Landscape-level optimization using tabu search and stand density-related forest management prescriptions.

*(English)*Zbl 1102.90017Summary: Spatial and temporal scheduling of forest management activities is becoming increasingly important due to recent developments in environmental regulations, goals and policies. A forest planning model was developed to select activities for stands in a forested area (178,000 ha), from a set of stand-centric optimal prescriptions, to best meet a higher-level landscape objective. The forest-level management problem addressed is complex, if not impossible to solve optimally, with current computing technologies, as integer decision variables are assumed. The higher-level landscape objective is to achieve the highest even-flow of timber harvest volume. Three types of tabu search processes were examined in the model: (1) a process with 1-opt moves only; (2) a process with 1-opt moves and a region-limited 2-opt move process; and (3) a process with 1-opt moves and 10 iterations through a smaller region-limited 2-opt move process. Aspiration criteria and short-term memory were employed within tabu search in an attempt to avoid becoming trapped in local optima. While the 1-opt move process alone created solutions (forest plans) that were adequate, and contained higher average harvest volumes than the other methods, the addition of the 2-opt move processes improved the solutions generated by intensifying the search around local optima. The solutions produced using the 2-opt move processes had less variation in periodic harvest volumes across the planning horizon. While the basic 1-opt tabu search process provides adequate feasible solutions to large, complex forest planning problems, we reinforce the notion suggested, but not proven with previous research, that 2-opt neighborhoods can help improve quality of large scale forest plans generated by tabu search. The contribution of this research is the description of a process which be developed for large forest planning problems (the problem examined is at least 1 order of magnitude greater than previous research, in terms of forested stands modeled), a process that could enable one to produce more efficient forest planning solutions than one could otherwise with standard 1-opt tabu search. In addition, we describe here the use of a set of optimal stand-level prescriptions to choose from when utilizing the 2-opt process, rather than a set of clearcut periods to consider. With this in mind, this research represents a fundamentally new application of operations research techniques to realistic forest planning problems.

##### MSC:

90B35 | Deterministic scheduling theory in operations research |

90C27 | Combinatorial optimization |

90C06 | Large-scale problems in mathematical programming |

90C59 | Approximation methods and heuristics in mathematical programming |

90B90 | Case-oriented studies in operations research |

91B76 | Environmental economics (natural resource models, harvesting, pollution, etc.) |

##### Keywords:

heuristics; combinatorial optimization; large scale optimization; environment; forest landscape planning
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\textit{P. Bettinger} et al., Eur. J. Oper. Res. 176, No. 2, 1265--1282 (2007; Zbl 1102.90017)

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##### References:

[1] | Arthaud, G.J.; Rose, D., A methodology for estimating production possibility frontiers for wildlife habitat and timber value at the landscape level, Canadian journal of forest research, 26, 12, 2191-2200, (1996) |

[2] | Bettinger, P., 2003. Heuristic Algorithm Teaching Tool (HATT), Warnell School of Forest Resources, University of Georgia, Athens, GA. Available from: <http://warnell.forestry.uga.edu/Warnell/Bettinger/planning/index.htm> (accessed 2/13/05). |

[3] | Bettinger, P.; Sessions, J.; Boston, K., Using tabu search to schedule timber harvests subject to spatial wildlife goals for big game, Ecological modelling, 94, 2/3, 111-123, (1997) |

[4] | Bettinger, P.; Sessions, J.; Johnson, K.N., Ensuring the compatibility of aquatic habitat and commodity production goals in eastern oregon with a tabu search procedure, Forest science, 44, 1, 96-112, (1998) |

[5] | Bettinger, P.; Boston, K.; Sessions, J., Intensifying a heuristic forest harvest scheduling search procedure with 2-opt decision choices, Canadian journal of forest research, 29, 11, 1784-1792, (1999) |

[6] | Bettinger, P.; Graetz, D.; Boston, K.; Sessions, J.; Chung, W., Eight heuristic planning techniques applied to three increasingly difficult wildlife planning problems, Silva fennica, 36, 2, 561-584, (2002) |

[7] | Bettinger, P.; Johnson, D.L.; Johnson, K.N., Spatial forest plan development with ecological and economic goals, Ecological modelling, 169, 2/3, 215-236, (2003) |

[8] | Bevers, M.; Hof, J., Spatially optimizing wildlife habitat edge effects in forest management linear and mixed-integer programs, Forest science, 45, 2, 249-258, (1999) |

[9] | Boston, K.; Bettinger, P., An analysis of Monte Carlo integer programming, simulated annealing, and tabu search heuristics for solving spatial harvest scheduling problems, Forest science, 45, 2, 292-301, (1999) |

[10] | Boston, K.; Bettinger, P., Combining tabu search and genetic algorithm heuristic techniques to solve spatial harvest scheduling problems, Forest science, 48, 1, 35-46, (2002) |

[11] | Brumelle, S.; Granot, D.; Halme, M.; Vertinsky, I., A tabu search algorithm for finding good forest harvest schedules satisfying Green-up constraints, European journal of operational research, 106, 2/3, 408-424, (1998) · Zbl 0991.90543 |

[12] | Caro, F.; Constantino, M.; Martins, I.; Weintraub, A., A 2-opt tabu search procedure for the multiperiod forest harvest scheduling problem with adjacency, greenup, old growth, and even flow constraints, Forest science, 49, 5, 738-751, (2003) |

[13] | Clark, M.M.; Meller, R.D.; McDonald, T.P., A three-stage heuristic for harvest scheduling with access road network development, Forest science, 46, 2, 204-218, (2000) |

[14] | Dannenbring, D.G., Procedures for estimating optimal solution values for large combinatorial problems, Management science, 23, 12, 1273-1283, (1977) · Zbl 0377.90051 |

[15] | Ducheyne, E.I.; De Wulf, R.; De Baets, B., Single versus multiple objective genetic algorithms for solving the even-flow forest management problem, Forest ecology and management, 201, 2/3, 259-273, (2004) |

[16] | Falcão, A.O.; Borges, J.G., Designing an evolution program solving integer forest management scheduling models: an application in Portugal, Forest science, 47, 2, 158-168, (2001) |

[17] | Glover, F., Tabu search—part I, ORSA journal on computing, 1, 3, 190-206, (1989) · Zbl 0753.90054 |

[18] | Glover, F., Tabu search—part II, ORSA journal on computing, 2, 1, 4-32, (1990) · Zbl 0771.90084 |

[19] | Golden, B.L.; Alt, F.B., Interval estimation of a global optimum for large combinatorial problems, Naval research logistics quarterly, 26, 1, 69-77, (1979) · Zbl 0397.90100 |

[20] | Graetz, D., Bettinger, P., 2005. Determining thinning regimes to reach stand density targets for any-aged stand management in the Blue Mountains of eastern Oregon. In: Bevers, M., Barrett, T.M. (Comps.), Systems Analysis in Forest Resources: Proceedings of the 2003 Symposium, USDA Forest Service, Pacific Northwest Research Station, Portland, OR. General Technical Report PNW-GTR-656, pp. 255-264. |

[21] | Haight, R.G.; Travis, L.E., Wildlife conservation planning using stochastic optimization and importance sampling, Forest science, 43, 1, 129-139, (1997) |

[22] | Heinonen, T.; Pukkala, T., A comparison of one- and two-compartment neighborhoods in heuristic search with spatial forest management goals, Silva fennica, 38, 3, 319-332, (2004) |

[23] | Hof, J.G.; Joyce, L.A., Spatial optimization for wildlife and timber in managed forest ecosystems, Forest science, 38, 3, 489-508, (1992) |

[24] | Hof, J.; Bevers, M.; Joyce, L.; Kent, B., An integer programming approach for spatially and temporally optimizing wildlife populations, Forest science, 40, 1, 177-191, (1994) |

[25] | Hoganson, H.M.; Borges, J.G., Using dynamic programming and overlapping subproblems to address adjacency in large harvest scheduling problems, Forest science, 44, 4, 526-538, (1998) |

[26] | Hoganson, H.M.; Rose, D.W., A simulation approach for optimal timber management scheduling, Forest science, 30, 1, 220-238, (1984) |

[27] | Jørgensen, S.E., Editorial: 25 years of ecological modelling by ecological modelling, Ecological modelling, 126, 2/3, 95-99, (2000) |

[28] | Kangas, J.; Pukkala, T., Operationalization of biological diversity as a decision objective in tactical forest planning, Canadian journal of forest research, 26, 1, 103-111, (1996) |

[29] | Kurttila, M.; Pukkala, T.; Loikkanen, J., The performance of alternative spatial objective types in forest planning calculations: A case for flying squirrel and moose, Forest ecology and management, 166, 1-3, 245-260, (2002) |

[30] | Lockwood, C.; Moore, T., Harvest scheduling with spatial constraints: A simulated annealing approach, Canadian journal of forest research, 23, 3, 468-478, (1993) |

[31] | Los, M.; Lardinois, C., Combinatorial programming, statistical optimization and the optimal transportation network problem, Transportation research, 16B, 2, 89-124, (1982) |

[32] | McDill, M.E.; Braze, J., Comparing adjacency constraint formulations for randomly generated forest planning problems with four age-class distributions, Forest science, 46, 3, 423-436, (2000) |

[33] | McDill, M.E.; Braze, J., Using the branch and bound algorithm to solve forest planning problems with adjacency constraints, Forest science, 47, 3, 403-418, (2001) |

[34] | McRoberts, K., A search model for evaluating combinatorially explosive problems, Operations research, 19, 6, 1331-1349, (1971) · Zbl 0228.90021 |

[35] | Murray, A.T., Spatial restrictions in harvest scheduling, Forest science, 45, 1, 45-52, (1999) |

[36] | Murray, A.T.; Church, R.L., Heuristic solution approaches to operational forest planning problems, OR spektrum, 17, 2/3, 193-203, (1995) · Zbl 0842.90077 |

[37] | Nelson, J.; Brodie, J.D., Comparison of a random search algorithm and mixed integer programming for solving area-based forest plans, Canadian journal of forest research, 20, 7, 934-942, (1990) |

[38] | Richards, E.W.; Gunn, E.A., A model and tabu search method to optimize stand harvest and road construction schedules, Forest science, 46, 2, 188-203, (2000) |

[39] | Sessions, J., Bettinger, P., 2001. Hierarchical planning: Pathway to the future? In: Proceedings of the First International Precision Forestry Symposium, University of Washington, Seattle, WA, pp. 185-190. |

[40] | Snyder, S.; ReVelle, C., Temporal and spatial harvesting of irregular systems of parcels, Canadian journal of forest research, 26, 6, 1079-1088, (1996) |

[41] | Van Deusen, P.C., Multiple solution harvest scheduling, Silva fennica, 33, 3, 207-216, (1999) |

[42] | Weintraub, A.; Jones, G.; Meacham, M.; Magendzo, A.; Magendzo, A.; Malchuk, D., Heuristic procedures for solving mixed-integer harvest scheduling—transportation planning models, Canadian journal of forest research, 25, 10, 1618-1626, (1995) |

[43] | Yoshimoto, A.; Haight, R.G.; Brodie, J.D., A comparison of the pattern search algorithm and the modified PATH algorithm for optimizing an individual tree model, Forest science, 36, 2, 394-412, (1990) |

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