Designing reliable sequences of DNA (Deoxyribonucleic Acid) is a critical task in the fields of DNA computing, and nanotechnology. The quality and reliability of the DNA sequence can directly affect the accuracy of the processing of information stored in sequences. This problem of designing reliable sequences belongs to the NP-hard class of problems. It has many incompatible design criteria, which cannot be optimized at the same time. Many objective evolutionary algorithms can balance conflicting design criteria by using a diverse population of solutions. This paper proposes an opposition-based Memetic Generalized Differential Evolution (MGDE3) to handle four conflicting design criteria for reliable DNA sequence design. Opposition-based learning and local search strategies are suggested to strengthen the explorative and exploitative properties of the proposed MGDE3. The proposed algorithm is bench-marked with small, medium, and large data sets against 7 highly-cited many-objective and multi-objective algorithms. Experimental results and statistical analysis reveal that MGDE3 significantly outperforms the compared algorithms. The proposed method generates reliable real-life sequences of DNA that are substantially better than the DNA sequences generated by other considered algorithms.