Random individual initialization tends to generate too many eccentric and homogeneous individuals which cause slow and premature convergence. It needs many operations (selection strategy, incest prevention and mutation) to fix, which consume too much computation and lose many good genes. The proposed complementary-parent strategy initializes every other pair of parents with dynamically or statically complementary chromosomes (such as 010101…0101 and 101010…1010). Crossover of every generation is only performed between the offspring from the same parents, during which the parents are completely replaced by their own children. Higher population diversity is got without gene lost at all, by which search ability is enhanced. Incest prevention, selection strategies and mutation are unnecessary and consequently cancelled (so it is named pseudo genetic algorithm). As indicated by the simulation results, the speed of elitist search is accelerated greatly and computation complexity is reduced by half.