Optimizing the trajectory of a wire arc additive manufacturing using the dhouib-matrix-4 metaheuristic

Abstract

In wire arc additive manufacturing (WAAM)—classified as a wire-based directed energy deposition (DED-Arc or WA-DED) process under ISO/ASTM 52900:2021—the welding torch must follow a layer-wise deposition trajectory that connects hundreds to thousands of discretized nodes while limiting arc start/stop events and minimizing non-productive travel. Trajectory optimization therefore directly affects build time, thermal history, and overall bead quality. This paper formulates each layer as an open shortest Hamiltonian path problem over nodes extracted from the sliced geometry and applies the Dhouib-Matrix-4 (DM4) metaheuristic, which combines a constructive initialization stage (DM-TSP1) with an iterative Far-to-Near (FtN) neighborhood improvement stage to generate high-quality routes efficiently as the problem size scales. Three benchmark case studies from the literature validate the approach: (i) a prismatic layer with 303 nodes at 6 mm spacing, (ii) a denser geometry with 383 nodes at 3.03 mm spacing over six layers, and (iii) a topologically complex layer with two internal holes and 1072 nodes. DM4 achieves a per-layer length of 1785.57 mm in Case 1 (improving two baselines: 1817.72 mm and 1819.61 mm), 1094 mm in Case 2 (a 12.7% reduction over the Pixel strategy at 1253 mm), and 3072.62 mm in Case 3 (marginally above the continuous Pixel strategy at 3038.70 mm). The results confirm that DM4 is an effective and scalable option for WAAM toolpath generation on simply connected geometries, while the Case 3 outcome motivates topology-aware extensions for multi-region layers as immediate future work.

Graphical Abstract