Recently, due to the growth in machine learning and data mining, for scheduling applications in China’s industrial intelligence, we are quite fortunate to witness a paradigm of evolutionary scheduling via learning, which includes a new tool of evolutionary transfer optimization (ETO). As a new subset in ETO, single-objective to multi-objective/many-objective optimization (SMO) acts as a powerful, abstract and general framework with wide industrial applications like shop scheduling and vehicle routing. In this paper, we focus on the general mechanism of selection that selects or gathers elite and high potential solutions towards gathering/transferring strength from single-objective problems, or gathering/transferring storms of knowledge from solved tasks. Extensive studies in vehicle routing problems with time windows (VRPTW) on well-studied benchmarks validate the great universality of the SMO framework. Our investigations (1) contribute to a deep understanding of SMO, (2) enrich the classical and fundamental theory of building blocks for genetic algorithms and memetic algorithms, and (3) provide a completive and potential solution for VRPTW.

Single-objective to multi-objective/many-objective optimization (SMO) is a new paradigm in the evolutionary transfer optimization (ETO), since there are only “1 + 4” pioneering works on SMOs so far, that is, “1” is continuous and is firstly performed by Professors L. Feng and H.D. Wang, and “4” are firstly proposed by our group for discrete cases. As a new computational paradigm, theoretical insights into SMOs are relatively rare now. Therefore, we present a proposal on the fine brushworks of SMOs for theoretical advances here, which is based on a case study of a permutation flow shop scheduling problem (PFSP) in manufacturing systems via lenses of building blocks, transferring gaps, auxiliary task and asynchronous rhythms. The empirical studies on well-studied benchmarks enrich the rough strokes of SMOs and guide future designs and practices in ETO based manufacturing scheduling, and even ETO based evolutionary processes for engineering optimization in other cases.

As a new abstract computational model in evolutionary transfer optimization (ETO), single-objective to multi-objective optimization (SMO) is conducted at the macroscopic level rather than the intermediate level for specific algorithms or the microscopic level for specific operators; this method aims to develop systems with a profound grasp of evolutionary dynamic and learning mechanism similar to human intelligence via a “decomposition” style (in the abstract of the well-known “Transformer” article “Attention is All You Need”, they use “attention” instead). To the best of our knowledge, it is the first work of SMO for discrete cases because we extend our conference paper and inherit its originality status. In this paper, by implementing the abstract SMO in specialized memetic algorithms, key knowledge from single-objective problems/tasks to the multi-objective core problem/task can be transferred or “gathered” for permutation flow shop scheduling problems, which will reduce the notorious complexity in combinatorial spaces for multi-objective settings in a straight method; this is because single-objective tasks are easier to complete than their multi-objective versions. Extensive experimental studies and theoretical results on benchmarks (1) emphasize our decomposition root in mathematical programming, such as Lagrangian relaxation and column generation; (2) provide two “where to go” strategies for both SMO and ETO; and (3) contribute to the mission of building safe and beneficial artificial general intelligence for manufacturing via evolutionary computation.