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This paper addresses the problem of joint routing and radio resource management in multihop cellular networks with fixed relays. The objective is to maximize the total network utility. This paper focuses on quality of service (QoS-) sensitive applications that are captured by sigmoidal-like utility functions. The non-concavity of the user utility functions, the complex relation between routing decisions and network resource allocation, and the dependence of link capacities on all interfering transmission powers render the problem non-convex, and extremely difficult to solve. However, we present a meta-heuristic based on genetic algorithms that solves the problem successfully, efficiently and globally.