GNGTS 2017 - 36° Convegno Nazionale

718 GNGTS 2017 S essione 3.3 Schatz, J. F., Simmons, G. (1972). Thermal conductivity of Earth materials at high temperatures. Journal of Geophysical Research , 77 (35), 6966–6983. DOI:10.1029/JB077i035p06966 Srivastava, K., Singh, R. N. (1998). Amodel for temperature variations in sedimentary basins due to random radiogenic heat sources. Geophysical Journal International , 135 (3), 727–730. DOI:10.1046/j.1365-246X.1998.00693.x Vil�� ��� ���������� ��� ������������� �� ������� ���������� ���� ���������� ����������� �� ���� ������ ������������ à ������ ��� ������������� �� ������� ���������� ���� ��������� , M., Fernàndez, M., Jiménez-Munt, I. (2010). Radiogenic heat production variability of some common lithological groups and its significance to lithospheric thermal modeling. Tectonophysics , 490 (3–4), 152–164. DOI:10.1016/ j.tecto.2010.05.003 Wedepohl, K. H. (1995). The composition of the continental crust. Geochimica et Cosmochimica Acta , 59 (7), 1217– 1232. DOI:10.1016/0016-7037(95)00038-2 An innovative method to attenuate genetic drift in genetic algorithm optimizations: Applications to analytic objective functions and residual statics correction S. Pierini, M. Aleardi, A. Mazzotti Earth Sciences Department, University of Pisa, Italy Introduction. The solution of geophysical non-linear inverse problems presents several challenges mainly related to convergence and computational cost. In addition, the performances of local optimization algorithms are strongly dependent on the initial model definition. For this reason, global optimization is often preferred in case of model spaces with complex topology (i.e. many local minima, small gradient of the objective function in a neighbourhood of the global minimum). Genetic Algorithms (GAs) (Holland, 1975) are a class of global optimization methods that have been proven very effective in solving geophysical optimization problems (Sajeva et al., 2016). In GA terminology, an individual, or chromosome, is a solution in the model space, whereas a population represents a set of individuals (i.e. an ensemble of possible solutions). A very simple GA flow starts with the generation of a random population of individuals over which the fitness function (namely the goodness of each solution) is evaluated. The fitness value stochastically contributes to the selection of the best individuals for the reproduction step in which a set of new solutions (offspring) is generated by combinations of parent individuals. The offspring are mutated, the fitness is evaluated, then a new generation is created by replacing some of the parent individuals with the generated offspring. The algorithm iterates until convergence conditions are satisfied. By assuming a population containing an infinite number of individuals, the convergence of the algorithm to the global minimum is guaranteed by the Holland theorem (Holland, 1975). For finite populations, the convergence of GAs is not guaranteed: this characteristic is often called “genetic drift”. A more heuristic description of the genetic drift phenomenon can be given in terms of population behaviour: after some generations, the chromosomes tend to converge in a convex neighbourhood of a minimum of the objective function (not necessary the global minimum), and thus the exploration of other promising portions of the model space is prevented. In the worst case, the population cannot escape from such convex neighbourhood, and a non-optimal solution is provided. Over the last decades, many strategies have been proposed to attenuate the genetic drift effect (Eldos, 2008; Aleardi and Mazzotti, 2017). For example, a possible approach is the so called niched genetic algorithm (NGA), in which the initial random population is divided into multiple subpopulations that are subjected to separate selection and evolution processes. In this work, we propose an innovative method to attenuate the genetic drift effect that we call “drift avoidance genetic algorithm” (DAGA). The implemented method combines some principles of NGAs and Monte-Carlo algorithm (MCA) with the aim to increase the exploration of the model space and to avoid premature convergence and/or entrapment into local minima.