An efficient multi-objective algorithm based on SA is presented to solve MORAP.The algorithm called knowledge-based archive MOSA (KBAMOSA) algorithm.KBAMOSA used a memory matrix to reinforce the neighborhood structure.KBAMOSA algorithm dominated the solutions obtained by NSGA-II.KBAMOSA is superior to AMOSA algorithm based on standard metrics. Redundancy allocation problem (RAP) is one of the best-developed problems in reliability engineering studies. This problem follows to optimize the reliability of a system containing s sub-systems under different constraints, including cost, weight, and volume restrictions using redundant components for each sub-system. Various solving methodologies have been used to optimize this problem, including exact, heuristic, and meta-heuristic algorithms. In this paper, an efficient multi-objective meta-heuristic algorithm based on simulated annealing (SA) is developed to solve multi-objective RAP (MORAP). This algorithm is knowledge-based archive multi-objective simulated annealing (KBAMOSA). KBAMOSA applies a memory matrix to reinforce the neighborhood structure to achieve better quality solutions. The results analysis and comparisons demonstrate the performance of the proposed algorithm for solving MORAP.