Rib-web structures are used for lightweight design in various applications. The most prominent cases are found in aerospace engineering, where intricate structures are produced by forging and subsequent machining or by machining from solid blocks of material. Due to the large scrap rate involved in conventional manufacturing, rib-web structures are suitable applications for additive manufacturing (AM) processes. Among the AM processes, wire-arc additive manufacturing (WAAM) is highly suitable for rib-web structures due to its high deposition rate and the potential to manufacture large-size parts. In WAAM, the welding strategy greatly influences the properties and quality of deposited parts. With an increasing number of starts and stops, the danger of uneven material build-up and welding defects increases. Unfortunately, most rib-web structures do not represent Eulerian paths, i.e. they cannot be manufactured with a continuous welding motion, in which every edge is visited only once. This study presents a novel strategy for generating optimal tool paths for WAAM of lightweight rib-web structures, mitigating the disadvantages of discontinuous welding paths such as welding defects and uneven build-up. It is shown that doubling the number of welding passes on each edge of the rib-web structure turns non-Eulerian paths into Eulerian paths, which can be welded continuously. When two or more weld beads are deposited on each edge, the vertices of the rib-web structure may suffer from underfilling. It is shown that this can be avoided by a correction strategy, which consists in manufacturing the part once, evaluating the size of voids in the junctions, and computing a correction to deposit the required amount of material into the center of the junction. While this strategy may be used if a single part is considered, it is shown that the tool path correction to be applied to arbitrary junction geometries can be represented by a neural network that is derived from an experimental database consisting of representative junction types. With this approach, paths for any rib-web geometry can be generated, which saves lead time in variant-rich production. The paths proposed in this work avoid non-welding moves and may hence outperform even single weld-bed strategies in terms of welding efficiency.