A Bilevel Optimization Approach for Joint Offloading Decision and Resource Allocation in Cooperative Mobile Edge Computing

This paper studies a multi-user cooperative mobile edge computing offloading (CoMECO) system in a multi-user interference environment, in which delay-sensitive tasks may be executed on local devices, cooperative devices, or the primary MEC server. In this system, we jointly optimize the offloading decision and computation resource allocation for minimizing the total energy consumption of all mobile users under the delay constraint. If this problem is solved directly, the offloading decision and computation resource allocation are generally generated separately at the same time. Note, however, that they are closely coupled. Therefore, under this condition, their dependency is not well considered, thus leading to poor performance. We transform this problem into a bilevel optimization problem, in which the offloading decision is generated in the upper level, and then the optimal allocation of computation resources is obtained in the lower level based on the given offloading decision. In this way, the dependency between the offloading decision and computation resource allocation can be fully taken into account. Subsequently, a bilevel optimization approach, called BiJOR, is proposed. In BiJOR, candidate modes are first pruned to reduce the number of infeasible offloading decisions. Afterward, the upper level optimization problem is solved by ant colony system (ACS). Furthermore, a sorting strategy is incorporated into ACS to construct feasible offloading decisions with a higher probability and a local search operator is designed in ACS to accelerate the convergence. For the lower level optimization problem, it is solved by the monotonic optimization method. In addition, BiJOR is extended to deal with a complex scenario with the channel selection. Extensive experiments are carried out to investigate the performance of BiJOR on two sets of instances with up to 400 mobile users. The experimental results demonstrate the effectiveness of BiJOR and the superiority of the CoMECO system

Revisiting the Pion Leading-Twist Distribution Amplitude within the QCD Background Field Theory

We study the pion leading-twist distribution amplitude (DA) within the framework of SVZ sum rules under the background field theory. To improve the accuracy of the sum rules, we expand both the quark propagator and the vertex (z\cdot \tensor{D})^n of the correlator up to dimension-six operators in the background field theory. The sum rules for the pion DA moments are obtained, in which all condensates up to dimension-six have been taken into consideration. Using the sum rules, we obtain \left|_{\rm 1\;GeV} = 0.338 \pm 0.032, \left|_{\rm 1\;GeV} = 0.211 \pm 0.030 and \left|_{\rm 1\;GeV} = 0.163 \pm 0.030. It is shown that the dimension-six condensates shall provide sizable contributions to the pion DA moments. We show that the first Gegenbauer moment of the pion leading-twist DA is $a^\pi_2|_{\rm 1\;GeV} = 0.403 \pm 0.093$, which is consistent with those obtained in the literature within errors but prefers a larger central value as indicated by lattice QCD predictions.Comment: 13 pages, 7 figure

Joint Deployment and Task Scheduling Optimization for Large-Scale Mobile Users in Multi-UAV Enabled Mobile Edge Computing

This article establishes a new multiunmanned aerial vehicle (multi-UAV)-enabled mobile edge computing (MEC) system, where a number of unmanned aerial vehicles (UAVs) are deployed as flying edge clouds for large-scale mobile users. In this system, we need to optimize the deployment of UAVs, by considering their number and locations. At the same time, to provide good services for all mobile users, it is necessary to optimize task scheduling. Specifically, for each mobile user, we need to determine whether its task is executed locally or on a UAV (i.e., offloading decision), and how many resources should be allocated (i.e., resource allocation). This article presents a two-layer optimization method for jointly optimizing the deployment of UAVs and task scheduling, with the aim of minimizing system energy consumption. By analyzing this system, we obtain the following property: the number of UAVs should be as small as possible under the condition that all tasks can be completed. Based on this property, in the upper layer, we propose a differential evolution algorithm with an elimination operator to optimize the deployment of UAVs, in which each individual represents a UAV's location and the entire population represents an entire deployment of UAVs. During the evolution, we first determine the maximum number of UAVs. Subsequently, the elimination operator gradually reduces the number of UAVs until at least one task cannot be executed under delay constraints. This process achieves an adaptive adjustment of the number of UAVs. In the lower layer, based on the given deployment of UAVs, we transform the task scheduling into a 0-1 integer programming problem. Due to the large-scale characteristic of this 0-1 integer programming problem, we propose an efficient greedy algorithm to obtain the near-optimal solution with much less time. The effectiveness of the proposed two-layer optimization method and the established multi-UAV-enabled MEC system is demonstrated on ten instances with up to 1000 mobile users