A many-objective population extremal optimization algorithm with an adaptive hybrid mutation operation.

*(English)*Zbl 1451.90171Summary: Many-objective optimization problems abbreviated as MaOPs with more than three objectives have attracted increasing interests due to their widely existing in a variety of real-world applications. This paper presents a novel many-objective population extremal optimization called MaOPEO-HM algorithm for MaOPs by introducing a reference set based many-objective optimization mechanism into a recently developed population extremal optimization framework and designing an adaptive hybrid mutation operation for updating the population. Despite of the successful applications of extremal optimization in different kinds of numerical and engineering optimization problems, it has never been explored to the many-objective optimization domain so far. Because most of the existing many-objective evolutionary algorithms are usually guided by a single mutation operation, which has insufficient ability to exploit the search space of MaOPs and will get stuck at any local efficient front, it is the first attempt to design a novel hybrid mutation scheme in MaOPEO-HM algorithm by combining the advantages of polynomial mutation operator and multi-non-uniform mutation operator effectively. The experiment results for DTLZ test problems with 3, 5, 8, 10, and 15 objectives and WFG test problems with 3, 5, and 8 objectives have demonstrated the superiority of the proposed MaOPEO-HM to five state-of-the-art decomposition-based many-objective evolutionary algorithms including NSGA-III, RVEA, EFR-RR, \( \theta \)-DEA, and MOEA/DD and two non-decomposition-based algorithms including GrEA and Two\(\_\)Arch2. Furthermore, the great ability of the designed adaptive hybrid mutation operation incorporated into many-objective population extremal optimization (MaOPEO) has also been illustrated by comparing MaOPEO-HM and two MaOPEO algorithms only based on traditional multi-non-uniform mutation or polynomial mutation for DTLZ problems.

##### MSC:

90C59 | Approximation methods and heuristics in mathematical programming |

68W50 | Evolutionary algorithms, genetic algorithms (computational aspects) |

90C29 | Multi-objective and goal programming |

##### Keywords:

many-objective optimization problems; many-objective evolutionary algorithms; many-objective population extremal optimization; adaptive hybrid mutation operation
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