Multi-objective forest planning at tree-level combining mixed integer programming and airborne laser scanning

Abstract

The development of forest planning at tree-level is nowadays feasible due to the advances in laser scanning. Tree-level data remains still not fully utilized in the context of tree selection mechanisms and harvest-scheduling models. Using spatial optimization with tree-level data can shift the situation. The research presented a decision-support model set based on mixed integer programming (MIP) to select trees based on economical and spatial goals. Trees were represented as polygons to conduct spatial optimization and account for perimeter boundary minimization while establishing adjacency constraints. The proposed model framework method was tested in a Stone pine (Pinus pinea L.) stand of almost 4400 trees in Spain where individual tree detection with airborne laser scanning data was conducted. The MIP-based tree selections were presented using different priorities for single and multi-objective optimizations to demonstrate the potential of spatial goals to make forest management planning more efficient when controlling the spatial arrangement of solutions. The results showed the general MIP formulation is feasible and all presented combinatorial problems reached global optimality fast. The use of MIP formulations to schedule tree-level decisions has positive cascading effects towards operational forest planning while expanding the current frontiers of tree-level forest planning based on heuristic optimization.