In synthetic biology, it is a challenge to increase the production of target proteins by maximizing their expression levels. In order to augment expression levels, we need to focus on both homologous recombination and codon adaptation, which are estimated by three objective functions, namely HD (Hamming distance), LRCS (length of repeated or common substring) and CAI (codon adaptation index). Optimizing these objective functions simultaneously becomes a multi-objective optimization problem. The aim is to find satisfying solutions that have high codon adaptation and a low incidence of homologous recombination. However, obtaining satisfactory solutions requires calculating the objective functions multiple times with many cycles and solutions. In this paper, we propose an approach to accelerate the method of designing a set of CDSs (CoDing sequences) based on NSGA-II (non-dominated sorting genetic algorithm II) on NVIDIA GPUs. The implementation accelerated by GPUs improves overall performance by 187.5 $\times$ using $100$ cycles and $128$ solutions. Our implementation allows us to use larger solutions and more cycles, leading to outstanding solution quality. The improved implementation provides much better solutions in a similar amount of time compared to other available methods by 1.22 $\times$ improvements in hypervolume. Furthermore, our approach on GPUs also suggests how to efficiently utilize the latest computational resources in bioinformatics. Finally, we discuss the impacts of the number of cycles and the number of solutions on designing a set of CDSs.

Maximizing protein expression levels poses a major challenge in bioengineering. To increase protein expression levels, numerous factors, including codon bias, codon context bias, hidden stop codons, homologous recombination, suitable guanine-cytosine ratio, and hairpin loop structure, are crucial and quantified by six objective functions: CAI, CPB, HSC, HD, GC3, and SL. Optimizing these six objectives simultaneously constitutes a multi-objective optimization problem, aiming to identify the favorable Pareto solutions rather than a singular optimal solution. However, achieving satisfactory solutions requires numerous cycles and solutions, thus leading to a large number of functional evaluations. While there are frameworks for multi-objective optimization problems, they often lack efficient support for objective function computation in protein encoding. In this paper, we proposed a method to design a set of coding sequences (CDSs) based on non-dominated sorting genetic algorithm III (NSGA-III), accelerated using NVIDIA graphical processing units (GPUs). Experimental results indicated that our method is 15,454 times faster than the Pymoo framework and is evaluated using 100 solutions and 100 cycles. Since our GPU implementation facilitated the use of larger solutions and more cycles, we were able to design a superior set of CDSs by increasing solutions to 400 and cycles to 12,800. In addition, our NSGA-III-based method consistently surpassed the NSGA-II approach when the number of cycles exceeded 3200 by utilizing 100 solutions. Finally, we observed that a gradual reduction of the mutation probability as the number of cycles increased yielded better quality results than maintaining a fixed mutation probability.