Long-term production scheduling of open pit mines using particle swarm and bat algorithms under grade uncertainty

摘要

Long-term production scheduling for open pit mines is a large-scale, complex optimization problem involving large data-sets, multiple hard and soft constraints, and uncertainty in the input parameters. Uncertainty in the input parameters may be caused by different geological, economic, or technical factors. The uncertainty caused by geological factors, which is commonly termed geological or grade uncertainty, is considered to be most important source of uncertainty among these factors. It is caused by the fact that the block grade values are estimated using very sparse drill-hole sample data and the actual grade values will only be known once a block is drilled and blasted. Geostatistical conditional simulation techniques provide a framework to quantify this geological/grade uncertainty by generating multiple, equally probable simulated realizations of the orebody. Different stochastic programming models have been proposed in recent years to integrate this grade uncertainty into the optimization process, but solving these models for actual-sized open pit mines is usually extremely difficult and computationally expensive. In this paper, two different computationally efficient population-based metaheuristic techniques based on particle swarm optimization (PSO) and the bat algorithm are used to solve one particular stochastic variant of the open pit mine scheduling problem, le. the two-stage stochastic programming model with recourse for determining the long-term production schedule of an open pit mine under the condition of grade uncertainty.