Most of the existing database query optimization techniques are designed to target traditional database systems with one-dimensional optimization objectives. These techniques usually aim to reduce either the query response time or the I/O cost of a query. Evidently, these optimization algorithms are not suitable for cloud database systems because they are provided to users as on-demand services which charge for their usage. In this case, users will take both query response time and monetary cost paid to the cloud service providers into consideration for selecting a database system product. Thus, query optimization for cloud database systems needs to target reducing monetary cost in addition to query response time. This means that query optimization has multiple objectives which are more challenging than one-dimensional objectives found in traditional paradigms. Similar problems exist when incorporating query re-optimization into the query execution process to obtain more accurate, multi-objective cost estimates. This paper presents a query optimization method that achieves two goals: 1) identifying a query execution plan that satisfies the multiple objectives provided by the user and 2) reducing the costs of running the query execution plan by performing adaptive query re-optimization during query execution. The experimental results show that the proposed method can save either the time cost or the monetary cost based on the type of queries.