PSI - Issue 44

Francesco Nigro et al. / Procedia Structural Integrity 44 (2023) 1704–1711 F. Nigro, R. Falcone, E. Martinelli/ Structural Integrity Procedia 00 (2022) 000–000

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value of the admissible ISV for the desired (target) seismic risk class. It is worth noting that the relative costs of the two kinds of intervention considered are more relevant than their absolute values, which (in the present work) only represent estimates, derived from the Prezzario Campania LL. PP. (2016), the reference document of the region in which the structure is ideally located. 2.4. Application of the genetic operators The optimization procedure formulating a Genetic Algorithm relies on the application of the genetic operators, which are needed in order to improve the fitness (quality) of the population and the quality of the “optimal” solution according to the GA, as well. Having evaluated the seismic performance and the fitness (in terms of objective function) of each chromosome, it is possible to classify the whole population with respect to the objective function itself. Thus, three main genetic operators are applied, in order to modify part of the current population, substituting some chromosomes with new chromosomes, usually named as “offsprings”. The main rule governing the application of the genetic operators consists in the Darwinian principle of “survival of the fittest” (individuals) which is inspired to the drive mechanisms of the evolution of species (Darwin, 1859). 2.4.1 Selection operator Firstly, the Selection operator is applied in order to divide the current population in two sub population, having defined a selection rate, X rate : • X rate × N ind chromosomes are called the “survived” part of the population, as they are copied in the following population without any modification in their genes; they are obviously taken among the fittest ones; • (1-X rate ) × N ind chromosomes represent the “discarded” population that will be substituted by the offsprings. Secondly, the Selection operator is employed in order to select the couples of “parent individuals” that will give birth to the aforementioned offsprings. The selection is performed using two different strategies, called Roulette Wheel and Random Pairing . The former tends to select as parents chromosomes characterized by good values of fitness, while the latter always selects as parents one of the “survived” chromosomes and one of the “discarded” chromosomes (that represent the remaining part of the population). Falcone (2017) gave a more detailed explanation of such selection strategies. In the present work it has been assumed X rate = 5%. Hence, only 5% of the chromosomes of each population “survives” to the application of the genetic operators. Moreover, the Random Pairing selection strategy has been applied in the 85% of cases, while the application of the Roulette Wheel strategy interested only the 15% of cases, whereas in the first formulation of the procedure both strategies were applied in the 50% of cases. Such choice may help to achieve a wider exploration of the search space, improving the quality of the “optimal” solution. 2.4.2 Crossover operator Thus, as the couple of parents is got selected, the Crossover operator combines their individual genotype according to a binary mask, which controls if the singles genes have to be switched between the two selected parents to generate the two offsprings. The choice of subdividing the chromosome genotype into a number of parts equal to the number of design variables is intended at achieving a wider exploration of the search space, maximizing the total number of possible combinations. 2.4.3 Mutation operator The principal function of the mutation operator is to avoid to get stuck in an eventual local minimum of the objective function, which is typical of those cases in which only crossover operator is applied. The application of the Mutation operator simply consists in a random alteration of some genes of the chromosome genotype. Nevertheless, it is important to note that an excessive application of the mutation operator usually makes the algorithm unstable, nullifying the advances in terms of chromosome quality gained by the application of the Crossover operator.