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DNA computing, a next-generation computing technology applying the parallelism of molecular biology, has been recently customized and adapted to solve hard combinatorial optimization problems. This paper proposes a DNA sequence generation algorithm to discover an optimal solution of 0/1 knapsack problem, which is NP-hard. This model applies the DNA coding method, an evolutionary algorithm, to generate superior DNA sequences with fewer errors. While difficult numerical optimization problems are unlikely to be solved by traditional methods, biological experiments prove that the proposed method achieves acceptable results. The experiments also demonstrate the superiority of our approach by comparing the average fitness values of sequences generated by Adleman's algorithm with those of DNA sequences generated by the proposed algorithm.