Keywords: open-pit mine, mine slope, geological database, slaked lime, genetic algorithms, order-based crossover, combinational optimization.

Limestone quarries where slaked lime is produced for steel makers have been urged to reduce the concentration of phosphorus in their products. In quite 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 address 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. Though 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 chosen 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. Since 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 town in Japan. In this paper, some simulations were tried in order to establish an optimum mining plan for such blending combinations.

At first, a DP (Dynamic Programming) method was applied. This method found most of the best combinations, but it required quite a long time. For instance, when choosing 5 blocks from 100 blocks there are approximately options, this grows to about options when choosing from 200 blocks. Since the processing time grows exponentially as the quarry size becomes larger, it is impossible to apply this method in large scale quarries or for long term planning. Therefore, a GA (Genetic Algorithm) was applied for these cases. It is difficult to search for the best combinations using GA because it basically is like Monte Carlo simulations [1]. However, it did find some better substitutes. In addition, GA could include some other conditions such as distance from shafts, noise problems or avoiding eyesore [2].

The GA method first estimates large scale or long-term possibilities of phosphorus adjustments, and then the DP method could solve the optimum combinations in practice. Moreover, the hybrid method that applied the DP to the GA method was examined.

To find the optimum mixing of low phosphorus blocks and high phosphorus blocks, the Dynamic Programming method and Genetic Algorithm method were examined. Regarding computer processing time, the GA method was much more effective than the DP method, however, a combination of the two methods could result in more than 20 - 30% improvement by trying some other crossover or mutation methods; these will be studied.

In a large scale mine or for long term planning, the GA method is available to check probabilities of optimum scheduling. On the assumptions from the GA method, the DP method would be effective in short run planning. Though phosphorus concentrations and the lifetime of the quarry were considered in this study, other conditions could be easily adopted. In addition, these DP or GA methods could be also adopted in open-pit metal mines that produce more than two kinds of minerals.

1

L.Davis, "Handbook of Genetic Algorithms", Nostrand Reinhold, New York, pp.1-42, 1991.

2

T. Ito, T. Nishiyama and H. Kusuda, "Computer Graphic Simulation of Changes in the Scene at Stone-Quarrying Sites", Geoinformatics, Vol.6, No.2, pp.65-72, 1995.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £95 +P&P)