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QoS-based Web service (WS) discovery has been recognized as the main solution for filtering and selecting between functionally equivalent WSs stored in registries or other types of repositories. There are two main techniques for QoS-based WS matchmaking (filtering): ontology-based and constraint programming (CP)-based. Unfortunately, the first technique is not efficient as it is based on the rather immature technology of ontology reasoning, while the second one is not accurate as it is based on syntactic QoS-based descriptions and faulty matchmaking metrics. In our previous work, we have developed an extensible and rich ontology language for QoS-based WS description. Moreover, we have devised a semantic alignment algorithm for aligning QoS-based WS descriptions so as to increase the accuracy of QoS-based WS matchmaking algorithms. Finally, we have developed two alternative CP-based QoS-based WS matchmaking algorithms: a unary-constrained and n-ary-constrained one. In this paper, we claim that mixed-integer programming (MIP) should be used as a matchmaking technique instead of CP and we provide experimental results proving it. In addition, we analyze and experimentally evaluate our matchmaking algorithms against a competing techniques one in order to demonstrate their efficiency and accuracy.