Abstract
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.
Highlights
Real-world problems in various fields, such as hybrid electric vehicle control problem [1], optimizing wireless networks [2], [3], feature selection for classification [4], service composition in clouds [5], resource allocation in radar networks [6], [7], intelligent traffic management [8], [9], and resource investment project scheduling [10], usually involve simultaneously optimizing at least two conflicting objectives
WORK This article focuses on the properties of complex multi-objective problems that vary throughout both the decision and objective spaces, and develops a fine-grained ensemble approach to choose a suitable evolutionary operator for a subspace during each generation
To assess the effectiveness of the proposed ensemble approach, extensive experiments on 35 complex multi-objective optimization problems (MOPs) are carried out to compare the FGEA with five baseline algorithms
Summary
Real-world problems in various fields, such as hybrid electric vehicle control problem [1], optimizing wireless networks [2], [3], feature selection for classification [4], service composition in clouds [5], resource allocation in radar networks [6], [7], intelligent traffic management [8], [9], and resource investment project scheduling [10], usually involve simultaneously optimizing at least two conflicting objectives. There exist numerous ensemble approaches adaptively choosing evolutionary operators during different optimization stages, such improving the capability of decomposition-based MOEAs in coping with MOPs. For instance, Hitomi et al recognized the difficulty in defining. Zhao et al employed a learning automaton technique to select evolutionary operators for decomposition-based MOEAs based on feedback from the optimization process, developed an adaptive strategy to adjust the reference vectors using the obtained solutions in the external archive [33]. To enhance the performance of decomposition-based MOEAs, Lin et al designed an adaptive mechanism for dynamically choosing evolutionary operators during the optimization process [35]. This article proposes a fine-grained ensemble approach, namely FGEA, to choose suitable evolutionary operators for different sub-spaces during different optimization stages.
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