In this paper, we propose a framework to accelerate the computational efficiency of evolutionary algorithms on large-scale multiobjective optimization. The main idea is to track the Pareto optimal set (PS) directly via problem reformulation. To begin with, the algorithm obtains a set of reference directions in the decision space and associates them with a set of weight variables for locating the PS. Afterwards, the original large-scale multiobjective optimization problem is reformulated into a low-dimensional single-objective optimization problem. In the reformulated problem, the decision space is reconstructed by the weight variables and the objective space is reduced by an indicator function. Thanks to the low dimensionality of the weight variables and reduced objective space, a set of quasi-optimal solutions can be obtained efficiently. Finally, a multiobjective evolutionary algorithm is used to spread the quasi-optimal solutions over the approximate Pareto optimal front evenly. Experiments have been conducted on a variety of large-scale multiobjective problems with up to 5000 decision variables. Four different types of representative algorithms are embedded into the proposed framework and compared with their original versions, respectively. Furthermore, the proposed framework has been compared with two state-of-the-art algorithms for large-scale multiobjective optimization. The experimental results have demonstrated the significant improvement benefited from the framework in terms of its performance and computational efficiency in large-scale multiobjective optimization.

中文翻译：

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通过问题重构加速大规模多目标优化

在本文中，我们提出了一个框架来加速进化算法在大规模多目标优化中的计算效率。主要思想是通过问题重构直接跟踪帕累托最优集 (PS)。首先，该算法在决策空间中获得一组参考方向，并将它们与一组用于定位 PS 的权重变量相关联。之后，将原来的大规模多目标优化问题重新表述为低维单目标优化问题。在重构问题中，决策空间由权重变量重构，目标空间由指标函数缩小。由于权重变量的低维数和减少的目标空间，可以有效地获得一组准最优解。最后，使用多目标进化算法将准最优解均匀地分布在近似帕累托最优前沿上。已经对具有多达 5000 个决策变量的各种大规模多目标问题进行了实验。四种不同类型的代表性算法被嵌入到所提出的框架中，并分别与它们的原始版本进行比较。此外，已将所提出的框架与用于大规模多目标优化的两种最先进的算法进行了比较。实验结果表明，该框架在大规模多目标优化中的性能和计算效率方面得到了显着改善。