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.