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## Journal of the Southern African Institute of Mining and Metallurgy

*On-line version* ISSN 2411-9717

*Print version* ISSN 0038-223X

#### Abstract

ARMSTRONG, M.; VINCENT, A.; GALLI, A. and MEHEUT, C.. **Genetic algorithms and scenario reduction**.* J. S. Afr. Inst. Min. Metall.* [online]. 2014, vol.114, n.3, pp.237-244.
ISSN 2411-9717.

Scenario reduction is designed for selecting a representative subset of geostatistical simulations out of a much larger set. Three steps are involved: measuring the dissimilarity between two simulations; finding a metric to measure the distance between any subset of *k* simulations and the full set of *N* simulations; and finding an efficient algorithm for selecting the subset that minimizes the metric. This paper focuses on the third question. We show that genetic algorithms are an efficient way of approaching the minimum when the population of subsets to be sampled is large. Two case studies based on the Walker Lake data-set are presented: firstly choosing *k*=4 simulations out of a total of 100, and secondly choosing 20 out of the same 100 simulations. In the first case it was possible to compute all possible combinations exhaustively and hence to demonstrate that the algorithm converges to the true minimum. This was not possible in the second case. Instead we demonstrate that it outperforms the random draw algorithm used in earlier work. A procedure for tracking individual selections during the iterative procedure was developed. This allows us to measure the evolution in the percentage of progeny resulting from crossing-over and from mutation that survived in the next generation. It gives valuable insight into how to choose the parameter values in the algorithm. Another key finding is that there is a trade-off between the number of individuals per generation and the number of generations required for the algorithm to converge.

**Keywords
:
**genetic algorithms; crossing-over; mutants; Walker Lake.