Comparison of a genetic algorithm and simulated annealing in an application to statistical image reconstruction

Genetic algorithms (GAs) are adaptive search techniques designed to find near-optimal solutions of large scale optimization problems with multiple local maxima. Standard versions of the GA are defined for objective functions which depend on a vector of binary variables. The problem of finding the maximum a posteriori (MAP) estimate of a binary image in Bayesian image analysis appears to be well suited to a GA as images have a natural binary representation and the posterior image probability is a multi-modal objective function. We use the numerical optimization problem posed in MAP image estimation as a test-bed on which to compare GAs with simulated annealing (SA), another all-purpose global optimization method. Our conclusions are that the GAs we have applied perform poorly, even after adaptation to this problem. This is somewhat unexpected, given the widespread claims of GAs' effectiveness, but it is in keeping with work by Jennison and Sheehan (1995) which suggests that GAs are not adept at handling problems involving a great many variables of roughly equal influence. We reach more positive conclusions concerning the use of the GA's crossover operation in recombining near-optimal solutions obtained by other methods. We propose a hybrid algorithm in which crossover is used to combine subsections of image reconstructions obtained using SA and we show that this algorithm is more effective and efficient than SA or a GA individually.