Multiobjective Optimization for Joint Task Offloading, Power Assignment, and Resource Allocation

“Multiobjective Optimization for Joint Task Offloading, Power Assignment, and Resource Allocation in Mobile Edge Computing” (Wang 等, 2022, p. 11737) (pdf) 移动边缘计算中联合任务卸载、功率分配和资源分配的多目标优化

Abstract

Mobile edge computing (MEC) is an emerging computational paradigm for providing storage and computing capabilities in network edge, to improve the experience of users, to shorten the delay, and to reduce the energy consumption of mobile devices. In this article, we consider a multiuser and multiserver scenario, where each user has an application composed of multiple independent tasks that need to be executed, and each MEC server is equipped on a base station (BS) for assisting mobile users to execute computation-intensive and time-sensitive tasks. Multiobjective optimization for joint task offloading, power assignment, and resource allocation is studied to maximize the offloading gains of users. A multivariable and multiobjective optimization problem with three objectives is constructed. An efficient multiobjective evolutionary algorithm is developed to solve the problems of minimizing the response time, minimizing the energy consumption, and minimizing the cost. Simulation results verify the effectiveness of our algorithm, and show the method significantly improves the user’s offloading benefits. According to the author’s knowledge, this is the first paper on the exploration of multiobjective optimization of multiuser with multiple tasks and multiserver MEC system, in which the worst user offloading revenue is regarded as the optimization objectives.

Keywords: #multi-objective_optimization #resource_allocation #power_capping #task_offloading [[evolutionary algorithms]] [[MOEA.D]]

Jounral: [[Internet of Thing]]

Features:

这篇文章的主要亮点就是多目标优化：任务卸载、功率分配、资源分配。自诩是第一篇关于多任务多用户多服务器的MEC多目标优化的研究。
解决的算法是改进的MOEA/D算法：“appropriate modifications” (Wang 等, 2022, p. 11742) (pdf) 适当的修改
作者中有位大佬：Peng Wang ,KenliLi , Senior Member, IEEE,BinXiao,Senior Member, IEEE, and Keqin Li , Fellow, IEEE

Introduction

“with multiusers and multiservers with limited resources, and designs an overall strategy plan for joint task offloading, power assignment, and resource allocation to maximize the overall user task offloading benefit.” (Wang 等, 2022, p. 11738) (pdf) 针对资源有限的多用户和多服务器，设计了联合任务卸载、功率分配和资源分配的总体策略计划，以最大化总体用户任务卸载效益。

“considers an MEC system with multiusers and multiservers, where the user MD has an application that can be decomposed into multiple independent computing tasks to be executed.” (Wang 等, 2022, p. 11738) (pdf) 考虑具有多用户和多服务器的MEC系统，其中用户MD具有可分解为多个独立计算任务以执行的应用程序。

consider the heterogeneity of MD and MEC severs
consider the differences in tasks
performance indicators measure the performance of the algorithm strategy

“In the multiuser and multiserver MEC system, there are four key issues to be solved.” (Wang 等, 2022, p. 11738) (pdf) 在多用户和多服务器MEC系统中，有四个关键问题需要解决:

choose which tasks to offload when MD has multiple tasks
decide how much power to provide when limited transmission power
choose task–>severs
non-convex problem

In response to these issues, the main contributions of this article are summarized as follows:

consider the differences among computing tasks and the heterogeneity among MEC severs
object: delay, energy consumption, and cost
the multiobjective evolutionary algorithm to slove
verify the performance and effectiveness of the algorithm

System Model

local computing
T m l o c = ∑ j ∈ L c m j f m T^{loc}_{m}=\sum_{j\in L}\frac{c^j_m}{f_m} Tmloc=j∈L∑fmcmj
E m l o c = ∑ j ∈ L η m c m j f m 2 E^{loc}_m=\sum_{j\in L}η_mc^j_mf^2_m Emloc=j∈L∑ηmcmjfm2
transmission process
T _ u p m , s j = d m j R m , s j T\_up^j_{m,s}=\frac{d^j_m}{R^j_{m,s}} T_upm,sj=Rm,sjdmj
E _ u p m , s j = p m , s j T _ u p m , s j E\_up^{j}_{m,s}=p_{m,s}^jT\_up^j_{m,s} E_upm,sj=pm,sjT_upm,sj
MEC sever computing
T _ e x e m , s j = c m j f m , s j T\_exe^j_{m,s}=\frac{c^j_m}{f^j_{m,s}} T_exem,sj=fm,sjcmj
M C m , s j = β s f m , s j MC^j_{m,s}=\beta_sf^j_{m,s} MCm,sj=βsfm,sj

Problem Formulation

T m = max ⁡ { T m l o c , max ⁡ j ∈ K m { T _ u p m , s j + T _ e x e m , s i } } T_m=\max\{T_{m}^{loc},\max_{j\in K_m}\{T\_up^j_{m,s}+T\_exe^i_{m,s}\}\} Tm=max{Tmloc,j∈Kmmax{T_upm,sj+T_exem,si}}
E m = ∑ j ∈ K m E _ u p m , s j + E m l o c E_m=\sum_{j\in K_m}E\_up^j_{m,s}+E^{loc}_m Em=j∈Km∑E_upm,sj+Emloc
M C m = ∑ j ∈ K m M C m , s j MC_m=\sum_{j \in K_m}MC^j_{m,s} MCm=j∈Km∑MCm,sj
“the average offloading utility of all MD users can reflect the benefits of the entire MEC system.” (Wang 等, 2022, p. 11741) (pdf) 所有MD用户的平均卸载效用可以反映整个MEC系统的益处。
T = ∑ m ∈ M { T m } ∣ M ∣ E = ∑ m ∈ M { E m } ∣ M ∣ M C = ∑ m ∈ M { M C m } ∣ M ∣ . \begin{aligned} T &=\frac{\sum_{m \in M}\left\{T_m\right\}}{|M|} \\ E &=\frac{\sum_{m \in M}\left\{E_m\right\}}{|M|} \\ \mathrm{MC} &=\frac{\sum_{m \in M}\left\{\mathrm{MC}_m\right\}}{|M|} . \end{aligned} TEMC=∣M∣∑m∈M{Tm}=∣M∣∑m∈M{Em}=∣M∣∑m∈M{MCm}.
Object Function:
min ⁡ x m j , p m j , f m , s j { T , E , M C } subject to: x m j ∈ { 0 , 1 , 2 , … , S } 0 ≤ p m j ≤ p m max ⁡ 0 ≤ f m , s j ≤ f s max ⁡ ∑ j ∈ J { p m j } ≤ p m max ⁡ ∑ m = 1 M ∑ j = 1 J f m , s j < f s max ⁡ \begin{aligned} &\min _{x_m^j, p_m^j, f_{m, s}^j}\{T, E, \mathrm{MC}\}\\ &\text { subject to: } x_m^j \in\{0,1,2, \ldots, S\}\\ &0 \leq p_m^j \leq p_m^{\max }\\ &0 \leq f_{m, s}^j \leq f_s^{\max }\\ &\sum_{j \in J}\left\{p_m^j\right\} \leq p_m^{\max }\\ &\sum_{m=1}^M \sum_{j=1}^J f_{m, s}^j<f_s^{\max } \end{aligned} xmj,pmj,fm,sjmin{T,E,MC} subject to: xmj∈{0,1,2,…,S}0≤pmj≤pmmax0≤fm,sj≤fsmaxj∈J∑{pmj}≤pmmaxm=1∑Mj=1∑Jfm,sj<fsmax

Algorithm

算法核心是MOEA/D算法

encode optimization problem: gene–>chromosomes
1. offloading strategy : X m 1 ∈ [ 1 , S ] X^1_m\in [1,S] Xm1∈[1,S]
2. up-link power assignment : P m 1 ∈ [ 0 , 1 ] P^1_m\in [0,1] Pm1∈[0,1]
3. resource allocation : f m l ∈ [ 0 , 1 ] f^l_m \in [0,1] fml∈[0,1]
modify the MOEA/D
1. Initialization: population P O P POP POP, crossing probility P c P_c Pc, mutation probability P m P_m Pm
2. reproduction: crossover operation + mutation operation
3. evolution : find the better solution as the next generation solution of the population
4. selection : choose a compromise solution
choose the best solution
Standardize the delay, energy consumption, and cost:
V ( T n ) = { T n , max ⁡ − T ( C S n ) T n , max ⁡ − T n , min ⁡ , T n , max ⁡ ≠ T n , min ⁡ 1 , T n , max ⁡ = T n , min ⁡ V ( E n ) = { E n , max ⁡ − E ( C S n ) E n , max ⁡ − E n , min ⁡ , E n , max ⁡ ≠ E n , min ⁡ 1 , E n , max ⁡ = E n , min ⁡ J ( M C n ) = { M C n , max ⁡ − M C ( C S n ) M C n , max ⁡ − M C n , min ⁡ , M C n , max ⁡ ≠ M C n , min ⁡ 1 , M C n , max ⁡ = M C n , min ⁡ \begin{aligned} &V\left(T^n\right)= \begin{cases}\frac{T^{n, \max }-T\left(\mathrm{CS}_n\right)}{T^{n, \max }-T^{n, \min },} & T^{n, \max } \neq T^{n, \min } \\ 1, & T^{n, \max }=T^{n, \min }\end{cases}\\ &V\left(E^n\right)= \begin{cases}\frac{E^{n, \max }-E\left(\mathrm{CS}_n\right)}{E^{n, \max }-E^{n, \min }}, & E^{n, \max } \neq E^{n, \min } \\ 1, & E^{n, \max }=E^{n, \min }\end{cases}\\ &J\left(\mathrm{MC}^n\right)= \begin{cases}\frac{\mathrm{MC}^{n, \max }-\mathrm{MC}\left(\mathrm{CS}_n\right)}{\mathrm{MC}^{n, \max }-\mathrm{MC}^{n, \min }}, & \mathrm{MC}^{n, \max } \neq \mathrm{MC}^{n, \min } \\ 1, & \mathrm{MC}^{n, \max }=\mathrm{MC}^{n, \min }\end{cases} \end{aligned} V(Tn)={Tn,max−Tn,min,Tn,max−T(CSn)1,Tn,max=Tn,minTn,max=Tn,minV(En)={En,max−En,minEn,max−E(CSn),1,En,max=En,minEn,max=En,minJ(MCn)={MCn,max−MCn,minMCn,max−MC(CSn),1,MCn,max=MCn,minMCn,max=MCn,min
The utility value of the n n nth solution is:
V ( C S ) = max ⁡ P O P { γ V ( T n ) + δ V ( E n ) + ζ V ( M C n ) } V(\mathrm{CS})=\max _{\mathrm{POP}}\left\{\gamma V\left(T^n\right)+\delta V\left(E^n\right)+\zeta V\left(\mathrm{MC}^n\right)\right\} V(CS)=POPmax{γV(Tn)+δV(En)+ζV(MCn)}
We choose the solution with the greatest benefit in the population as the final solution.