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In this article, a water wave optimization algorithm with a single wave mechanism, called single water wave optimization (SWWO), is proposed to solve the no-wait flow-shop scheduling problem (NWFSP) with the objective of minimizing the makespan. In the proposed SWWO, an improved Nawaz–Enscore–Ham (NEH) heuristic is applied to construct a high-quality initial candidate. In the propagation operation, a self-adaptive block-shift operation is employed. In the breaking operation, a variable neighbourhood search operation is utilized to explore the local optimal solution. According to the schema theory as presented in genetic algorithms, a crossover operation is adopted as the refraction operation. Finally, the computational results based on several benchmarks and statistical performance comparisons are presented. The experimental results demonstrate the effectiveness and efficiency of the proposed SWWO for solving the NWFSP. [ABSTRACT FROM AUTHOR]