Update current solution: If the solution is feasible and improves NPV, update the best feasible solution. Every K iterations: Increase λ if the corresponding constraint is violated; Decrease λ if the corresponding constraint is respected; Update temperature T ← α·T. Polishing Phase: Apply hill climbing to the best feasible solution; Accept only strictly feasible moves with positive NPV gain. Output: Best mining sequences achieved. The pipeline includes the achievement of an initial solution that respects precedence employing a topological sort procedure; diversity operations, such as shifting the period of a blocks and swapping the periods of two blocks; parallel processing to increase efficiency; a dynamic penalty policy, in which constraint violations increase the values of and , while the respect of constraint decreases them; and a hill climbing procedure to polish the best achieved solution. 2.4 General comments Numerical experiments were performed on a computer with an Intel® Core™ i5-8400T processor running at 1.70 GHz, 16 GB of RAM, and a 64-bit Windows operating system. Precedences between blocks were determined using a heuristic to reach a slope angle of 45º using 3 levels. The simulated annealing metaheuristic was built from scratch, with parameters 0 = 15, cooling rate = 0,01, and initial values of = = 2 with an adjusting rate of 5% applied every 5,000 iterations. The stopping criterion employed was achieving 80,000,000 iterations. The experiments were implemented in Python, and the libraries pandas, numpy, math, heapq, random, time, copy, os, dataclasses, concurrent, and typing were used. The proposed methodology can be summarised in the flowchart in Figure 3. Figure 3 – Flowchart of the proposed methodology for incorporating geometallurgical variables into the mine sequencing problem and solving it using a simulated annealing metaheuristic. 3. RESULTS AND DISCUSSION
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