Fuel distribution is a critical bottleneck in open-pit mining operations, where unplanned equipment downtime due to fuel depletion directly increases operational costs and disrupts production continuity. Optimizing fuel truck routing under real-time, dynamic conditions, accounting for equipment locations, fuel levels, and refueling priorities, remains an insufficiently addressed problem in the existing vehicle routing literature. This study evaluates and compares three algorithmic approaches for solving the priority-constrained fuel truck routing problem in open-pit mining: Brute Force (BF), Branch and Bound with a Reduced Matrix Approach (B & B), and Ant Colony Optimization (ACO). The algorithms are tested on two datasets from a North American coal mine, a primary dataset of 14 equipment units and a supplementary dataset of 38 units, using geodesic distances and a three-tier priority structure based on real-time fuel levels. A modified B & B formulation employing matrix reduction and dummy variables is applied to enforce priority group constraints without premature depot returns. ACO parameters are tuned for the priority-constrained routing environment with a fixed depot start. On the primary dataset, BF yields the optimal path of 54.39 km in 1.68 seconds, B & B produces a near-optimal path of 55.01 km in 1.41 seconds, and ACO achieves a heuristic path of 55.01 km in 0.22 seconds. Scalability analysis shows that BF becomes computationally infeasible beyond 17 equipment units, B & B beyond 29 units, while ACO consistently delivers near-optimal solutions across all tested scales within approximately 1 second. ACO is identified as the most suitable algorithm for real-time fuel truck routing in large-scale open-pit mining operations, offering the best balance between solution quality and computational efficiency, with a deviation of 1.13% from the optimal path.

The muonography method is an innovative method for obtaining information about the internal condition of massive natural features and industrial facilities using cosmic radiation particles, namely high-energy atmospheric muons. The method studies the features of the passage of these particles through extended objects located on the earth’s surface and below it that allows for the detection of hidden density anomalies and their monitoring. Muonography can be used to solve a wide range of applied problems, from searching for mineral resources to assessing possible natural and man-made risks for civil infrastructure. The method is based on the analysis of the characteristics of muon fluxes after they pass through a target (the subject of research: a natural feature, or industrial facility, etc.). The presence of hidden areas of increased or decreased density inside a target changes the number of muons that have passed through it. Probing muons are recorded using detectors installed below and/or to the side of the area under study. Comparing the recorded muon fluxes with the expected ones allows not only to conclude about the presence of a hidden area of increased or decreased density, but also to determine its location and estimate its dimensions. Muonography is a promising tool for solving geological and geophysical problems, not only as a supplement to traditional approaches, but also as an independent experimental method for searching for mineral deposits, forecasting and analyzing the consequences of seismic and volcanic processes, assessing deformations in fault zones in landslide areas, karst massifs, etc. The authors of the paper have more than ten years of experience in conducting muonographic experiments using nuclear emulsion detectors that record atmospheric muons. As a result, unique developments were performed regarding the experimental setup, processing, and analysis of data obtained using photographic nuclear emulsion. The paper discusses the prospects and features of the muonographic technique as applied to geological and geophysical research.