Deriving local cost models for query optimization in a multidatabase system (MDBS) is a challenging issue due to local autonomy. It becomes even more difficult when dynamic environmental factors are taken into consideration. In this paper, we study how to evolve a cost model to capture a slowly-changing dynamic MDBS environment so that the cost model is kept up-to-date all the time. We propose a novel evolutionary technique, called the shifting method, to tackle this issue. The key idea is to adjust a cost model by adding the up-to-date performance information of a new sample query into and, in the meantime, removing the out-of-date information of the oldest sample query from consideration at each step. It is shown that this method is more efficient than the direct re-building approach. The relevant issues including derivation of recurrence update formulas, development of efficient algorithm, analysis of complexities as well as some aspects of implementation are studied. Our theoretical and experimental results demonstrate that the proposed shifting method is quite promising in deriving accurate evolutionary cost models for a slowly-changing dynamic MDBS environment.