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Due to significant industrial demands toward software systems with increasing complexity and challenging quality requirements, software architecture design has become an important development activity and the research domain is rapidly evolving. In the last decades, software architecture optimization methods, which aim to automate the search for an optimal architecture design with respect to a (set of) quality attribute(s), have proliferated. However, the reported results are fragmented over different research communities, multiple system domains, and multiple quality attributes. To integrate the existing research results, we have performed a systematic literature review and analyzed the results of 188 research papers from the different research communities. Based on this survey, a taxonomy has been created which is used to classify the existing research. Furthermore, the systematic analysis of the research literature provided in this review aims to help the research community in consolidating the existing research efforts and deriving a research agenda for future developments.