Margaret Armstrong, Cerna, Mines-Paristech (FR)
A Vincent, Cerna, Mines-Paristech (FR)
A Galli, Cerna, Mines-Paristech (FR)
C Méheut, Aviomex Pty Ltd (FR)
Nowadays many more conditional simulations of orebodies and reservoirs can be generated than in the past. In some applications it is possible post-process all of them but in others this is impossible. For example, in mining pit optimisation and scheduling is computer intensive and time consuming; similarly for fluid flow simulations and reservoir architecture in the oil industry. When only a certain number of the conditional simulations (k say) can be post-processed, the question is how to choose a representative set of that size out of the full set of N simulations. Unless N and k are small, this problem is well known to be NP hard.
The problem can be split into three parts:
1. Measuring the dissimilarity between two simulations (dij)
2. Finding a metric M(S) to measure the distance between the full set of N simulations and any given subset S of size k
3. Finding an efficient algorithm for selecting the best one (i.e. the one that minimises M(S))
Armstrong et al (2010 & 2011) proposed using a metric based on the scenario reduction metric developed by Heitsch & Romisch (2007), together with a random search algorithm. This paper proposes an improved algorithm that uses genetic algorithms for selecting the best subset.
This procedure is tested on a hypothetical gold mine based on the Walker Lake data.
Armstrong, M., A.A. Ndiaye & A. Galli (2010) Scenario Reduction in Mining, presented at the IAMG Annual Meeting in Budapest, 29 August - 2 Sept 2010
Armstrong, M., A.A. Ndiaye, R. Razantsimba & A. Galli (2011) Scenario Reduction Applied to Geostatistical Simulations, accepted for publication in Maths Geosciences.
Heitsch & Romisch (2007) Scenario tree modelling for multistage stochastic programs, Mathematical Programming,Ser A DOI 10.1007/s10107-007-0197-2