Decomposition-based multi-objective optimization algorithms have been widely accepted as a competitive technique in solving complex multi-objective optimization problems (MOPs). Motivated by the facts that evolutionary operators are sensitive to the properties of problems, and even different search stages of an evolutionary operator often pose distinct properties when solving a problem. So far, numerous ensemble approaches have been designed to adaptively choose evolutionary operators for evolving population during different optimization stages. Then, during one stage, all the subproblems/subspaces in these existing ensemble approaches use the same evolutionary operator. But, for a complex MOP, the properties of its subproblems/subspaces are different. Based on the fact that existing ensemble approaches ignore this point, this article develops a fine-grained ensemble approach, namely FGEA, to choose suitable evolutionary operators for different subspaces during one generation. To be specific, the local and global contributions for each evolutionary operator in each subproblem/subspace are first defined. Then, an adaptive strategy is designed to encourage evolutionary operators making more contributions to obtain more opportunities to generate more offspring solutions. When choosing an evolutionary operator for a subspace, the proposed adaptive strategy considers both the local and global contributions of the evolutionary operators. Finally, based on 35 complex MOPs, we evaluate the effectiveness of the proposed FGEA by comparing it with five baseline algorithms. The experimental results reveal the competitive performance of the FGEA, which achieves the lowest inverted generational distance (IGD) values and the highest hypervolume values on 20 and 19 MOPs, respectively.
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