Chance-Constrained Bi-Objective Evolutionary Optimization for the Open-Pit Mining Operational Planning Problem

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.

Strategic mine production scheduling under geological uncertainty is conventionally formulated as a stochastic optimization problem in which a fixed extraction sequence and routing decisions are computed ex ante. This plan-driven paradigm treats uncertainty as passive: decisions are hedged across geological scenarios, but planning does not anticipate how future observations will inform future decisions. We propose a different perspective by formulating mine scheduling as a Partially Observable Markov Decision Process (POMDP), in which extraction and routing decisions are made sequentially with planning explicitly integrating the expectation of future belief updates. To achieve computational tractability, we introduce a hybrid SA-POMDP architecture that combines simulated annealing-based (SA) value approximation with ensemble-based belief updating via ensemble smoother with multiple data assimilation (ES-MDA). At each decision epoch, candidate actions are evaluated through their expected long-term value under the current belief, and the belief is updated as mining observations are assimilated. This yields an adaptive policy rather than a fixed plan. We evaluate the framework on a copper-gold open-pit mining complex with multiple processing destinations. Under a statistically consistent prior, the SA-POMDP reduces the expectation-reality gap from 22.3% to 4.6%, improving realized NPV by USD8.4M relative to one-shot stochastic optimization. Under systematic prior misspecification of 10%, the adaptive framework outperforms static planning by up to USD44.6M (36.9%), demonstrating structural robustness beyond scenario hedging. These results show that sequential belief updating transforms geological uncertainty from a passive constraint into an active component of value creation.

Open-pit mine scheduling is a critical process for maximizing economic return under complex geotechnical and operational constraints. While Mixed-Integer Linear Programming (MILP) provides mathematically optimal baselines, its exponential computational complexity and inability to adapt in real time limit its practical deployment in dynamic industrial environments. This work introduces a simulator-driven Large Language Model (LLM) scheduling framework in which the LLM acts as an autonomous decision-making agent, guided at each step by a custom simulator that encodes geotechnical precedence, extraction-processing coupling, and dynamic capacity constraints directly into the action generation mechanism. Operating entirely zero-shot within a closed, data-secure environment, the framework produces complete, interpretable extraction and processing schedules without cloud-based inference, domain-specific fine-tuning, or retraining. To provide a trustworthy performance benchmark, a novel MILP formulation is developed that incorporates realistic operational and geotechnical constraints. Evaluated across mining instances of varying scale and time periods, the LLM-based framework recovers between 94% and 99% of the MILP optimal NPV while scaling linearly in computation time. These results position simulator-constrained LLM agents as a practical and scalable alternative to classical optimization for long-horizon industrial scheduling under complex operational constraints.