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A novel model-based multiobjective evolutionary algorithm

Zhiming Song, Maocai Wang, Guangming Dai, Xiaoyu Chen

As is known that the Pareto set of a continuous multi-objective optimization problem with m objective functions is a piecewise continuous (m-1)-dimensional manifold in the decision space under some mild conditions. However, how to utilize the regularity to design multi-objective optimization algorithms has become the research focus. In this paper, based on this regularity, a model-based multi-objective evolutionary algorithm with regression analysis (MMEA-RA) is put forward to solve continuous multi-objective optimization problems with variable linkages. In the algorithm, the optimization problem is modelled as a promising area in the decision space by a probability distribution, and the centroid of the probability distribution is (m-1)-dimensional piecewise continuous manifold. The least squares method is used to construct such a model. A selection strategy based the non-dominated sorting is used to choose the individuals to the next generation. The new algorithm is tested and compared with NSGA-II and RM-MEDA. The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages. At the same time, MMEA-RA has higher efficiency than the other two algorithm. A few shortcomings of MMEA-RA have also been identified and discussed in this paper