An improved rime optimization algorithm for cloud manufacturing scheduling under open shop environment

Cloud manufacturing (CMfg) is an advanced networked intelligent manufacturing model, which virtualizes distributed resources and delivers mass-customized production services, thereby imposing stringent requirements on scheduling efficiency. The scheduling of the CMfg workshop layer is an important supporting technology for the smooth implementation of the CMfg scheduling scheme. The relevant literature has focused mainly on flow-shop and job-shop formulations, in which each operation is bound to a fixed routing sequence. Although this facilitates tractable modelling and algorithm design, it constrains routing flexibility and may prevent more successful schedules with superior makespan and resource-balancing performance. The open-shop paradigm lifts these precedence restrictions, allowing operations to be processed in any order; such freedom is particularly advantageous in CMfg environments. This paper investigates the CMfg scheduling problem in the open-shop environments, and a MILP model is formulated to minimize makespan. Owing to the NP-hard nature of the problem, a multi-population rime optimization algorithm with elite-ordinary co-evolving (EOMPRIME) is developed. The elite-ordinary synergistic multi-population guidance mechanism is proposed, where search intensification is driven by an elite sub-population; diversification is maintained by an ordinary sub-population. Its performance is examined through extensive numerical experiments, which soundly confirm the effectiveness and efficiency of the proposed method.