Nested relational models were proposed as natural extensions of the relational model to support new emerging database applications. Prototype implementations of nested relational database systems (NRDBSs) have been done by some research groups. However, there remain many research issues on nested relations. One important issue is query processing, in particular query optimization. In NRDBSs, efficient execution of queries involving hierarchical data structures inherent in nested relations is required. In this paper, we focus on two join-type operations on nested relations: nested join and embed, and propose an algorithm to derive a cost optimal execution sequence of nested joins and embeds for a given query graph. The cost optimality of the derived sequence is formally proved. The complexity of the algorithm is proved to be O(N 2), when N nested relations are included in the query graph.

The selection of mutation strategy greatly affects the performance of differential evolution algorithm (DE). For different types of optimization problems, different mutation strategies should be selected. How to choose a suitable mutation strategy for different problems is a challenging task. To deal with this challenge, this paper proposes a novel DE algorithm based on local fitness landscape, called FLIDE. In the proposed method, fitness landscape information is obtained to guide the selection of mutation operators. In this way, different problems can be solved with proper evolutionary mechanisms. Moreover, a population adjustment method is used to balance the search ability and population diversity. On one hand, the diversity of the population in the early stage is enhanced with a relative large population. One the other hand, the computational cost is reduced in the later stage with a relative small population. The evolutionary information is utilized as much as possible to guide the search direction. The proposed method is compared with five popular algorithms on 30 test functions with different characteristics. Experimental results show that the proposed FLIDE is more effective on problems with high dimensions.