Artificial immune systems (AIS) are computational systems inspired by the principles and processes of the vertebrate immune system. The AIS-based algorithms typically exploit the immune system's characteristics of learning and adaptability to solve some complicated problems. Although, several AIS-based algorithms have proposed to solve multi-objective optimization problems (MOPs), little focus have been placed on the issues that adaptively use the online discovered solutions. Here, we proposed an adaptive selection scheme and an adaptive ranks clone scheme by the online discovered solutions in different ranks. Accordingly, the dynamic information of the online antibody population is efficiently exploited, which is beneficial to the search process. Furthermore, it has been widely approved that one-off deletion could not obtain excellent diversity in the final population; therefore, a k-nearest neighbor list (where k is the number of objectives) is established and maintained to eliminate the solutions in the archive population. The k-nearest neighbors of each antibody are founded and stored in a list memory. Once an antibody with minimal product of k-nearest neighbors is deleted, the neighborhood relations of the remaining antibodies in the list memory are updated. Finally, the proposed algorithm is tested on 10 well-known and frequently used multi-objective problems and two many-objective problems with 4, 6, and 8 objectives. Compared with five other state-of-the-art multi-objective algorithms, namely NSGA-II, SPEA2, IBEA, HYPE, and NNIA, our method achieves comparable results in terms of convergence, diversity metrics, and computational time.