A new heuristic method for solving spatially constrained forest planning problems based on mitigation of infeasibilities radiating outward from a forced choice

Abstract

A new heuristic method to mitigate infeasibilities when a choice is forced into a solution was developed to solve spatially constrained forest planning problems. One unique aspect of the heuristic is the introduction of unchosen decision choices into a solution regardless of the resulting infeasibilities, which are then mitigated by selecting next-best choices for those spatial units that are affected, but in a radiating manner away from the initial choice. As subsequent changes are made to correct the affected spatial units, more infeasibilities may occur, and these are corrected as well in an outward manner from the initial choice. A single iteration of the model may involve a number of changes to the status of the decision variables, making this an n-opt heuristic process. The second unique aspect of the search process is the periodic reversion of the search to a saved (in computer memory) best solution. Tests have shown that the reversion is needed to ensure better solutions are located. This new heuristic produced solutions to spatial problems that are of equal or comparable in quality to traditional integer programming solutions, and solutions that are better than those produced by two other basic heuristics. Three small hypothetical forest examples illustrate the performance of the heuristic against standard versions of threshold accepting and tabu search. In each of the three examples, the variation in solutions generated from random starting points is smaller with the new heuristic, and the difference in solution values between the new heuristic and the other two heuristics is significant (p<0.05) when using an analysis of variance. However, what remains to be seen is whether the new method can be applied successfully to the broader range of operations research problems in forestry and other fields.