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In this paper, we propose a novel immune dominance selection multi-objective optimization algorithm (IDSMOA) to solve multi-objective numerical and engineering optimization problems in the real world. IDSMOA was inspired by the mechanism that controls how B cells and T cells differentiate, recombine, and mutate self-adjustably to produce new lymphocytes matching antigens with high affinity, then how lymphocytes cooperatively eliminate antigens. The main idea of IDSMOA is to promote 2 populations, population B and population T, to coevolve through an immune selection operator, immune clone operator, immune gen operator, and memory selection operator to produce satisfying Pareto front. Therefore, several operators enable IDSMOA to exploit and excavate the search space, and decrease the number of dominance resistant solutions (DRSs). We compared IDSMOA performance with 3 known multi-objective optimization algorithms and IDSMOA without the combination operator in simulation experiments optimizing 12 benchmark functions. Our simulations indicated that IDSMOA is a competitive optimization tool for multi-objective optimization problems. [ABSTRACT FROM AUTHOR]