Most artificial neural networks used in practical applications are based on simple neuron types in a multi-layer architecture. Here, we propose to solve optimization problems using a recurrent network of spiking neurons mimic king the response behavior of biological neurons. Such networks can compute a series of different solutions for a given problem and converge in to a periodical sequence of such solutions. The goal of this paper is to prove that neural networks like the SRM (Spike Response Model) are able to solve nonlinear optimization problems. We demonstrate this for the traveling salesman problem. Our network model is able to compute multiple solutions and can use its dynamics to leave local minima in which classical models would be stuck. F or adapting the model, we introduce a suitable network architecture and show how to encode the problem directly into the network weights.