Architectural styles help to improve the Product Line Architecture (PLA) design by providing a better organization of its elements, which results in some benefits, like flexibility, extensibility and maintainability. The PLA design can also be improved by using a search based optimization approach, taking into account different metrics, such as cohesion, coupling and feature modularization. However, the application of search operators changes the PLA organization, and consequently may violate the architectural styles rules, impacting negatively in the architecture understanding. To overcome such limitation, this work introduces a set of search operators to be used in the search based design with the goal of preserving the architectural styles during the optimization process. Such operators consider rules of the layered and client/server architectural styles, generally used in the search based design of conventional architectures and PLAs. The operators are implemented and evaluated in the context of MOA4PLA, a Multi-objective Optimization Approach for PLA Design. Results from an empirical evaluation show that the proposed operators contribute to obtain better solutions, preserving the adopted style and also improving some software metric values.