A New Heuristic Method for Solving Spatially Constrained Forest Planning Problems Based on Mitigation of Infeasibilities Radiating Outward from a Forced Choice

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.

[1]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[2]  Kevin Boston,et al.  Combining tabu search and genetic algorithm heuristic techniques to solve spatial harvest scheduling problems , 2002 .

[3]  C. Lockwood,et al.  Harvest scheduling with spatial constraints: a simulated annealing approach , 1993 .

[4]  Ola Sallnäs,et al.  Harvest scheduling under adjacency constraints — a case study from the Swedish sub‐alpine region , 1993 .

[5]  Atsushi Yoshimoto,et al.  Comparative analysis of algorithms to generate adjacency constraints , 1994 .

[6]  C. Revelle,et al.  Dynamic Selection of Harvests with Adjacency Restrictions: The SHARe Model , 1997 .

[7]  M. S. Jamnick,et al.  An operational, spatially constrained harvest scheduling model , 1990 .

[8]  Jianping Zhu,et al.  The Effects of Spatial Harvest Scheduling Constraints on the Value of a Medium-Sized Forest Holding in the Southeastern United States , 2005 .

[9]  Marc E. McDill,et al.  Comparing adjacency constraint formulations for randomly generated forest planning problems with four age-class distributions. , 2000 .

[10]  J. D. Brodie,et al.  Comparison of a random search algorithm and mixed integer programming for solving area-based forest plans. , 1990 .

[11]  Alan T. Murray.  Spatial restrictions in harvest scheduling , 1999 .

[12]  John Sessions,et al.  Using Tabu search to schedule timber harvests subject to spatial wildlife goals for big game , 1997 .

[13]  P. Bettinger,et al.  Spatial forest planning: To adopt, or not to adopt? , 2003 .

[14]  Richard L. Church,et al.  Heuristic solution approaches to operational forest planning problems , 1995 .

[15]  J. Douglas Brodie,et al.  Adjacency constraints in harvest scheduling: an aggregation heuristic , 1990 .

[16]  Timo Pukkala,et al.  A comparison of one- and two-compartment neighbourhoods in heuristic search with spatial forest management goals , 2004 .

[17]  Marc E. McDill,et al.  Using the branch and bound algorithm to solve forest planning problems with adjacency constraints , 2001 .

[18]  Kevin Boston,et al.  An analysis of Monte Carlo integer programming, simulated annealing, and tabu search heuristics for solving spatial harvest scheduling problems. , 1999 .

[19]  Pete Bettinger,et al.  Spatial forest plan development with ecological and economic goals , 2003 .

[20]  Alan T. Murray,et al.  Incorporating average and maximum area restrictions in harvest scheduling models , 2004 .

[21]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[22]  A. Weintraub,et al.  Heuristic procedures for solving mixed-integer harvest scheduling–transportation planning models , 1995 .

[23]  Jerold T. Hahn,et al.  Empirical yield tables for Wisconsin. , 1976 .

[24]  Pete Bettinger,et al.  The Key Literature of, and Trends in, Forest-Level Management Planning in North America, 1950–2001 , 2004 .

[25]  José G. Borges,et al.  Combining a decomposition strategy with dynamic programming to solve spatially constrained forest management scheduling problems , 1999 .

[26]  John Sessions,et al.  Intensifying a heuristic forest harvest scheduling search procedure with 2-opt decision choices , 1999 .

[27]  John Sessions,et al.  Ensuring the Compatibility of Aquatic Habitat and Commodity Production Goals in Eastern Oregon with a Tabu Search Procedure , 1998, Forest Science.

[28]  Paul C. Van Deusen,et al.  Multiple solution harvest scheduling , 1999 .

[29]  J. Borges,et al.  Combining random and systematic search heuristic procedures for solving spatially constrained forest management scheduling models , 2002 .

[30]  Marc E. McDill,et al.  Harvest Scheduling with Area-Based Adjacency Constraints , 2002, Forest Science.

[31]  John Sessions,et al.  Eight heuristic planning techniques applied to three increasingly difficult wildlife planning problems , 2002 .

[32]  B. Bruce Bare,et al.  Spatially constrained timber harvest scheduling , 1989 .

[33]  F. Barahona,et al.  A column generation algorithm for solving general forest planning problems with adjacency constraints , 1994 .

[34]  Gerhard W. Dueck,et al.  Threshold accepting: a general purpose optimization algorithm appearing superior to simulated anneal , 1990 .

[35]  Jyrki Kangas,et al.  Operationalization of biological diversity as a decision objective in tactical forest planning , 1996 .

[36]  Jyrki Kangas,et al.  A heuristic optimization method for forest planning and decision making , 1993 .

[37]  José G. Borges,et al.  Using dynamic programming and overlapping subproblems to address adjacency in large harvest scheduling problems , 1998 .