A Personalized Task Allocation Strategy in Mobile Crowdsensing for Minimizing Total Cost
Abstract
:1. Introduction
 A cost estimation method is proposed by taking the user’s preference for the sensing task into consideration. Furthermore, the minimizing cost problem is formulated as solving a heterogeneous, asymmetric, multiple TSP.
 Through transforming multipleTSP to singleTSP, we first propose a greedy algorithm: PTAMGreedy when the task is urgent, which is proved to have a bound to the optimal solution.
 When the task is not urgent, we further propose a genetic algorithm mixed with heuristic: PTAMGenetic to minimize the total cost. The genetic algorithm consumes a lot of calculation time while achieving a better total cost performance.
 We conduct a number of simulations based on three widelyused realworld traces. The simulation results show that, PTAMGreedy achieves a bounded cost performance, and PTAMGenetic achieves the lowest total cost compared with the other task allocation strategies.
2. System Overview
2.1. System Model
2.2. Problem Description
3. Personalized Task Allocation Strategy
3.1. Cost Estimation and MultipleTSP Formulation
3.2. Transformation from MultipleTSP to SingleTSP
 1.
 We define the virtual location set corresponding to task location ${s}_{j}$ as ${L}_{j}=\{{s}_{j}^{i}:i=1,\cdots ,n\}$. Moreover, we make user that there is only one edge that comes into and departs from ${L}_{j}$.
 2.
 Assume that ${s}_{j}^{i}$ is the first virtual location in ${L}_{j}$ visited by the path in the optimal solution, after that, the path will visit all the remaining virtual locations in ${L}_{j}$ before leaving ${L}_{j}$.
 3.
 The user route, ${P}_{i}$, from the initial location ${u}_{i}$ to its corresponding terminal point ${u}_{i}^{v}$ in ${y}_{opt}$ will not pass through any other users’ initial locations and terminal points.
 4.
 The cost of the optimal solution $C\left({y}_{opt}\right)$ is equal to the summation of all the route costs of users, i.e., ${\sum}_{i=1}^{n}C\left({P}_{i}\right)$.
3.3. SingleTSP Solution
3.3.1. Greedy Algorithm
Algorithm 1 PTAMGreedy. 
Input: the transformed graph G = (V,E, $C\left(E\right)$) Output: a Hamiltonian tour on G

Algorithm 2 GHT. 
Input: a graph G = (V,E, $C\left(E\right)$) Output: a Hamiltonian tour on G

Algorithm 3 GHTCAN. 
Input: a graph G = (V,E, $C\left(E\right)$) Output: a Hamiltonian tour on G

3.3.2. Genetic Algorithm
Algorithm 4 PTAMGenetic Algorithm. 

Algorithm 5 PTAMGcrossover (${g}_{a},{g}_{b}$). 

Algorithm 6 PTAMGmutation (g). 

4. Performance Evaluation
4.1. The Traces Used
4.2. Algorithms in Comparison
4.3. Simulation Results
5. Related Work
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Notation  Description 

$U,S,A$  the set of users, the set of tasks, the set of users’ preferences 
${A}_{{u}_{i}},{A}_{{s}_{i}}$  the preferences of user i, the preferences of task location ${s}_{i}$ that could satisfy some preferences of users 
${u}_{i},{u}_{i}^{v}$  the initial location of the user i, the terminal point of the user i on the transformed graph 
${s}_{j}^{i}$  the jth virtual task location of user i 
$m,n$  the number of task locations, the number of users 
${C}^{i}({u}_{i},{s}_{i})$  the cost of user i from ${u}_{i}$ to task ${s}_{i}$ 
${C}^{i}({s}_{p},{s}_{q})$  the cost of user i from ${s}_{p}$ to ${s}_{q}$ 
$D({u}_{i},{s}_{i})$  the physical distance between ${u}_{i}$ and ${s}_{i}$ 
$D({s}_{p},{s}_{q})$  the physical distance between ${s}_{p}$ and ${s}_{q}$ 
${x}_{iq}$  the ${u}_{i}$’s preference level for task ${s}_{q}$ 
${d}_{iq}$  the discount for ${u}_{i}$ to task ${s}_{q}$ 
${P}_{i}$  the path of user i in the transformed graph from the initial location ${u}_{i}$ to its corresponding terminal point ${u}_{i}^{v}$ in the optimal solution 
${R}_{i}$  the tour of user i in multipleTSP 
G  a transformed graph 
V  the collection of nodes in graph G 
E  the collection of edges in graph G 
Y  a cycle cover in graph G 
${Y}_{1},\dots {Y}_{l}$  the cycles in cycle cover Y 
${I}_{k}$  the set of all indices i, such that ${Y}_{i}$ is a kverticescycle ($k\ge 2$) 
Parameter  Results  

PTAMGreedy  Optimal  Proportion  Bound  
$C\left({e}_{max}\right)=15$  62  62  1  1.19 
$C\left({e}_{max}\right)=16$  68  63  1.08  1.23 
$C\left({e}_{max}\right)=17$  70  64  1.06  1.26 
$C\left({e}_{max}\right)=18$  74  66  1.15  1.30 
$C\left({e}_{max}\right)=19$  77  74  1.04  1.34 
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Gao, H.; Zhao, H. A Personalized Task Allocation Strategy in Mobile Crowdsensing for Minimizing Total Cost. Sensors 2022, 22, 2751. https://doi.org/10.3390/s22072751
Gao H, Zhao H. A Personalized Task Allocation Strategy in Mobile Crowdsensing for Minimizing Total Cost. Sensors. 2022; 22(7):2751. https://doi.org/10.3390/s22072751
Chicago/Turabian StyleGao, Hengfei, and Hongwei Zhao. 2022. "A Personalized Task Allocation Strategy in Mobile Crowdsensing for Minimizing Total Cost" Sensors 22, no. 7: 2751. https://doi.org/10.3390/s22072751