Abstract: Addressing high-dimensional portfolio optimization problems, this paper introduces a multi-objective evolutionary algorithm based on nondominated sorting and hybrid search that integrates decomposition methods and multiple subpopulation strategies. Considering the limitations of existing evolutionary algorithms in dealing with large-scale problems due to their expansive search spaces, a decomposition-based strategy is introduced. This strategy effectively divides the population into three subgroups by analyzing the distance between individuals and reference points. To enhance population diversity and avoid local optima, the algorithm incorporates individual positional characteristics and utilizes a hybrid of local and global search strategies. Furthermore, the algorithm effectively generates high-quality solutions through a decomposition-based dual-environment selection mechanism. In LSMOP experiments with 100, 500, and 1 000 decision variables, the algorithm demonstrates performance surpassing several advanced evolutionary algorithms. Lastly, applying this algorithm to the CVaR model with transaction costs and comparing it with three other multi-objective evolutionary algorithms further confirms its advantages in practical applications.

Key words: multi-objective optimization, evolutionary algorithm, nondominated sorting, hybrid search

摘要： 针对高维投资组合优化问题，提出了一种基于非支配排序和混合搜索的多目标优化算法。考虑到现有进化算法在大规模问题处理上受限于其广泛的搜索空间，引入了基于分解的策略。该策略通过分析个体与参考点的距离，有效地将种群划分为三个子群体。为提升种群多样性并避免局部最优，算法结合了个体的位置特征，并采用了混合局部和全局搜索策略。此外，通过基于分解的双重环境选择机制，有效生成优质解。在包含100、500和1 000个决策变量的LSMOP实验中，该算法展现出超越多个先进进化算法的性能。最后，应用该算法于包含交易成本的CVaR模型，并与其他三种多目标进化算法进行比较，进一步证实了其在实际应用中的优势。

关键词: 多目标优化, 进化算法, 非支配排序, 混合搜索