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Emerging Internet-of-Everything (IoE) services require connected devices to respond instantly and operate for long durations. As smart mobile devices (SMDs) are often powered by batteries of limited capacity, offloading some computational tasks to nearby edge servers is a promising solution to reduce the latency and energy consumption of SMDs in operation. However, a challenge of computation offloading in the IoE system is the large number of SMDs that need to be handled. To address this problem, in this paper, we propose an intelligent two-stage computation offloading scheme with multiple optimization objectives. In the first stage, we categorize the computation tasks into classes (e.g., computation-intensive, data-intensive) and make early offloading decisions on some classes of tasks with offloading preferences. In the second stage, we make offloading decisions on the remaining tasks by solving a multi-objective optimization problem using the powerful Non-dominated Sorting Genetic Algorithm (NSGA-II). This two-stage design can help reduce the size of task instances in the second optimization stage, thus accelerating the convergence of the NSGA-II algorithm. The extensive simulation results show that, compared to the existing NSGA-II algorithm-based optimization methods, the proposed offloading scheme improves the performance by 10% in terms of latency and energy consumption. • The data transmission and task execution processes are modeled as queueing systems. • A model is proposed to balance the data-intensive and computation-intensive tasks. • An algorithm is proposed to make offloading decisions in advance for heavy tasks using preferences. • The modified NSGA-II algorithm is applied to the remaining computation tasks to obtain the optimal offloading decisions. • Comprehensive experiments are conducted for comparisons of the proposed method with some benchmark methods. [ABSTRACT FROM AUTHOR]