A derivative-free optimization (DFO) algorithm is presented. The distinguishing feature of the algorithm is that it allows for the use of function values that have been made available through prior runs of a DFO algorithm for solving prior related optimization problems. Applications in which sequences of related optimization problems are solved such that the proposed algorithm is applicable include certain least-squares and simulation-based optimization problems. A convergence guarantee of a generic algorithmic framework that exploits prior function evaluations is presented, then a particular instance of the framework is proposed and analyzed. The results of numerical experiments when solving engineering test problems show that the algorithm gains advantage over a state-of-the-art DFO algorithm when prior function values are available.