In a service-oriented online social network consisting of service providers and consumers as participants, a service consumer can search trustworthy service providers via the social network between them. This requires the evaluation of the trustworthiness of a service provider along a potentially very large number of social trust paths from the service consumer to the service provider. Thus, a challenging problem is how to identify K optimal social trust paths that can yield the K most trustworthy evaluation results based on service consumers' evaluation criteria. In this paper, we first present a complex social network structure and a concept, Quality of Trust (QoT). We then model the K optimal social trust paths selection with multiple end-to-end QoT constraints as the Multiple Constrained K Optimal Paths (MCOP-K) selection problem, which is NP-Complete. For solving this challenging problem, based on Dijkstra's shortest path algorithm and our optimization strategies, we propose a heuristic algorithm H-OSTP-K with the time complexity of O(m +Knlogn). The results of our experiments conducted on a real dataset of online social networks illustrate that H-OSTP-K outperforms existing methods in the quality of identified social trust paths.