Service-Oriented software architecture becomes a common computing practice in developing enterprise applications. When software components are located on different computing platforms, there will be a need for computing a minimum cost graph that connects the service providers to the service requester. Unfortunately, computing such a graph can take quite a long time. The problem could be simple if there is only one service provider. Unfortunately, this is not always the case and in several applications there is a need to reach all providers simultaneously. The problem gets more complicated if there are specific constraints imposed by the requester or service providers. One of these constraints is to get the service through certain intermediate delegate systems. Hence, in this paper a new framework is proposed based on genetic algorithms to tackle this problem. Simulation studies have been carried out to evaluate the performance of the proposed model. The results of simulation studies indicate that the proposed model is able to compute a near-optimal graph that satisfies the imposed constraints.Index Terms-Software systems, software architecture, serviceoriented architecture, service provider, genetic algorithms.