This article investigates a wireless-powered mobile edge computing (MEC) system, where the service provider (SP) provides the device owner (DO) with both computing resources and energy to execute tasks from Internet-of-Things devices. In this system, SP first sets the prices of computing resources and energy whereas DO then makes the optimal response according to the given prices. In order to jointly optimize the prices of computing resources and energy, we formulate a bilevel optimization problem (BOP), in which the upper level generates the prices of computing resources and energy for SP and then under the given prices, the lower level optimizes the mode selection, broadcast power, and computing resource allocation for DO. This BOP is difficult to address due to the mixed variables at the lower level. To this end, we first derive the relationships between the optimal broadcast power and the mode selection and between the optimal computing resource allocation and the mode selection. After that, it is only necessary to consider the discrete variables (i.e., mode selection) at the lower level. Note, however, that the transformed BOP is still difficult to solve because of the extremely large search space. To solve the transformed BOP, we propose a divide-and-conquer bilevel optimization algorithm (called DACBO). Based on device status, task information, and available resources, DACBO first groups tasks into three independent small-size sets. Afterward, analytical methods are devised for the first two sets. As for the last one, we develop a nested bilevel optimization algorithm that uses differential evolution and variable neighborhood search (VNS) at the upper and lower levels, respectively. In addition, a greedy method is developed to quickly construct a good initial solution for VNS. The effectiveness of DACBO is verified on a set of instances by comparing with other algorithms.

中文翻译：

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无线供电 MEC 中计算资源和能源联合定价的分而治之双层优化算法


本文研究了无线供电的移动边缘计算 (MEC) 系统，其中服务提供商 (SP) 为设备所有者 (DO) 提供计算资源和能源以执行物联网设备的任务。在该系统中，SP首先设定计算资源和能源的价格，而DO然后根据给定的价格做出最优响应。为了共同优化计算资源和能源的价格，我们制定了双层优化问题（BOP），其中上层生成SP的计算资源和能源价格，然后在给定的价格下，下层优化DO 的模式选择、广播功率和计算资源分配。由于较低层面的变量混合，国际收支平衡难以解决。为此，我们首先推导出最优广播功率与模式选择之间以及最优计算资源分配与模式选择之间的关系。之后，只需要考虑较低层次的离散变量（即模式选择）。但请注意，由于搜索空间极大，变换后的 BOP 仍然难以求解。为了解决变换后的 BOP，我们提出了一种分而治之的双层优化算法（称为 DACBO）。根据设备状态、任务信息和可用资源，DACBO 首先将任务分为三个独立的小规模集合。随后，为前两组设计了分析方法。对于最后一个，我们开发了一种嵌套双层优化算法，该算法分别在上层和下层使用差分进化和变量邻域搜索（VNS）。 此外，还开发了一种贪婪方法来快速构建良好的 VNS 初始解决方案。通过与其他算法的比较，在一组实例上验证了 DACBO 的有效性。