Evolutionary sequential transfer optimization (ESTO), which attempts to enhance the evolutionary search of a target task using the knowledge captured from several previously-solved source tasks, has been receiving increasing research attention in recent years. Despite the tremendous approaches developed, it is worth noting that existing benchmark problems for ESTO are not well designed, as they are often simply extended from other benchmarks in which the relationships between the source and target tasks are not well analyzed. Consequently, the comparisons conducted on these problems are not systematic and can only provide numerical results without a deeper analysis of how an ESTO algorithm performs on problems with different properties. Taking this clue, this two-part paper revisits a large body of solution-based ESTO algorithms on a group of newly developed test problems, to help researchers and practitioners gain a deeper understanding of how to better exploit optimization experience towards enhanced optimization performance. Part A of the series designs a problem generator based on several newly defined concepts to generate benchmark problems with diverse properties, which are competitive in resembling real-world problems. Part B of the series empirically revisits various algorithms by answering five key research questions related to knowledge transfer. The results demonstrated that the performance of many ESTO algorithms is highly problem-dependent, which suggest the necessity of more research efforts on transferability measurement and enhancement in ESTO algorithm design. The source code of the benchmark suite developed in part A is available at https://github.com/XmingHsueh/Revisiting-S-ESTOs-PartA.