In cable-stayed bridges, especially asymmetric bridges, counterweights are always made to work together with cable pretension forces to get a reasonable finished state. To solve the optimization problem of the cable-stayed bridge considering the counterweights, the integrated optimization method (IOM) for estimating cable forces and counterweights is proposed. In this method, the counterweights are proposed to act on the anchor points. After that, the summary of the minimum weighted total bending energy and the summary of the counterweights are considered as two objective functions of a multiobjective problem. Finally, the dynamic weighted coefficient method is used to solve this problem and realize the Pareto solution set. IOM presents detailed procedures in a simple numerical model and is then applied to the Yong-ding special-shaped cable-stayed bridge. The results show that not only IOM can realize the priority selection of the loading position of the counterweights but also get a better reasonable finish state because of the introduction of the counterweight dimension; the dynamic weighted coefficient method can quickly find the Pareto optimal solution set and be further screened by decision-makers; counterweight is very helpful to reduce torsion and other spatial effects in cable-stayed bridges. IOM can be used as a universal optimization method for cable-stayed bridges.

中文翻译：

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通用斜拉桥索力和配重的多目标优化

在斜拉桥中，尤其是非对称桥中，总是使配重与电缆的预紧力一起工作以达到合理的最终状态。为了解决斜拉桥考虑配重的优化问题，提出了一种综合优化方法（IOM）来估算索力和配重。在这种方法中，建议配重作用在锚点上。此后，最小加权总弯曲能量的汇总和配重的汇总被视为多目标问题的两个目标函数。最后，采用动态加权系数法解决了这一问题，实现了帕累托解集。IOM通过简单的数值模型给出详细的过程，然后将其应用于永定异型斜拉桥。结果表明，由于配重尺寸的引入，IOM不仅可以实现配重加载位置的优先选择，而且可以得到更好的合理精加工状态。动态加权系数法可以快速找到帕累托最优解集，并由决策者进一步筛选。配重对于减少斜拉桥的扭转和其他空间影响非常有用。IOM可以用作斜拉桥的通用优化方法。结果表明，由于配重尺寸的引入，IOM不仅可以实现配重加载位置的优先选择，而且可以得到更好的合理精加工状态。动态加权系数法可以快速找到帕累托最优解集，并由决策者进一步筛选。配重对于减少斜拉桥的扭转和其他空间影响非常有用。IOM可以用作斜拉桥的通用优化方法。结果表明，由于配重尺寸的引入，IOM不仅可以实现配重加载位置的优先选择，而且可以得到更好的合理精加工状态。动态加权系数法可以快速找到帕累托最优解集，并由决策者进一步筛选。配重对于减少斜拉桥的扭转和其他空间影响非常有用。IOM可以用作斜拉桥的通用优化方法。