This paper proposes a fast optimization method by combining queen-bee evolution and derivative evaluation in genetic algorithms. These two operations make it possible for genetic algorithms to focus on highly fitted individuals and rapidly evolved individuals, respectively. Even though the two operations can also increase the probability that genetic algorithms fall into premature convergence phenomenon, that can be controlled by strong mutation rates. That is, the two operations and the strong mutation strengthen exploitation and exploration of the genetic algorithms, respectively. As a result, the genetic algorithm employing queen-bee evolution and derivative evaluation finds optimum solutions more quickly than those employing one of them. This was proved by experiments with one pattern matching problem and two function optimization problems.