DNA computing is based on biochemical reactions of DNA molecules. It may give incorrect computations. So, to make the biochemical reactions more accurate good DNA Sequences are needed. DNA Sequence design involves with a number of conflicting design criteria. We formulate the DNA Sequence design as a multi-objective optimization problem and solve it by implementing an algorithm without using any existing optimization algorithm. The method is implemented into the DNA sequence design system, 'DNA_Sequence_Generator', with a suite of sequence-analysis tools to help in improving and get the best solutions. The performance of our algorithm is compared with other sequence design methods. Our experimental results shows that the good sequence design by 'DNA_Sequence_Generator' outperforms in its reliability the existing sequence design techniques such as conventional EAs, Simulated Annealing, and specialized heuristic methods.