We present NEAT-TCP, a novel technique to automatically generate congestion control algorithms in a data-driven fashion while optimizing towards a specified global system utility. NEAT-TCP employs an artificial neural network (ANN) in each node and generates a population of ANNs by means of an evolutionary algorithm called NEAT. The ANNs run independently from each other at the communication endpoints and take only features as inputs that are locally available at these nodes. We define the system utility as a combined maximization of overall throughput and throughput fairness between flows according to Jain's fairness index. The nodes are deployed in a grid topology in ns-3 simulations, which makes it particularly difficult to maximize the utility due to different interference levels for the data flows. In our experiments, NEAT-TCP achieves 69% more fairness, 66% less mean end-to-end delay and 71% less packet loss in relation to TCP New Reno at the cost of 19% less overall throughput, which meets our multi-criteria objective.