On the use of evolutionary optimization for the dynamic chance constrained open-pit mine scheduling problem

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.

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.

Dynamic multi-objective optimization with a variable number of objectives is difficult because objective-dimensional variations may significantly change the Pareto front and degrade algorithm adaptability. This paper proposes an unbounded archive-based transfer strategy (UATS), which maintains an unbounded archive of offspring solutions within each environment stage and extracts feasible nondominated solutions as transferable elites when objective changes occur. UATS is embedded into SPEA2SDE to construct UATS-SPEA2SDE, enabling the algorithm to reuse historical evolutionary information while retaining the convergence and diversity advantages of shift-based density estimation. Experiments are conducted on four benchmark problems under three objective-changing settings, where UATS-SPEA2SDE is compared with a restart-based SPEA2SDE baseline and four representative dynamic multi-objective optimization algorithms. The results indicate that the archive-guided transfer improves recovery after environmental changes and enhances adaptability to objective-number variations.