Multiobjective genetic algorithms (MOGAs) have proven to be powerful in solving multiobjective problems in the accelerator field. Nevertheless, for explorative problems that have many variables and local optima, the performance of MOGAs is not always satisfactory, especially when a small population size is used due to practical limitations, e.g., limited computing resources. To deal with this challenge, in this paper an enhanced MOGA, neural network-based MOGA (NBMOGA), is proposed. In this method, the data produced with the standard MOGA are used to train a neural network. The neural network is fast to produce a large pool of objective function estimates, with sufficiently high accuracy. A subset of the most competitive estimates is selected to form a population (matching MOGA population size), which is then evaluated with the MOGA evaluator. By taking three classic multiobjective problems as examples, we demonstrate that the proposed method promises a faster convergence and a higher degree of diversity than that available with the standard MOGA and other three optimization methods that have been applied in the accelerator field, i.e., the multiobjective particle swarm optimization (MOPSO), the combination of MOPSO and MOGA, and the clustering enhanced MOGA. And then this method is applied to a time-consuming optimization problem, the dynamic aperture and Touschek lifetime optimization of the high energy photon source. It turns out that, within the same optimization time, a better set of solutions in the objective space can be obtained with the NBMOGA than using other methods. The Touschek lifetime can be improved by about 10% compared with using the standard MOGA, with approximately the same dynamic aperture area. Besides, a higher degree of diversity among solutions is observed with the NBMOGA than using other tested methods.

中文翻译：

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基于神经网络的非线性梁动力学多目标优化算法

事实证明，多目标遗传算法（MOGA）在解决加速器领域中的多目标问题方面功能强大。然而，对于具有许多变量和局部最优的探索性问题，MOGA的性能并不总是令人满意，特别是当由于实际限制（例如，有限的计算资源）而使用的人口规模较小时。为了应对这一挑战，本文提出了一种增强型MOGA，即基于神经网络的MOGA（NBMOGA）。在这种方法中，使用标准MOGA生成的数据来训练神经网络。神经网络能够以足够高的精度快速生成大量目标函数估计值。选择最具竞争力的估算值的一个子集以形成总体（与MOGA总体大小匹配），然后使用MOGA评估程序对其进行评估。通过以三个经典的多目标问题为例，我们证明了与标准的MOGA和在加速器领域中应用的其他三种优化方法相比，该方法具有更快的收敛性和更高的多样性。粒子群优化（MOPSO），MOPSO和MOGA的组合以及聚类增强的MOGA。然后将该方法应用于耗时的优化问题，高能光子源的动态孔径和Touschek寿命优化。事实证明，在相同的优化时间内，使用NBMOGA可以获得比使用其他方法更好的目标空间解决方案集。与使用标准MOGA相比，Touschek的使用寿命可以提高大约10％，具有大致相同的动态光圈面积。此外，与使用其他测试方法相比，使用NBMOGA可以观察到溶液之间具有更高的多样性。