An improved meta-heuristic approach to extraction sequencing and block routing

represented by a block model that divides the orebody into a three-dimensional array of blocks. Each block consists of a cluster of similar characteristics such as rock type and ore grade, and has attributes such as tonnage of ore contained within the block and an expected economic value (Bley et al., 2010). For each block, the mine production scheduling problem consists of the decisions of (1) whether to mine a block, (2) when to mine that block, and (3) how to process the mined block. The overall objective is to maximize the net present value (NPV) while meeting feasibility constraints such as production, blending, sequencing, and pit slope (Dagdelen, 2001). Three main sub-problems of scheduling are the determination of production rates, discrimination between ore and waste, and block sequencing (Kumral, 2013a). These problems are interdependent; one sub-problem cannot be solved if the others have not been solved previously. However, in common applications, production rates are usually assumed and the other sub-problems are solved under this assumption (Menabde et al., 2004; Nehring et al., 2010; Asad and Topal, 2011). This leads to sub-optimal results. Our approach introduces a concept of cut-off range, which regards the cut-off grade as guidance and optimizes it within the range provided. This is a step toward simultaneously optimizing production rates along with process destination discrimination and extraction sequencing. Exact methods such as mixed integer programming (MIP) have been used for the block sequencing problem to obtain an optimal result for various cases (Kumral, 2013b; Little et al., 2013; Nehring et al., 2012; de Carvalho Jr. et al., 2012) and yields a deterministic plan. However, MIP suffers from certain drawbacks. The size of the problem increases exponentially as the level of complexity (such as multiple metals, process destinations, rock types) increases (Rothlauf, 2011). To overcome the data size problem in MIP, block aggregation is suggested (Tabesh and AskariNasab, 2011; Topal, 2011) but naturally, this results in loss of optimality. Also, given that the block model is based on drill-hole data but is usually generated by geostatistical simulation, it is impossible in practice for the generated schedule to be optimal. Considering the amount of time MIP takes with large datasets and that MIP is unnecessarily precise in our case, a faster, approximately-optimal algorithm is much more suited to the practical need. Another widely used exact method is the Lerchs-Grossman algorithm (Lerchs and Grossman, 1964), which yields the ultimate pit. This is an algorithm based on graph theory that converts each block to nodes. Although faster than MIP, in addition to the problems in MIP, when using Lerchs-Grossman algorithm it is difficult to assign varying pit slopes at different points and determine mining and processing capacities for each period. Dagdelen and Johnson (1986) attempted to handle the An improved meta-heuristic approach to extraction sequencing and block routing