A Test of Mining Simulations for Phosphorus Adjustment in a Limestone Quarry - Dynamic Programming Compared with a Genetic Algorithm

Abstract

Limestone quarries where slaked lime is produced for steel makers have been urged to reduce the concentration of phosphorus in their products. In a few quarries in Japan, limestone blocks with low concentrations are blended with limestone blocks with high concentrations to stay below the limit of permitted phosphorus quality. The life of the quarry is extended as long as possible by this blending. Some quarries have a geological database with accurate records of the operations for phosphorus adjustment.

However, the combination problem of these blocks typically is addressed by Dynamic Programming; that is, all combinations of possible limestone blocks are examined in the solving process; the combination numbers are so huge that the optimum combination cannot be solved in practical process times. Although it took 8 hours to solve for 600 blocks with a 2GHz high performance personal computer, it would take more than 36 days to approximately solve for 1200 blocks, and 3,378 days are estimated to solve 2,400 blocks. Therefore, a Genetic Algorithm was used to try and work out the optimum combination. First, blocks that can be removed are selected in the quarry and their removal sequence makes the genotype. The Order-base or the Grefenstette method was applied to avoid generating lethal genes in crossover. The fitness value was estimated by the number of products that included less than the permitted concentration of phosphorus.

The GA process took less than 3 hours to solve for 1,200 blocks. Because the processing time is almost proportional to the block numbers, this GA method is practical in large quarries. Moreover, this method is easy to apply to other conditions in mining plans, such as environmental protection, noise prevention and eyesore problems. These problems are becoming important factors in quarries near towns in Japan.