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Lots of real-world optimization problems are inherently constrained multi-objective optimization problems (CMOPs), but the existing constrained multi-objective optimization evolutionary algorithms (CMOEAs) often fail to balance convergence and diversity effectively. Therefore, a novel constrained multi-objective optimization evolutionary algorithm based on three-stage multi-population coevolution (CMOEA-TMC) for complex CMOPs is proposed. CMOEA-TMC contains two populations, called
mainPop
and
helpPop
, which evolve with and without consideration of constraints, respectively. The proposed algorithm divides the search process into three stages. In the first stage, fast convergence is achieved by transforming the original multi-objective problems into multiple single-objective problems. Coarse-grained parallel evolution of subpopulations in
mainPop
and guidance information provided by
helpPop
can facilitate
mainPop
to quickly approach the Pareto front. In the second stage, the objective function of
mainPop
changes to the original problem. Coevolution of
mainPop
and
helpPop
by sharing offsprings can produce solutions with better diversity. In the third stage, the mining of the global optimal solutions is performed, discarding
helpPop
to save computational resources. For CMOEA-TMC, the combination of parallel evolution, coevolution, and staging strategy makes it easier for
mainPop
to converge and maintain good diversity. Experimental results on 33 benchmark CMOPs and a real-world boiler combustion optimization case show that CMOEA-TMC is more competitive than the other five advanced CMOEAs.