Using objective clustering for solving many-objective optimization problems.

*(English)*Zbl 1299.90445Summary: Many-objective optimization problems involving a large number (more than four) of objectives have attracted considerable attention from the evolutionary multiobjective optimization field recently. With the increasing number of objectives, many-objective optimization problems may lead to stagnation in search process, high computational cost, increased dimensionality of Pareto-optimal front, and difficult visualization of the objective space. In this paper, a special kind of many-objective problems which has redundant objectives and which can be degenerated to a lower dimensional Pareto-optimal front has been investigated. Different from the works in the previous literatures, a novel metric, interdependence coefficient, which represents the nonlinear relationship between pairs of objectives, is introduced in this paper. In order to remove redundant objectives, PAM clustering algorithm is employed to identify redundant objectives by merging the less conflict objectives into the same cluster, and one of the least conflict objectives is removed. Furthermore, the potential of the proposed algorithm is demonstrated by a set of benchmark test problems scaled up to 20 objectives and a practical engineering design problem.

##### MSC:

90C90 | Applications of mathematical programming |

90C29 | Multi-objective and goal programming |

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

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\textit{X. Guo} et al., Math. Probl. Eng. 2013, Article ID 584909, 12 p. (2013; Zbl 1299.90445)

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