Abstract No‐wait flow shop scheduling problems (NWFSPs) are widespread in practical applications. The authors propose a quantum‐inspired cuckoo co‐evolutionary algorithm for the NWFSP to minimize the makespan. There are three algorithm components: quantum solution construction, quantum population evolution, and an improved neighbourhood local search. They generate initial solutions, search solutions, and improve solution qualities, respectively. Parameters of the proposed algorithm are calibrated statistically. The proposal with calibrated parameters is compared with three existing algorithms on Reeves and Taillard benchmark instances with middle scales. Experimental results show that the proposal outperforms the compared algorithms.
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