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a b s t r a c tThis paper aims to provide a solution method for a real-world scheduling case from a welding process, which is one of the important processes in modern industry. The unique characteristic of the welding scheduling problem (WSP) is that multiple machines can process one operation at a time. Thus, WSP is a new scheduling problem. We first formulate a new multi-objective mixed integer programming model for this WSP based on a comprehensive investigation. This model involves some realistic constraints, controllable processing times (CPT), sequence dependent setup times (SDST) and job dependent transportation times (JDTT). Then we propose a multi-objective discrete grey wolf optimizer (MODGWO) considering not only production efficiency but also machine load on this real-world scheduling case. The solution is encoded as a two-part representation including a permutation vector and a machine assignment matrix. A reduction machine load strategy is used to adjust the number of machines aiming to minimize the machine load. To evaluate the effectiveness of the proposed MODGWO, we compare it with other well-known multi-objective evolutionary algorithms including NSGA-II and SPEA2 on a set of instances. Experimental results demonstrate that the proposed MODGWO is superior to the compared algorithms in terms of convergence, spread and coverage on most instances. Finally, MODGWO is successfully applied to this real-world WSP. This implies that the proposed model is feasible and the proposed algorithm can solve this real-world scheduling problem very well.

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