The optimization method for determining open pit limit is important, as it is crucial to achieve the most profitable outcome from the limited amount of reserves available. However, importance must be also given to geotechnical aspects to ensure that safety requirements are met. Thus, overall slope angle (OSAs) must be incorporated in the optimization process. In the conventional methods, there were problems in incorporating various OSAs, or they were included in the pit design after the completion of the optimization procedure. To include variable OSAs in the optimization, cone-based method is still considered as one of the most suitable approaches. To apply this method, a new mathematical model incorporating various OSAs into the ultimate pit problem through mixed integer programming (MIP) and simulated annealing is proposed. Four different cases of change in OSAs in the pit were included in the algorithm. The proposed method was verified by applying it to five different cases, and the OSA was achieved with a considerably low difference of 0°–2° while optimizing the ultimate pit. The comparison between the introduced algorithm and the Lerchs–Grossman algorithm indicated that an improvement within a range of 8–20% can be achieved.

确定露天矿限制的优化方法很重要，因为从有限的可用储量中获得最有利可图的结果至关重要。但是，还必须重视岩土工程方面，以确保满足安全要求。因此，在优化过程中必须包含整体倾斜角 (OSA)。在传统方法中，在合并各种OSA时存在问题，或者在完成优化程序后将它们包括在坑设计中。为了在优化中包含可变 OSA，基于锥体的方法仍然被认为是最合适的方法之一。为了应用这种方法，提出了一种通过混合整数规划（MIP）和模拟退火将各种 OSA 纳入最终坑问题的新数学模型。算法中包括了坑内 OSA 变化的四种不同情况。通过将其应用于五种不同的情况来验证所提出的方法，并且在优化最终凹坑的同时，以 0°–2° 的相当低的差异实现了 OSA。引入的算法与 Lerchs-Grossman 算法之间的比较表明，可以实现 8-20% 范围内的改进。