Highest-Level Implementation of the Push–Relabel Algorithm to Solve the Ultimate Pit Limit Problem

Nowadays due to the existence of the economic and geological uncertainties and the increasing use of scenario-based project evaluation in the design of open-pit mines, it is necessary to find an exact algorithm that can determine the ultimate pit limit in a short period of time. Determining the ultimate pit limit is an important optimization problem that is solved to define what will be eventually extracted from the ground, and directly impacts the mining costs, revenue, choosing mining equipment, and approximation of surface infrastructures outside the pit. This problem is solved in order to maximize the non-discounted profit under the precedence relation (access) constraints. In this paper, the Highest-Level Push-Relabel (HI-PR) implementation of the push–relabel algorithm is discussed and applied in order to solve the ultimate pit limit optimization problem. HI-PR uses the highest-label selection rule, global update, and gap heuristics to reduce the computations. The proposed algorithm is implemented to solve the ultimate pit limit for the nine real-life benchmark case study publicly available on the Minelib website. The results obtained show that the HI-PR algorithm can reach the optimum solution in a less computational time than the currently implemented algorithms. For the largest dataset, which includes 112687 blocks and 3,035,483 constraints, the average solution time in 100 runs of the algorithm is 4 s, while IBM CPLEX, as an exact solver, could not find any feasible solution in 24 hours. This speeding-up capability can significantly improve the current challenges in the real-time mine planning and reconciliation, where fast and reliable solutions are required.