Optimal Parameter Settings for Solving Harvest Scheduling Models with Adjacency Constraints
キーワード:
harvest scheduling、 adjacency constraints、 forest management、 area restriction models、 unit restriction models要旨
Optimal parameter settings to improve the efficiency of solving harvest scheduling models with adjacency constraints were examined using Ilog’s Cplex® 11.2 optimizer tuning tool. A total of 160 randomly generated hypothetical forests were created with either 50 or 100 stands and four age-class distributions. Mixed integer programming problems were formulated in Model I form with four different adjacency constraint types, two Unit Restriction Model (URM) adjacency constraints (Pairwise and Maximal Clique) and two Area Restriction Model (ARM) formulations (Path and Generalized Management Unit). A total of 640 problem sets―where a set is a common forest size, age-class distribution, and adjacency constraint type―were tuned to determine optimal parameter settings and then were solved at both the default and optimal settings. In general, mean solution time was less for a given problem set using the optimal parameters compared to the default parameters. The results discussed provide a simple approach to decrease the solution time of solving mixed integer forest planning problems with adjacency constraints.
参考文献
Barahona, F., R. Epstein, and A. Weintraub. 1992. Habitat dispersion in forest planning and the stable set problem. Oper. Res. 40(1): S14-S20.
Barrett, T., J. Gilless, and L. Davis. 1998. Economic and fragmentation effects of clearcut restrictions. For. Sci. 44(4): 569-577.
Bettinger, P., K. Boston, and J. Sessions. 1999. Combinatorial optimization of elk habitat and timber harvest volume. Env. Mod. and Ass. 4(2-3): 143-153.
Boston, K., and P. Bettinger. 1999. An analysis of Monte Carlo integer programming, simulated annealing, and tabu search heuristics for solving spatial harvest scheduling problems. For. Sci. 45(2): 292-301.
Boston, K., and P. Bettinger. 2002. Combining tabu search and genetic algorithms heuristic techniques to solve spatial harvest scheduling problems. For. Sci. 48(1): 35-46.
Caro, F., M. Constantino, I. Martins, and A. Weintraub. 2003. A 2-Opt tabu search procedure for the multi-period forest harvesting problem with adjacency, green-up, old growth and even flow constraints. For. Sci. 49(5): 738-751.
Constantino, M., I. Martins, and J. Borges. 2006. A new mixed integer programming model for harvest scheduling subject to maximum area restrictions. Oper. Res. 56(3): 542-551.
Crowe, K., J. Nelson, and M. Boyland. 2003. Solving the area restricted harvest scheduling model using the branch and bound algorithm. Can. J. For. Res. 33(9): 1804-1814.
Goycoolea, M., A. Murray, F. Barahona, R. Epstein, and A. Weintraub. 2005. Harvest scheduling subject to maximum area restrictions: exploring exact approaches. Oper. Res. 53(3): 490-500.
Goycoolea, M., A. Murray, J.P. Vielma, and A. Weintraub. 2009. Evaluating approaches for solving the area restriction model in harvest scheduling. For. Sci. 55(2): 149-165.
Hoganson, H.M., and J.G. Borges. 1998. Using dynamic programming and overlapping subproblems to address adjacency in large harvest scheduling problems. For. Sci. 44(4): 526-538.
ILOG. 2008. CPLEX 11.2 user's manual. ILOG, Inc., Incline Village, Nevada.
Johnson, K.N., and H.L. Scheurman. 1977. Techniques for prescribing optimal timber harvest and investment under different objective - discussion and synthesis. For. Sci. Monogr. 18.
Lockwood, C., and T. Moore. 1993. Harvest scheduling with spatial constraints: a simulated annealing approach. Can. J. For. Res. 23: 468-478.
McDill, M.E., and J. Braze. 2000. Comparing adjacency constraint formulations for randomly generated forest planning problems with four age class distributions. For. Sci. 46(3): 423-436.
McDill, M.E., and J. Braze. 2001. Using the branch and bound algorithm to solve forest planning problems with adjacency constraints. For. Sci. 47(3): 403-418.
McDill, M.E., S.A. Rebain, and J. Braze. 2002. Harvest scheduling with area-based adjacency constraints. For. Sci. 48(4): 631-642.
Murray, A.T. 1999. Spatial restrictions in harvest scheduling. For. Sci. 45(1):1-8.
Murray, A.T., and R.L. Church. 1995. Heuristic solution approaches to operational forest planning problems. OR Spekt. 17: 193-203.
Murray, A.T., and A. Weintraub. 2002. Scale and unit specification influences in harvest scheduling with maximum area restrictions. For. Sci. 48(4): 779-788.
Nelson, J., and J.D. Brodie. 1990. Comparison of a random search algorithm and mixed integer programming for solving area-based forest plans. Can. J. For. Res. 20: 934-942.
O'Hare, A., B.H. Faaland, and B.B. Bare. 1989. Spatially constrained timber harvest scheduling. Can. J. For. Res. 19: 715-724.
R Development Core Team. 2008. R: Language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
Richards, E.W., and E.A. Gunn. 2000. A model and tabu search method to optimize stand harvest and road construction schedules. For. Sci. 46(2): 188-203.
Thompson, E.F., B.G. Halterman, T.S. Lyon, and R.L. Miller. 1973. Integrating timber and wildlife management planning. For. Chron. 47: 247-250.
Weintraub, A., G. Jones, A. Magendzo, M. Meacham, and M. Kirby. 1994. A heuristic system to solve mixed integer forest planning models. Oper. Res. 42(6): 1010-1024.
Williams, H.P. 1993. Model building in mathematical programming. Ed. 4. Wiley, New York. 356 p.
ダウンロード
発行日
巻号
セクション
ライセンス
Authors who publish with this journal agree to the following terms:- Authors grant the journal right of first publication, with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) following the publication by the journal, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
