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A simple immune-based multi-objective optimizer (IBMO) is proposed,and a rigorous running time analysis of IBMO on three proposed bi-objective pseudo-Boolean functions (Bi-Trap,Bi-Plateau and Bi-Jump) is presented.The running time of a global simple evolutionary multi-objective optimizer (GSEMO) using standard bit mutation operator with IBMO using somatic contiguous hypermutation (CHM) operator is compared with these three functions.The results show that the immune-based hypermutation can significantly beat standard bit mutation on some well-known multi-objective pseudo-Boolean functions.The proofs allow us to understand the relationship between the characteristics of the problems and the features of the algorithms more deeply.These analysis results also give us a good inspiration to analyze and design a bio-inspired search heuristics.