Fig. 5

Three-objective genetic algorithm-informed design suggestions. a Diversity analysis of all the best solutions obtained by the 3-objective optimization for (r = 5, m = 6 for \(x_i={s, e, r, w, a, G}\); \(x_6=y\)) library design in terms of the number of unique permutations (y-axis) and the total number of permutations (x-axis), where each solution is represented with the number of permutations unique by sequence (green points) and by mass (red points). b 2D Pareto front of the best, i.e., near optimal solutions (green dots) and all the remaining solutions (blue dots) from the final generation representing mass diversity (x-axis) and sequence diversity (y-axis) relative to the total number of permutations. c Sequence logo of library design encircled in subfigure (b). Despite lower mass diversity (81%), the library design maintains high sequence diversity (98%), making it an attractive synthetic possibility. d–f Refer to the optimization results for the r = 5, m = 7 for \(x_i={s,e,r,w,a,G,i}\); \(x_3=p\), \(x_7=y\) library design