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**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.**

Most existing multiobjective
evolutionary algorithms aim at approximating the Pareto front (PF), which is the
distribution of the Pareto-optimal solutions in the objective space. In many
real-life applications, however, a good approximation to the Pareto set (PS),
which is the distribution of the Paretooptimal
solutions in the decision space, is also required by a decision maker. This
paper considers a class of multiobjective
optimization problems (MOPs), in which the dimensionalities of the PS and the
PF manifolds are different so that a good approximation to the PF might not
approximate the PS very well. It proposes a probabilistic model-based multiobjective evolutionary algorithm, called MMEA, for
approximating the PS and the PF simultaneously for an MOP in this class. In the
modelling phase of MMEA, the population is clustered into a number of
subpopulations based on their distribution in the objective space, the
principal component analysis technique is used to estimate the dimensionality
of the PS manifold in each subpopulation, and then a probabilistic model is
built for modeling the distribution of the Pareto-optimal
solutions in the decision space. Sucha a modeling procedure could promote the population diversity
in both the decision and objective spaces. MMEA is compared withthree
other methods, KP1, Omni-Optimizer and RM-MEDA, on a set of test instances, ﬁve
of which are proposed in this paper. The experimental results clearly suggest
that, overall, MMEA performs signiﬁcantly
better than the three compared algorithms in approximating both the PS and the
PF.