关键词: 关键词：多目标优化, 分层, 双关联, 收敛性, 多样性

Abstract:
Abstract: In this paper， Two level Double Association-based Evolutionary Algorithm for multi-objective optimization（T-DAEA） is proposed to solve the curse of dimensionality in multi-objective optimization problem as the number of objectives increases. The proposed angle-based bi-association strategy considers the empty subspace and associates it with the solution with the highest fitness， increasing the probability of exploring unknown regions. In addition， a new quality assessment scheme is designed to quantify the quality of each solution in the subspace by first measuring the convergence and diversity of each solution， then designing dynamic penalty coefficients to balance the convergence and diversity by penalizing the global diversity distribution of the solutions， and performing an adaptive hierarchical ordering of the solutions that have completed the assessment to ensure the selection of the best solution. The performance of the proposed algorithm， T-DAEA， is validated and compared with four state-of-the-art multi-objective evolutionary algorithms on a number of well known benchmark problems （up to 20 objectives）. Experimental results show that the algorithm is highly competitive in terms of both convergence enhancement and diversity maintenance. 

Key words: Key words: multi-objective optimization, hierarchical, bicorrelation, convergence, diversity