Although conventional computer technology made a huge leap forward in the past decade, a vast number of computational problems remain inaccessible due to their inherently complex nature. One solution to deal with this computational complexity is to highly parallelize computations and to explore new technologies beyond semiconductor computers. Here, we report on the operation of a device employing a biological computation approach that solves an instance of a classical nondeterministic-polynomial-time complete ("NP-complete") problem, subset sum problem. This new approach called network-based biocomputation (NBC) consists of a specifically designed nanostructured network that encodes an instance of the subset-sum problem. The network is then simultaneously explored by a large number of molecular-motor-driven protein filaments, whose path through the network determines the solution of the given subset-sum problem in a time- and energy efficient manner. The nanofabricated structures rely on a combination of physical and chemical guiding of the microtubules through channels. Therefore, the nanochannels have to meet tight requirements for the biochemical treatment as well as the microtubule guidance. The material stack used for the nanochannels ensures that the motor protein kinesin-1 attaches only at the floor of the nanochannels. Further optimizations in the nanofabrication have greatly improved the smoothness of channel floor and walls, while optimizations in motor-protein expression and purification have improved the activity of the motor proteins. Together, these optimizations provide us with the opportunity to increase the complexity as well as the reliability of our devices. In the future, this will allow the fabrication and operation of large-scale networks, intended to solve computational problems that are currently too time- and energy-consuming for conventional computers.