Performance Characteristics Of Simulated Annealing To Build Markov Fields
Kevin P. Parks, Laurence R. Bentley · WIT transactions on ecology and the environment · 1970
Simulated annealing is a global optimization method which permits stochastic generation of structured fields useful for populating simulator grids. Though computationally expensive, annealing methods have appeal because they allow incorporation of information from disparate sources to reduce the space of uncertainty explored. In this paper, Markov transitional structures are used to inform structure in two-dimensional categorical fields. Markov transitional structures can be derived from geological conceptual models, outcrop study, or core descriptions. They can be encoded into an objective function using the multipoint histogram approach. Some practical performance issues of using simulated annealing to construct Markov categorical fields are considered here. First, point swapping within a discrete field already populated with the necessary proportions of each category is found to produce results superior to drawing new nodal values from the underlying population distribution. Second, the convergence behaviour of annealing is shown to depend on the size of grid relative to the length-scales of categorical bodies implicit in the Markov transition structure. Lastly, in our experience, a combination of true simulated annealing (Metropolis algorithm) and iterative improvement (steepest descent) provides the most efficient approach to constructing complex Markov categorical fields by this method.