsourcing" *Algorithms* 14, no. 3: 77.
https://doi.org/10.3390/a14030077