In this paper hybrid flowshop scheduling problem where some jobs, not all, have to follow no-wait restriction (that is, the operations of that job must be processed with no stop) is examined. In the literature, all papers assume that all jobs of the shops have to follow no-wait restrictions. First, this paper mathematically formulates the problem with two different mixed integer linear models under proposed considerations. The models are evaluated using two performance measures of size

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... y and computational complexity. The small instances of the problem are solved using commercial software of mathematical programming. To solve larger instances of problem, two solution algorithms have been developed. These two algorithms are based on imperialist competitive algorithm and simulated annealing. A comprehensive numerical experiment including small and large instances is conducted to evaluate the models and algorithms. The results show that the imperialist competitive algorithm outperforms simulated annealing