GNGTS 2017 - 36° Convegno Nazionale

GNGTS 2017 S essione 3.3 719 The DAGA performances are first tested on two analytic objective functions often used to test optimization algorithms. Then, the DAGA approach is applied to a well-known non-linear geophysical optimization problem: residual statics correction. The DAGA method is also compared with standard NGA and MCA implementations. The DAGA method. With the aim to increase the exploration capabilities of GAs, we first hybridize NGA and MCA by triggering catastrophic events over the evolving subpopulations (Eldos, 2008). A catastrophe is a random phenomenon, centred around a subpopulation that, basing on stochastic criteria, destroys a certain number of chromosomes in the central subpopulation and, to a lesser extent, in the neighbour subpopulations. After a subpopulation has been hit by a catastrophic event, its number of individuals decreases. For this reason, the destroyed chromosomes are progressively replaced over the following generations by new individuals migrating from the other subpopulations, and by new randomly generated solutions. The centre of the catastrophe is stochastically selected basing on the mean fitness values of the entire ensemble of subpopulations. The intensity of the catastrophic event (the number of chromosomes that will be removed) is randomly determined basing on a gaussian distribution with a user-defined variance and an adaptive mean value, which decreases as the number of generation increases (i.e. as the minimum of the objective function is approached). Note that in case of a catastrophic event the best chromosomes are always preserved to ensure that the optimization does not waste time re-discovering previously promising solutions. In case of genetic drift, the genetic diversity is lost, or in other words, the entire population contains several copies of the same individual. In this case a considerable amount of time is wasted in performing forward modelling for very similar solutions. To tackle this issue, we include in our algorithm an additional strategy that systematically performs random replacements in each generation. Let t be a user-defined parameter; the algorithm identifies t couples of similar individuals for each subpopulation and one of the individuals for each couple is replaced with a randomly generated solution. Similarly to the catastrophic event, we again preserve the best individuals. Thanks to this operation, the genetic diversity within each population is preserved and the exploration of the model space is maximized. The previous considerations make it clear that the DAGA approach is mainly aimed at increasing the exploration capability of a standard niched genetic algorithm and at efficiently exploring the most promising portions of the model space. Obviously in applying the DAGA method a good compromisemust be found between exploration and exploitation of the algorithm. In practical applications, this translates in finding (usually by a trial and error procedure) an optimal set of user-defined parameters for the problem at hand. Indeed, a too strong exploration will heavily increase the computational time and slow down the convergence, while a too strong exploitation will result in premature convergence toward sub-optimal solutions. As a final remark, note that the inclusion of several Monte Carlo principles into the genetic algorithm optimization kernel, results in an increased computational effort. For this reason, an accurate code optimization is crucial to ensure the applicability of the method. Analytic test functions. The performances of the DAGA method are first evaluated on the analytic Rastrigin and Schwefel functions. The DAGA method is also compared with standard implementations of NGA and MCA. In particular, for each method and for each objective function, we perform a set of 50 tests, and for each generation we progressively count the number of tests that attain convergence. The convergence criterion is based on a Euclidean measure of distance from the global minimum (Sajeva et al., 2017). To allow for a meaningful comparison, the total number of evaluated models is maintained constant for each considered method. The Rastrigin function is a linear combination of a paraboloid and a harmonic function: (1) where n is the dimension of the model space. Fig.1a shows a 2-D Rastrigin function computed within [-5, 5] n . The global minimum is located at [0, …, 0] and is surrounded by regularly