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In a service-oriented online social network consisting of service providers and consumers, a service consumer can search trustworthy service providers via the social network. This requires the evaluation of the trustworthiness of a service provider along a certain social trust path from the service consumer to the service provider. However, there are usually many social trust paths between participants in social networks. Thus, a challenging problem is which social trust path is the optimal one that can yield the most trustworthy evaluation result In this paper, we first present a novel complex social network structure and a new concept, Quality of Trust (QoT). We then model the optimal social trust path selection with multiple end-to-end QoT constraints as a Multi-Constrained Optimal Path (MCOP) selection problem which is NP-Complete. For solving this challenging problem, we propose an efficient heuristic algorithm, H_OSTP. The results of our experiments conducted on a large real dataset of online social networks illustrate that our proposed algorithm significantly outperforms existing approaches.