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Runtime adaptation of Web service compositions can usually be done in several ways, so it is necessary to decide which adaptation approach to take. The PhD research presented in this paper provides a novel decision making approach, new management algorithms, and a middleware architecture for runtime adaptation of Web service compositions in ways that maximize business value, while satisfying all given constraints. All necessary information about possible adaptations and their business metrics are specified as policies in the WS-Policy4MASC language and the optimization problem is modeled in the powerful constraint programming language MiniZinc. The decision making algorithms integrated into the MiniZnMASC middleware allows it to determine how to adapt each Web service composition instance so the overall business value is maximized, while satisfying all given constraints (e.g., about resource limitations). Experiments with the MiniZnMASC prototype showed that the new solutions are feasible, functionally correct, business beneficial, with low performance overhead, and with linear scalability.