It has been widely recognized that evolutionary computation is one of the most effective techniques for solving complex optimization problems. As a group of meta-heuristics inspired by nature, the superiority of evolutionary algorithms is mainly attributed to the evolution of multiple candidate solutions, which can strike a balance between exploration and exploitation. However, the effectiveness of evolutionary algorithms is generally at the expense of efficiency, which reduces the prevalence of evolutionary algorithms in solving real-world optimization problems. In 2017, we proposed the evolutionary multi-objective optimization platform PlatEMO to facilitate the use of multi-objective evolutionary algorithms (MOEAs), where some delicate techniques were developed to improve the computational efficiency of MOEAs. These techniques have not been introduced before, since users need not care about them when using existing MOEAs or developing new MOEAs. To deepen the understanding of the core mechanisms of PlatEMO, this paper gives a comprehensive introduction to these techniques, including new non-dominated sorting approaches, matrix calculation, and parallel computing. Several comparative experiments are conducted for a quantitative understanding of the efficiency improvement brought by these techniques.