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This work investigates one multi-objective immune genetic algorithm to solve dynamic constrained single-objective multimodal optimization problems in terms of the concept of constraint-dominance and biological immune inspirations. The algorithm assumes searching multiple global optimal solutions along diverse searching directions, by means of the environmental detection and two evolving subpopulations. It exploits various kinds of promising regions through executing the periodical suppression mechanism and periodically adjusting the mutation magnitude. The sufficient diversity of population can be maintained relying upon a dynamic suppression index, and meanwhile the high-quality solutions can be found rapidly during the process of solution search. Comparative experiments show that the proposed approach can not only outperform the compared algorithms, but also rapidly acquire the global optima in each environment for each test problem, and thus it is a competitive optimizer.