A hybrid multiobjective evolutionary algorithm model based on local linear embedding

Based on the following property: under mild conditions, it can be induced from the Karush-Kuhn-Tucker condition that the Pareto set, in the decision space, of a continuous multiobjective optimisation problems MOPs is a piecewise continuous m − 1 − D manifold where m is the number of objectives, a hybrid multiobjective evolutionary algorithm model based on local linear embedding is proposed for continuous MOPs. At each generation: 1 via local linear embedding and its improved algorithms, the proposed algorithm digs out a nonlinear manifold in the decision space; 2 the new trial solutions are built through the manifold of step 1; 3 a non-dominated sorting-based selection is used for choosing solutions and produce the next generation. Systematic experiments have shown that the algorithm can find out nonlinear manifold hidden in the decision space of MOPs and guide rapid convergence of algorithm.

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