Heredity is guaranteed by faithful DNA replication whereas evolution depends upon errors accompanying DNA replication. This contradiction existing between heredity and evolution cannot be resolved in an individual organism, but only in terms of a population, in that a delicate balance exists between wild type and variants in a population which is necessary for the survival of the species. Namely, there seems to be a key in the mechanism of DNA replication to solve some problems of evolution. DNA is replicated semiconservatively using the leading and discontinuous lagging strands. According to our 'disparity theory of evolution', the existence of a sufficient fidelity difference between the leading and lagging strands is advantageous in terms of evolution, because the diversity of genotypes is enlarged but genotypes that have occurred in the past are guaranteed. In theory, by artificially increasing the fidelity difference between the leading and lagging strand ('disparity mutator'), evolution is accelerated while avoiding the extinction of the population. Using a disparity mutator, we should be able to improve living things, including multicellular organisms, within constrained conditions. A double-stranded genetic algorithm, which mimics the structure and replication manner of DNA, is promising for solving optimization problems.