Differential Evolution for Maximum Cuboid Extraction in Sustainable Stone Cutting: Application to a Granite Rock Example

Maximizing the extraction of usable volume in the form of a cuboid from polyhedra is a complex optimization challenge. It has immediate application in mining and stone-cutting, with significant implications for sustainable resource utilization. This study addresses the problem by employing Differential Evolution (DE), a population-based evolutionary algorithm, to identify the axis-independent maximum cuboid within polyhedra. Using a granite rock as a test case, the algorithm iteratively refines solutions through mutation, crossover, and selection operators. The algorithm’s behaviour and performance is evaluated via 20 independent runs. The results are presented through convergence plots and snapshots illustrating the evolution of the solutions. Our findings demonstrate the potential of DE in solving these complex geometric optimization problems and contributing to sustainable mining practices.