The investigation in this article makes the following important contributions to combinatorial optimization of computation offloading in fog computing. First, we rigorously define the two problems of optimal computation offloading with energy constraint and optimal computation offloading with time constraint. We do this in such a way that between execution time and energy consumption, we can fix one and minimize the other. We prove that our optimization problems are NP-hard, even for very special cases. Second, we develop a unique and effective approach for solving the proposed combinatorial optimization problems, namely, a two-stage method. In the first stage, we generate a computation offloading strategy. In the second stage, we decide the computation speed and the communication speeds. This method is applicable to both optimization problems. Third, we use a simple yet efficient greedy method to produce a computation offloading strategy by taking all aspects into consideration, including the properties of the communication channels, the power consumption models of computation and communication, the tasks already assigned and allocated, and the characteristics of the current task being considered. Fourth, we experimentally evaluate the performance of our heuristic algorithms. We observe that while various heuristics do exhibit noticeably different performance, there can be a single and simple heuristic that can perform very well. Furthermore, the method of compound algorithm can be applied to obtain slightly improved performance. Fifth, we emphasize that our problems and algorithms can be easily extended to study combined performance and cost optimization (such as cost–performance ratio and weighted cost-performance sum optimization) and to accommodate more realistic and complicated fog computing environments (such as preloaded mobile edge servers and multiple users) with little extra effort. To the best of our knowledge, there has been no similar study in the existing fog computing literature.

中文翻译：

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雾计算中移动用户的启发式计算卸载算法

本文的研究对雾计算中计算卸载的组合优化做出了以下重要贡献。首先，我们严格定义了能量约束的最优计算卸载和时间约束的最优计算卸载两个问题。我们这样做的方式是，在执行时间和能源消耗之间，我们可以修复一个并最小化另一个。我们证明了我们的优化问题是 NP-hard，即使对于非常特殊的情况。其次，我们开发了一种独特而有效的方法来解决所提出的组合优化问题，即两阶段方法。在第一阶段，我们生成计算卸载策略。在第二阶段，我们决定计算速度和通信速度。该方法适用于两个优化问题。第三，我们使用一种简单而有效的贪心方法来产生计算卸载策略，考虑到各个方面，包括通信通道的属性，计算和通信的功耗模型，已经分配和分配的任务，以及特征正在考虑的当前任务。第四，我们通过实验评估我们启发式算法的性能。我们观察到，虽然各种启发式算法确实表现出明显不同的性能，但可能有一个单一且简单的启发式算法可以表现得非常好。此外，可以应用复合算法的方法来获得稍微提高的性能。第五，我们强调我们的问题和算法可以很容易地扩展到研究组合的性能和成本优化（例如成本性能比和加权成本性能总和优化）并适应更现实和复杂的雾计算环境（例如预加载的移动边缘服务器）和多个用户）几乎没有额外的努力。据我们所知，现有的雾计算文献中没有类似的研究。