Multiobjective Evolutionary Algorithm based on Regularity
[Qingfu Zhang's homepage]

Q. Zhang, A. Zhou, Y. Jin, RM-MEDA: A Regularity Model Based Multiobjective Estimation of Distribution Algorithm, IEEE Trans. on Evolutionary Computation, vol. 12, no. 1, pp 41-63,  2008.

MATLAB code  

C++ code

Erratum to figure 20. 

Under mild conditions, it can be induced from the Karush-Kuhn-Tuckercondition that the Pareto set, in the decision space, of a continuous multiobjective optimization problem is $(m-1)$-D piecewise continuous, where $m$ is the number of objectives. Based on this regularity property, we propose a Regularity Model based Multiobjective Estimation of Distribution Algorithm (RM-MEDA) for continuous multiobjective optimization problems with variable linkages. At each generation, the proposed algorithm models a promising area in the decision space by a probability distribution whose centroid is a $(m-1)$-D piecewise continuous manifold. The Local PCA algorithm is used for building such a model. New trial solutions are sampled from the model thus built. A non-dominated sorting based selection is used for choosing solutions for the next generation. Systematic experiments have shown that, overall, RM-MEDA outperforms other three state-of-the-art algorithms, GDE3, PCX-NSGA-II and MIDEA, on a set of test instances with variable linkages. We have demonstrated that, compared with GDE3, RM-MEDA is not sensitive to algorithmic parameters, and has good scalability to the number of decision variables in the case of nonlinear variable linkages. A few shortcomings of RM-MEDA have also been identified and discussed in this paper.

 

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last updated March, 2006, Q. Zhang