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In the era of big data, new storage media are urgently needed because the storage capacity for global data cannot meet the exponential growth of information. Deoxyribonucleic acid (DNA) storage, where primer and address sequences play a crucial role, is one of the most promising storage media because of its high density, large capacity and durability. In this study, we describe an enhanced gradient-based optimizer that includes the Cauchy and Levy mutation strategy (CLGBO) to construct DNA coding sets, which are used as primer and address libraries. Our experimental results show that the lower bounds of DNA storage coding sets obtained using the CLGBO algorithm are increased by 4.3–13.5% compared with previous work. The non-adjacent subsequence constraint was introduced to reduce the error rate in the storage process. This helps to resolve the problem that arises when consecutive repetitive subsequences in the sequence cause errors in DNA storage. We made use of the CLGBO algorithm and the non-adjacent subsequence constraint to construct larger and more highly robust coding sets.

In this paper, we introduce the general computing methods of multiple integration, and analysis the limitation and range in the application of solving the practice problems. Monte Carlo method of uniform random sampling number has explained the basic idea of Monte Carlo algorithm and its application in multiple integrals. Thus, from theory and example, we give a rapid calculation based on MATLAB tool, and could obtain a valuable approximation.

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