Mixed Static and Dynamic Optimization of Four-Parameter Functionally Graded Completely Doubly Curved and Degenerate Shells and Panels Using GDQ Method

Pseudocode 1

Genetic Algorithm pseudocode.

Step (1) Set a max and min value for each gene

Step (2) Set the max number of generations (𝑇), the convergence tolerance (𝜀) and the number of consecutive no improvements

    loops (𝑛_𝜀) after which algorithm ends, the number of genes (𝑛_𝑔), and the number of population (𝑛_pop) members

Step (3) Initialize the first generation of population (𝑃) by randomly set 𝑛_pop chromosomes, each one made by 𝑛_𝑔 genes

Step (4) while (𝑖<𝑇) or (𝜀 for 𝑛_𝜀 loops false)

Step (5)    Select 𝑃^′⊂𝑃 (mating pool), initialize 𝑃^′′=0 (set of children)

Step (6)     for 𝑗=1 to 𝑛

Step (7)      Randomly select individuals (chromosomes 𝑥_𝑎 and 𝑥_𝑏) from 𝑃^′

Step (8)      Obtain 𝑥_child by applying crossover to 𝑥_𝑎 and 𝑥_𝑏 (with probability 𝑝_cross)

Step (9)       Mutate produced child 𝑥_child to 𝑥_𝑎 and 𝑥_𝑏 (with probability 𝑝_mut)

Step (10)      Apply elitarism (if set)

Step (11)      Update population 𝑃^′′=𝑃^′∪𝑥_child

Step (12)      end for

Step (13)  P = survival respect to the fitness* (𝑃^′, 𝑃^′′)

Step (14) end while

Step (15) best chromosome detection

*In this case the fitness is multiplied by a penalty term if one of the sets [𝑎^(𝑘),𝑏^(𝑘),𝑐^(𝑘),𝑝^(𝑘)] leads to volume fractions which are

not feasible (e.g. percentage of one constituent in the thickness larger than 1, less than 0, imaginary number).