The present paper is aimed to investigate a Redundancy Allocation Problem (RAP) to maximize the reliability and minimize the costs for a K-out-of-Nsystem. Within a subsystem, it should be chosen one among the strategies of the single component, parallel components, and cold-standby components. Additionally, it should be observed the weight and volume constraints of the parts for designing the system. Further, each subsystem should have at least K parts for activation. For modeling, after the initial chromosomes, four multi-objective meta-heuristic algorithms (MODE, NSGA-II, MOICA and PESA-II) have been studied. The above mentioned algorithms were compared with two methods of C (L, B) and TOPSIS, and then, NSGA-II algorithm has been elected as the best to be used. Ultimately, the final results of the algorithms were evaluated with various determined weights of target functions by TOPSIS, and later, the strategy of cold-standby components has led to best results with highest reliability and lowest costs. As the result, the cold-standby configuration of parts combined with the strategies of single component or parallel components might provide for the better conditions in the system.