This paper studies a mobile edge computing-enabled wireless blockchain network, in which a set of Internet of Things (IoT) devices can act as miners to participate in mining. In this blockchain network, we jointly optimize the mining decision and resource allocation to maximize the total profit of all miners. When using evolutionary algorithms to solve this problem, each individual usually represents the mining decisions and resource allocations of all miners, which results in the redundant search space due to the fact that not all miners participate in mining. In this paper, we propose a new differential evolution (DE) algorithm, called DEMiDRA. In DEMiDRA, each individual represents the resource allocation of a participating miner and the resource allocations of all participating miners constitute the whole population. Then, DE is adopted to optimize the resource allocation. As for the optimization of the mining decision, we need to select miners to participate in mining and update the number of participating miners. Since the population size is equal to the number of participating miners, we transform the update of the number of participating miners into the adjustment of the population size and design an adaptive strategy. Besides, a tabu strategy is developed to prevent unpromising miners from participating in mining. The effectiveness of DEMiDRA is verified by comparing it with three other algorithms on a set of instances.

本文研究了启用移动边缘计算的无线区块链网络，其中一组物联网（IoT）设备可以充当矿工来参与挖掘。在这个区块链网络中，我们共同优化了采矿决策和资源分配，以最大化所有矿工的总利润。当使用进化算法来解决这个问题时，每个人通常代表所有矿工的采矿决策和资源分配，由于并非所有矿工都参与采矿，因此导致了冗余的搜索空间。在本文中，我们提出了一种新的差分进化（DE）算法，称为DEMiDRA。在DEMiDRA中，每个人代表一个参与的矿工的资源分配，所有参与的矿工的资源分配构成整个人口。然后，采用DE来优化资源分配。至于采矿决策的优化，我们需要选择矿工参与采矿，并更新参与矿工的人数。由于人口规模等于参与矿工的数量，因此我们将参与矿工数量的更新转换为人口规模的调整，并设计了一种自适应策略。此外，还制定了禁忌策略，以防止毫无希望的矿工参与采矿。通过将DEMiDRA与一组实例上的其他三种算法进行比较，可以验证DEMiDRA的有效性。由于人口规模等于参与矿工的数量，因此我们将参与矿工数量的更新转换为人口规模的调整，并设计了一种自适应策略。此外，还制定了禁忌策略，以防止毫无希望的矿工参与采矿。通过将DEMiDRA与一组实例上的其他三种算法进行比较，可以验证DEMiDRA的有效性。由于人口规模等于参与矿工的数量，因此我们将参与矿工数量的更新转换为人口规模的调整，并设计了一种自适应策略。此外，还制定了禁忌策略，以防止毫无希望的矿工参与采矿。通过将DEMiDRA与一组实例上的其他三种算法进行比较，可以验证DEMiDRA的有效性。