The hybrid flow-shop scheduling problem (HFSP) is used in a wide range of industries and is very hard to solve. There has been a great deal of research on HFSP with the objective of makespan, but related research mainly focused on the algorithmic level, ignoring characters of HFSP. In this paper, through the study of the characters of HFSP itself, together with the design of the algorithm, new records on benchmarks are obtained. Firstly, the property of unconditional feasibility of HFSP (UFH) is formally proven. Based on UFH, the disjunctive-graph-based encoding scheme is considered convenient and accurate to HFSP, and the constraints for feasible neighborhood solutions are superfluous to HFSP. New specialized neighborhood structures are developed for HFSP accordingly. Secondly, traditional schedule types (such as active schedule) are found to be further explored. A novel type of schedule, all-active schedule (AAS) is proposed to tap the potential of one scheduling process. Thirdly, an improved co-evolutionary memetic algorithm (ICMA) based on UFH and AAS is proposed to solve HFSP. To balance exploration and exploitation, the co-evolutionary framework with multiple groups is adopted. Path reconnection is used as a crossover operator, and a non-dominated selection mechanism is also employed. In the end, the effectiveness of ICMA is experimentally demonstrated. 1 new solution on Carlier benchmark (proposed in 2000) and 45 new solutions on Jose benchmark (proposed in 2020) are found by ICMA, outperforming all previous outstanding algorithms.
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