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A Kriging-assisted multi-stage evolutionary algorithm for expensive many-objective optimization problems
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DOI：10.1007/s00158-024-03748-4.png)
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For expensive problems, as the number of objectives and the number of decision variables increase, the number of non-dominated solutions in the population increases dramatically, and the population does not have enough convergence pressure to converge to the true pareto frontier. A Kriging-assisted Multi-stage Evolutionary Algorithm (K-MSEA) is proposed to enhance the exploratory capacity of populations in expensive many-objective optimization problems. A multi-stage strategy is used in K-MSEA. Mating selection and environmental selection of populations are divided into three stages based on convergence and diversity indices. Targeted selection of individuals should be conducted at each stage of population development. The population independently chooses the appropriate stage in accordance with the current demands of convergence and diversity. Differential evolutionary algorithm is used to improve the search ability of the population. To guide the population in the correct direction, K-MSEA employs an elite retention strategy in environmental selection. The population utilizes individual renewal, where underperforming parents are replaced by better-performing offspring. The surrogate model is then updated with the uncertainty information supplied by the Kriging model. Finally, K-MSEA is benchmarked against five other algorithms in experiments on two benchmark problems and two realistic expensive problems. Mathematical analysis demonstrates that K-MSEA is more competitive than others.
Keyword:
Expensive many-objective optimization problems
Multi-stage
Differential evolutionary
Elite retention strategy
Kriging model
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