This paper studies the optimization design of a wireless powered mobile edge computing (WP-MEC) system with multiple edge servers, in which the heterogeneous delay requirements for tasks are considered. To achieve optimal computing performance of the WP-MEC, a computation rate maximization problem is formulated by jointly optimizing wireless power transmission time, offloading decision and resources allocation. It is a mixed-integer nonlinear programming problem that is NP-hard. In order to solve the problem, we decompose it into two sub-problems, a multiple knapsack sub-problem of user tasks offloading and a one-dimensional optimization sub-problem of wireless power transmission time. The multiple knapsack sub-problem is then solved using an integer encoding differential evolution algorithm. The algorithm can adequately consider various combinations of items among multiple feasible knapsacks, thus making it easier to find the solution with largest overall profit. Moreover, a multiple intervals golden-section search algorithm is designed for the one-dimensional optimization sub-problem of wireless power transmission time. The algorithm evaluates the given wireless power transmission time using the optimal solution to the corresponding multiple knapsacks problem, and can find the optimal wireless power transmission time by jointly optimizing multiple intervals. Next, a new computation offloading scheme, MKCTO, is proposed by integrating the two algorithms. Finally, the performance of MKCTO is verified by extensive numerical experiments and compared with other four benchmark schemes. The results show that MKCTO can achieve satisfactory performance of computation offloading, and outperform the other four schemes.

本文研究了具有多个边缘服务器的无线供电移动边缘计算（WP-MEC）系统的优化设计，其中考虑了任务的异构延迟要求。为了实现 WP-MEC 的最佳计算性能，通过联合优化无线电力传输时间、卸载决策和资源分配来制定计算速率最大化问题。这是一个 NP-hard 的混合整数非线性规划问题。为了解决这个问题，我们将其分解为两个子问题，一个用户任务卸载的多背包子问题和一个无线电力传输时间的一维优化子问题。然后使用整数编码差分进化算法解决多背包子问题。该算法可以充分考虑多个可行背包中物品的各种组合，从而更容易找到总体利润最大的解决方案。此外，针对无线电力传输时间的一维优化子问题，设计了一种多区间黄金分割搜索算法。该算法利用对应的多个背包问题的最优解来评估给定的无线电力传输时间，通过联合优化多个区间可以找到最优的无线电力传输时间。接下来，通过整合这两种算法，提出了一种新的计算卸载方案MKCTO。最后，通过大量的数值实验验证了 MKCTO 的性能，并与其他四种基准方案进行了比较。