A branch-and-bound procedure for forest harvest scheduling problems addressing aspects of habitat availability
In the literature, the most widely referred approaches regarding forest harvesting scheduling problems involving environmental concerns have typically addressed constraints on the maximum clear‐cut area. Nevertheless, the solutions arising from those approaches in general display a loss of habitat a...
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| Published in: | International transactions in operational research Vol. 20; no. 5; pp. 689 - 709 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Oxford
Blackwell Publishing Ltd
01.09.2013
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| ISSN: | 0969-6016, 1475-3995 |
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| Abstract | In the literature, the most widely referred approaches regarding forest harvesting scheduling problems involving environmental concerns have typically addressed constraints on the maximum clear‐cut area. Nevertheless, the solutions arising from those approaches in general display a loss of habitat availability. Such loss endangers the survival of many wild species. This study presents a branch‐and‐bound procedure designed to find good feasible solutions, in a reasonable time, to forest harvest scheduling problems with constraints on the clear‐cut area and habitat availability. Two measures are applied for the habitat availability constraints: the area of all habitats and the connectivity between them. In each branch of the branch‐and‐bound tree, a partial solution leads to two children nodes, corresponding to the cases of harvesting or not harvesting a given stand in a given period. Pruning is based on constraint violations or unreachable objective values. Computational results are reported. |
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| AbstractList | In the literature, the most widely referred approaches regarding forest harvesting scheduling problems involving environmental concerns have typically addressed constraints on the maximum clear-cut area. Nevertheless, the solutions arising from those approaches in general display a loss of habitat availability. Such loss endangers the survival of many wild species. This study presents a branch-and-bound procedure designed to find good feasible solutions, in a reasonable time, to forest harvest scheduling problems with constraints on the clear-cut area and habitat availability. Two measures are applied for the habitat availability constraints: the area of all habitats and the connectivity between them. In each branch of the branch-and-bound tree, a partial solution leads to two children nodes, corresponding to the cases of harvesting or not harvesting a given stand in a given period. Pruning is based on constraint violations or unreachable objective values. Computational results are reported. In the literature, the most widely referred approaches regarding forest harvesting scheduling problems involving environmental concerns have typically addressed constraints on the maximum clear-cut area. Nevertheless, the solutions arising from those approaches in general display a loss of habitat availability. Such loss endangers the survival of many wild species. This study presents a branch-and-bound procedure designed to find good feasible solutions, in a reasonable time, to forest harvest scheduling problems with constraints on the clear-cut area and habitat availability. Two measures are applied for the habitat availability constraints: the area of all habitats and the connectivity between them. In each branch of the branch-and-bound tree, a partial solution leads to two children nodes, corresponding to the cases of harvesting or not harvesting a given stand in a given period. Pruning is based on constraint violations or unreachable objective values. Computational results are reported [PUBLICATION ABSTRACT]. |
| Author | Constantino, Miguel Neto, Teresa Martins, Isabel Pedroso, João Pedro |
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| Cites_doi | 10.1016/j.ejor.2003.07.021 10.2307/2265590 10.1007/s10589-010-9347-1 10.1007/BF02275261 10.1007/978-94-015-9906-1_7 10.1139/x98-076 10.5751/ES-00015-010104 10.1139/x00-103 10.1093/forestscience/48.4.631 10.1287/opre.1070.0472 10.1016/j.landurbplan.2007.03.005 10.1006/jema.2000.0373 10.1016/S0378-1127(01)00664-8 10.1093/forestscience/49.4.608 10.7208/chicago/9780226219950.001.0001 10.1093/forestscience/40.1.177 10.2307/3544927 10.1139/x94-167 10.1007/s10980-006-0013-z 10.1016/j.foreco.2007.09.033 10.1093/forestscience/49.5.738 10.1111/1475-3995.00424 10.1139/x95-198 10.1139/X07-033 10.5558/tfc81359-3 10.1093/forestscience/54.3.367 10.1093/forestscience/48.3.608 10.1016/j.cor.2008.08.013 10.1016/j.ejor.2009.04.027 10.1287/opre.1040.0169 10.1093/forestscience/55.2.149 10.1093/forestscience/48.4.779 10.1016/j.ejor.2005.09.016 10.1093/forestscience/52.1.93 10.1139/x03-101 10.1016/j.foreco.2005.03.059 10.1007/s10878-006-9035-3 |
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| References | Vielma, J.P., Murray, A.T., Ryan, D.M., Weintraub, A., 2007. Improving computational capabilities for addressing volume constraints in forest harvest scheduling problems. European Journal of Operational Research 176, 2, 1246-1264. Martins, I., Constantino, M., Borges, J.G., 2005. A column generation approach for solving a non-temporal forest harvest model with spatial structure constraints. European Journal of Operational Research 161, 2, 478-498. Yoshimoto, A., Brodie, J.D., 1994. Comparative analysis of algorithms to generate adjacency constraints. Canadian Journal of Forest Research 24, 1277-1288. Kurtilla, M., Pukkala, T., Loikkanen, J., 2002. The performance of alternative spatial objective types in forest planning calculations: A case for flying squirrel and moose. Forest Ecology and Management 166, 245-260. Martins, I., Alvelos, F., Constantino, M., 2012. A branch-and-price approach for harvest scheduling subject to maximum area restrictions. Computational Optimization and Applications 51, 362-385. Saura, S., Pascual-Hortal, L., 2007. A new habitat availability index to integrate connectivity in landscape conservation planning: Comparison with existing indices and application to a case study. Landscape and Urban Planning 83, 2-3, 91-103. Pedroso, J.P., Kubo, M., 2010. Heuristics and exact methods for number partitioning. European Journal of Operational Research 202, 73-81. Sbihi, A., 2007. A best first search exact algorithm for the multiple-choice multidimensional knapsack problem. Journal of Combinatorial Optimization 13, 4, 337-351. Goycoolea, M., Murray, A.T., Barahona, F., Epstein, R., Weintraub, A., 2005. Harvest scheduling subject to maximum area restrictions: Exploring exact approaches. Operations Research 53, 3, 490-500. Taylor, P., Fahrig, L., Henein, K., Merriam, G., 1993. Connectivity is a vital element of landscape structure. Oikos 68, 3, 571-573. Artigues, C., Gendreau, M., Rousseau, L.M., Vergnaud, A., 2009. Solving an integrated employee timetabling and job-shop scheduling problem via hybrid branch-and-bound. Computers & Operations Research 36, 8, 2330-2340. Öhman, K., Eriksson, L.O., 1998. The core area concept in forming contiguous areas for long term forest planning. Canadian Journal of Forest Research 28, 7, 1032-1039. Wei, Y., Hoganson, H.M., 2007. Scheduling forest core area production using mixed integer programming. Canadian Journal of Forest Research 37, 10, 1924-1932. Crowe, K., Nelson, J., Boyland, M., 2003. Solving the area-restricted harvest-scheduling model using the branch and bound algorithm. Canadian Journal of Forest Research 33, 9, 1804-1814. McDill, M.E., Rebain, S.A., Braze, J., 2002. Harvest scheduling with area-based adjacency constraints. Forest Science 48, 4, 631-642. Wei, Y., Hoganson, H.M., 2008. Tests of a dynamic programming-based heuristic for scheduling forest core area production over large landscapes. Forest Science 54, 3, 367-380. Harris, L.D., 1984. The Fragmented Forest: Island Biogeography Theory and the Preservation of Biotic Diversity. University of Chicago Press, Chicago, IL. Goycoolea, M., Murray, A.T., Vielma, J.P., Weintraub, A., 2009. Evaluating approaches for solving the area restricted model in harvest scheduling. Forest Science 55, 2, 149-165. Shumaker, N.H., 1996. Using landscape indices to predict habitat connectivity. Ecology 77, 4, 1210-1225. Franklin, J.F., Forman, R.T., 1987. Creating landscape patterns by forest cutting: Ecological consequences and principles. Landscape Ecology 1, 1, 5-18. Öhman, K., Lämȧs, T., 2005. Reducing forest fragmentation in long-term forest planning by using the shape index. Forest Ecology and Management 212, 346-357. Rebain, S., McDill, M.E., 2003a. A mixed-integer formulation of the minimum patch size problem. Forest Science 49, 4, 608-618. Constantino, M., Martins, I., Borges, J.G., 2008. A new mixed integer programming model for harvest scheduling subject to maximum area restrictions. Operations Research 56, 3, 542-551. Caro, F., Constantino, M., Martins, I., Weintraub, A., 2003. A 2-Opt Tabu Search procedure for the multiperiod forest harvesting problem with adjacency, greenup, old growth, and even flow constraints. Forest Science 49, 5, 738-751. Baskent, E.Z., Jordan, G.A., 1995. Characterizing spatial structure of forest landscapes. Canadian Journal of Forest Research 25, 11, 1830-1849. Öhman, K., 2000. Creating continuous areas of old forest in long term forest planning. Canadian Journal of Forest Research 30, 11, 1817-1823. Murray, A.T., Weintraub, A., 2002. Scale and unit specification influences in harvest scheduling with maximum area restrictions. Forest Science 48, 779-789. Bunn, A.G., Urban, D.L., Keitt, T.H., 2000. Landscape connectivity: A conservation application of graph theory. Journal of Environmental Management 2, 10, 265-278. Hof, J., Bevers, M., Joyce, L., Kent, B., 1994. An integer programming approach for spatially and temporally optimizing wildlife populations. Forest Science 40, 1, 177-191. Rebain, S., McDill, M.E., 2003b. Can mature patch constraints mitigate the fragmenting effect of harvest opening size restrictions? International Transactions in Operations Research 10, 5, 499-513. Hortal, L.P., Saura, S., 2006. Comparison and development of new graph-based connectivity indices: Towards the prioritization of habitat patches and corridors for conservation. Landscape Ecology 21, 959-967. Keitt, T.H., Urban, D.L., Milne, B.L., 1997. Detecting critical scales in fragmented landscapes. Conservation Ecology 1, 16-17. Öhman, K., Wikström, P., 2008. Incorporating aspects of habitat fragmentation into long-term forest planning using mixed integer programming. Forest Ecology and Management 255, 440-446. Tóth, S.F., McDill, M.E., Rebain, S., 2006. Finding the efficient frontier of a bi-criteria, spatially-explicit, harvest scheduling problem. Forest Science 52, 1, 93-107. Falcão, A., Borges, J.G., 2002. Combining random and systematic search heuristic procedures for solving spatially constrained forest management scheduling models. Forest Science 48, 3, 608-621. Mathey, A.H., Kremar, E., Vertinsky, I., 2005. Re-evaluating our approach to forest management planning: A complex journey. Forestry Chronicle 81, 3, 359-364. 1987; 1 1993; 68 1998; 28 2006; 52 2005; 212 2010; 202 2008; 56 1995 1994; 24 2000; 2 1997; 1 2008; 54 2004 2005; 81 2002 2007; 13 1994; 40 2003; 33 2007; 37 1999 2012; 51 1996; 77 2009; 55 2009; 36 2002; 48 2005; 161 2006; 21 1995; 25 2007; 176 2003b; 10 2002; 166 2000; 30 2003a; 49 2005; 53 2003; 49 1984 2007; 83 2008; 255 e_1_2_7_6_1 e_1_2_7_4_1 Caro F. (e_1_2_7_5_1) 2003; 49 e_1_2_7_3_1 e_1_2_7_9_1 Murray A.T. (e_1_2_7_24_1) 2002; 48 e_1_2_7_7_1 e_1_2_7_18_1 e_1_2_7_16_1 e_1_2_7_2_1 e_1_2_7_41_1 e_1_2_7_13_1 e_1_2_7_11_1 e_1_2_7_10_1 e_1_2_7_26_1 e_1_2_7_27_1 o A. (e_1_2_7_8_1) 2002; 48 e_1_2_7_28_1 e_1_2_7_29_1 Hof J. (e_1_2_7_14_1) 1994; 40 McDill M.E. (e_1_2_7_19_1) 2002; 48 Tóth S.F. (e_1_2_7_37_1) 2006; 52 Rebain S. (e_1_2_7_31_1) 2003; 49 Goycoolea M. (e_1_2_7_12_1) 2009; 55 Keitt T.H. (e_1_2_7_17_1) 1997; 1 Wei Y. (e_1_2_7_40_1) 2008; 54 e_1_2_7_30_1 e_1_2_7_25_1 Hoganson H.M. (e_1_2_7_15_1) 2004 e_1_2_7_32_1 e_1_2_7_23_1 e_1_2_7_33_1 e_1_2_7_22_1 e_1_2_7_34_1 e_1_2_7_21_1 e_1_2_7_35_1 e_1_2_7_20_1 e_1_2_7_36_1 e_1_2_7_38_1 e_1_2_7_39_1 |
| References_xml | – reference: Wei, Y., Hoganson, H.M., 2008. Tests of a dynamic programming-based heuristic for scheduling forest core area production over large landscapes. Forest Science 54, 3, 367-380. – reference: Kurtilla, M., Pukkala, T., Loikkanen, J., 2002. The performance of alternative spatial objective types in forest planning calculations: A case for flying squirrel and moose. Forest Ecology and Management 166, 245-260. – reference: Constantino, M., Martins, I., Borges, J.G., 2008. A new mixed integer programming model for harvest scheduling subject to maximum area restrictions. Operations Research 56, 3, 542-551. – reference: Artigues, C., Gendreau, M., Rousseau, L.M., Vergnaud, A., 2009. Solving an integrated employee timetabling and job-shop scheduling problem via hybrid branch-and-bound. Computers & Operations Research 36, 8, 2330-2340. – reference: Yoshimoto, A., Brodie, J.D., 1994. Comparative analysis of algorithms to generate adjacency constraints. Canadian Journal of Forest Research 24, 1277-1288. – reference: Caro, F., Constantino, M., Martins, I., Weintraub, A., 2003. A 2-Opt Tabu Search procedure for the multiperiod forest harvesting problem with adjacency, greenup, old growth, and even flow constraints. Forest Science 49, 5, 738-751. – reference: Öhman, K., Wikström, P., 2008. Incorporating aspects of habitat fragmentation into long-term forest planning using mixed integer programming. Forest Ecology and Management 255, 440-446. – reference: Hof, J., Bevers, M., Joyce, L., Kent, B., 1994. An integer programming approach for spatially and temporally optimizing wildlife populations. Forest Science 40, 1, 177-191. – reference: Bunn, A.G., Urban, D.L., Keitt, T.H., 2000. Landscape connectivity: A conservation application of graph theory. Journal of Environmental Management 2, 10, 265-278. – reference: Murray, A.T., Weintraub, A., 2002. Scale and unit specification influences in harvest scheduling with maximum area restrictions. Forest Science 48, 779-789. – reference: Goycoolea, M., Murray, A.T., Vielma, J.P., Weintraub, A., 2009. Evaluating approaches for solving the area restricted model in harvest scheduling. Forest Science 55, 2, 149-165. – reference: Keitt, T.H., Urban, D.L., Milne, B.L., 1997. Detecting critical scales in fragmented landscapes. Conservation Ecology 1, 16-17. – reference: Rebain, S., McDill, M.E., 2003b. Can mature patch constraints mitigate the fragmenting effect of harvest opening size restrictions? International Transactions in Operations Research 10, 5, 499-513. – reference: Sbihi, A., 2007. A best first search exact algorithm for the multiple-choice multidimensional knapsack problem. Journal of Combinatorial Optimization 13, 4, 337-351. – reference: Shumaker, N.H., 1996. Using landscape indices to predict habitat connectivity. Ecology 77, 4, 1210-1225. – reference: Crowe, K., Nelson, J., Boyland, M., 2003. Solving the area-restricted harvest-scheduling model using the branch and bound algorithm. Canadian Journal of Forest Research 33, 9, 1804-1814. – reference: Mathey, A.H., Kremar, E., Vertinsky, I., 2005. Re-evaluating our approach to forest management planning: A complex journey. Forestry Chronicle 81, 3, 359-364. – reference: Hortal, L.P., Saura, S., 2006. Comparison and development of new graph-based connectivity indices: Towards the prioritization of habitat patches and corridors for conservation. Landscape Ecology 21, 959-967. – reference: Öhman, K., Lämȧs, T., 2005. Reducing forest fragmentation in long-term forest planning by using the shape index. Forest Ecology and Management 212, 346-357. – reference: Martins, I., Constantino, M., Borges, J.G., 2005. A column generation approach for solving a non-temporal forest harvest model with spatial structure constraints. European Journal of Operational Research 161, 2, 478-498. – reference: Franklin, J.F., Forman, R.T., 1987. Creating landscape patterns by forest cutting: Ecological consequences and principles. Landscape Ecology 1, 1, 5-18. – reference: Wei, Y., Hoganson, H.M., 2007. Scheduling forest core area production using mixed integer programming. Canadian Journal of Forest Research 37, 10, 1924-1932. – reference: Saura, S., Pascual-Hortal, L., 2007. A new habitat availability index to integrate connectivity in landscape conservation planning: Comparison with existing indices and application to a case study. Landscape and Urban Planning 83, 2-3, 91-103. – reference: Goycoolea, M., Murray, A.T., Barahona, F., Epstein, R., Weintraub, A., 2005. Harvest scheduling subject to maximum area restrictions: Exploring exact approaches. Operations Research 53, 3, 490-500. – reference: Öhman, K., Eriksson, L.O., 1998. The core area concept in forming contiguous areas for long term forest planning. Canadian Journal of Forest Research 28, 7, 1032-1039. – reference: Falcão, A., Borges, J.G., 2002. Combining random and systematic search heuristic procedures for solving spatially constrained forest management scheduling models. Forest Science 48, 3, 608-621. – reference: Öhman, K., 2000. Creating continuous areas of old forest in long term forest planning. Canadian Journal of Forest Research 30, 11, 1817-1823. – reference: Harris, L.D., 1984. The Fragmented Forest: Island Biogeography Theory and the Preservation of Biotic Diversity. University of Chicago Press, Chicago, IL. – reference: Baskent, E.Z., Jordan, G.A., 1995. Characterizing spatial structure of forest landscapes. Canadian Journal of Forest Research 25, 11, 1830-1849. – reference: McDill, M.E., Rebain, S.A., Braze, J., 2002. Harvest scheduling with area-based adjacency constraints. Forest Science 48, 4, 631-642. – reference: Taylor, P., Fahrig, L., Henein, K., Merriam, G., 1993. Connectivity is a vital element of landscape structure. Oikos 68, 3, 571-573. – reference: Martins, I., Alvelos, F., Constantino, M., 2012. A branch-and-price approach for harvest scheduling subject to maximum area restrictions. Computational Optimization and Applications 51, 362-385. – reference: Vielma, J.P., Murray, A.T., Ryan, D.M., Weintraub, A., 2007. Improving computational capabilities for addressing volume constraints in forest harvest scheduling problems. European Journal of Operational Research 176, 2, 1246-1264. – reference: Tóth, S.F., McDill, M.E., Rebain, S., 2006. Finding the efficient frontier of a bi-criteria, spatially-explicit, harvest scheduling problem. Forest Science 52, 1, 93-107. – reference: Pedroso, J.P., Kubo, M., 2010. Heuristics and exact methods for number partitioning. European Journal of Operational Research 202, 73-81. – reference: Rebain, S., McDill, M.E., 2003a. A mixed-integer formulation of the minimum patch size problem. 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| Title | A branch-and-bound procedure for forest harvest scheduling problems addressing aspects of habitat availability |
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