A Hybrid Spatial-Graph Strategy for the Laser Cutting Path Planning Problem

The Laser Cutting Path Planning Problem (LCPP) minimizes the total air-move time to process all contours in a nesting layout under precedence constraints requiring inner parts to be cut before their enclosing polygons. Since the problem is NP-hard, exact approaches are limited to small instances, while metaheuristics often disregard spatial structure. A hybrid spatial-graph strategy is proposed in three phases: spatial decomposition via QuadTree in the scaled Chebyshev coordinate space, proximity-graph construction via KD-tree k-nearest-neighbor queries, and hierarchical path generation via minimum spanning tree and precedence-aware depth first search, with feasibility guaranteed by construction. The method is evaluated on 282 instances from ESICUP benchmarks and synthetic layouts. The hybrid strategy consistently achieved better objective values than the considered evolutionary baselines across all evaluated instances, achieving mean air-move reductions of 28.9% and 24.8% and runtime speedups of 72x and 177x, respectively.