An efficient method for optimizing nested open pits with operational bottom space
Bibliographic record
Abstract
Abstract Determining a set of nested pits to support the design of an open pit mine that leads to high economic value is crucial for the strategic planning of these operations; thus, practitioners rely on optimization methods for finding high‐value solutions. However, current approaches are not sufficient as they lack at least one of the following features: fast computations of optimal solutions, good geometric properties, and nestedness of the pits. In this work, we propose an optimization model to address the problem of determining multiple nested pits by introducing a cost‐based penalty for not meeting precedence constraints linked to a minimum bottom width. Using penalties instead of constraints is novel and turns out to have several advantages. First, the constraint matrix is totally unimodular; thus, the problem can be solved efficiently. Second, the model can be parameterized to generate nested pits. Therefore, our model is the first published model that is efficient, can be solved to optimality, preserves the nestedness of the solutions, and produces geometries more amenable for mine design, without the need for heuristics. Finally, we devise an iterative method that profits from the nestedness of the solutions to speed up the resolution and test the model in three different data sets, with different geometrical and cost parameters for a total of 135 different instances. The results show that the geometry of the bottom pits is indeed improved and that we can solve the problems up to optimality up to 80% faster than an off‐the‐shelf solver.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".