Open-pit mine scheduling is a complex real world optimization problem that involves uncertain economic values and dynamically changing resource capacities. Evolutionary algorithms are particularly effective in these scenarios, as they can easily adapt to uncertain and changing environments. However, uncertainty and dynamic changes are often studied in isolation in real-world problems. In this paper, we study a dynamic chance-constrained open-pit mine scheduling problem in which block economic values are stochastic and mining and processing capacities vary over time. We adopt a bi-objective evolutionary formulation that simultaneously maximizes expected discounted profit and minimizes its standard deviation. To address dynamic changes, we propose a diversity-based change response mechanism that repairs a subset of infeasible solutions and introduces additional feasible solutions whenever a change is detected. We evaluate the effectiveness of this mechanism across four multi-objective evolutionary algorithms and compare it with a baseline re-evaluation-based change-response strategy. Experimental results on six mining instances demonstrate that the proposed approach consistently outperforms the baseline methods across different uncertainty levels and change frequencies.

翻译：露天矿调度是一个复杂的现实世界优化问题，涉及不确定的经济价值和动态变化的资源容量。进化算法在此类场景中尤为有效，因为它们能轻松适应不确定和变化的环境。然而，在现实问题中，不确定性和动态变化往往被孤立研究。本文研究了一个动态机会约束的露天矿调度问题，其中块体经济价值具有随机性，且采矿和加工能力随时间变化。我们采用双目标进化建模方法，同时最大化期望折现利润并最小化其标准差。针对动态变化，我们提出了一种基于多样性的变化响应机制，该机制在检测到变化时修复部分不可行解并引入额外可行解。我们在四种多目标进化算法中评估了该机制的有效性，并将其与基于重新评估的变化响应基线策略进行比较。在六个采矿实例上的实验结果表明，在不同不确定性水平和变化频率下，所提方法始终优于基线方法。