In this paper, a new model of capacitated lot sizing and scheduling in a permutation flow shop is developed. In this model demand can be totally backlogged. Setups can be carryover and are sequence-dependent. It is well-known from literatures that capacitated lot sizing problem in permutation flow shop systems are NP-hard. This means the model is solved in polynomial time and metaheuristics algorithms are capable of solving these problems within reasonable computing load. Metaheuristic algorithms ?nd more applications in recent researches. On this concern this paper proposes two evolutionary algorithms, one of the most popular namely, Genetic Algorithm (GA) and one of the most powerful population base algorithms namely, Imperialist Competitive Algorithm (ICA). The proposed algorithms are calibrate by Taguchi method and be compared against a presented lower bound. Some numerical examples are solved by both the algorithms and the lower bound. The quality of solution obtained by the proposed algorithm showed superiority of ICA to GA.