Genetic algorithms and scenario reduction
M Armstrong, A Vincent, A Galli, C Méheut
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.