Particle Swarm Optimization in High Dimensional Spaces
Global optimization methods including Particle Swarm Optimization are usually used to solve optimization problems when the number of parameters is small (hundreds). In the case of inverse problems the objective (or fitness) function used for sampling requires the solution of multiple forward solves. In inverse problems, both a large number of parameters, and very costly forward evaluations hamper the use of global algorithms. In this paper we address the first problem, showing that the sampling can be performed in a reduced model space. We show the application of this idea to a history matching problem of a synthetic oil reservoir. The reduction of the dimension is accomplished in this case by Principal Component analysis on a set of scenarios that are built based on prior information using stochastic simulation techniques. The use of a reduced base helps to regularize the inverse problem and to find a set of equivalent models that fit the data within a prescribed tolerance, allowing uncertainty analysis around the minimum misfit solution. This methodology can be used with other global optimization algorithms. PSO has been chosen because its shows very interesting exploration/exploitation capabilities.
KeywordsPSO model reduction techniques inverse problems uncertainty
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- 1.Castro, S.A., Caers, J., Mukerji, T.: The Stanford VI reservoir. Tech. Rep. 18th Annual Report, Stanford Center for Reservoir Forecasting (SCRF). Stanford University, California, USA (May 2005)Google Scholar
- 2.Echeverría, D., Mukerji, T.: A robust scheme for spatio-temporal inverse modeling of oil reservoirs. In: Anderssen, R., Braddock, R., Newham, L. (eds.) 18th World IMACS / MODSIM Congress, Cairns, Australia, pp. 4206–4212 (July 2009)Google Scholar
- 5.Fernández-Martínez, J.L., García-Gonzalo, E., Fernández-Muniz, Z., Mukerji, T.: How to design a powerful family of particle swarm optimizers for inverse modeling. New trends on bio-inspired computation. In: Transactions of the Institute of Measurement and Control (2010) (accepted for publication)Google Scholar
- 6.Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings IEEE International Conference on Neural Networks (ICNN 1995), Perth, WA, Australia, vol. 4, pp. 1942–1948 (November-December 1995)Google Scholar
- 7.Pearson, K.: On lines and planes of closest fit to systems of points in space. Philosophical Magazine 2(6), 559–572 (1901)Google Scholar