Which pit optimization algorithm guarantees finding the mathematically optimal pit shell, considering all possible pit configurations?

The pit optimization algorithm that guarantees finding the mathematically optimal pit shell, considering all possible pit configurations, is the Lerchs-Grossmann (LG) algorithm. Pit optimization aims to determine the pit limits that maximize the overall profitability of a mining project. The LG algorithm is a graph theory-based approach that formulates the pit optimization problem as a maximum closure problem on a directed graph. A directed graph is a network of nodes (representing blocks in the orebody) and arcs (representing the precedence constraints due to slope angles). The algorithm represents each block in the orebody as a node in the graph, assigning it a value equal to its economic value (revenue from extracted ore minus the cost of mining and processing). Overlying blocks are connected by arcs, reflecting the requirement that to mine a block, all blocks above it must also be mined. The LG algorithm then finds the maximum closure of the graph, which is the set of blocks that maximizes the total value while respecting the precedence constraints. This maximum closure corresponds to the optimal pit shell. The Lerchs-Grossmann algorithm's strength lies in its ability to consider all possible pit configurations simultaneously, guaranteeing that the resulting pit shell is the most profitable one, given the input parameters such as ore grades, metal prices, mining costs, processing costs, and slope angles. While other algorithms like the floating cone algorithm offer faster computation, they only provide approximate solutions and do not guarantee optimality.