FORS 8450 Advanced Forest Planning Lecture 8 Threshold Accepting Example

Development of a research plan for testing several silvicultural approaches to develop mid- to late-successional forest structure The development of a long-term, replicated study to test hypotheses and evaluate the success of various silvicultural approaches The major ecological and silvicultural focus of the replicated study is to test the effect of gap size on the success of Douglas-fir regeneration Objectives

Development of a plan for comparing long-rotation even-aged management with uneven-aged management approaches Leave open the opportunity to examine the relative successes of even-aged and uneven-aged approaches at developing mid- to late-successional forest structure Objectives

The development of a foundation for an adaptive management strategy should the College decide to pursue a Habitat Conservation Plan for a pair of spotted owls that are nesting in the South Zone of the forest The development and maintenance of high levels of nesting, roosting, and foraging habitat for the owls Development of a strategy to provide adequate habitat for northern spotted owls Objectives

Generation of revenue to support the College of Forestry A portion of the operating expenses of the College of Forestry comes from revenue generated by the Research Forest The implementation of the research experiment will result in a positive net revenue The overall forest plan for the South Zone should produce a minimum net present value Objectives

Spatial Elements of the Landscape McDonald-Dunn forest, South Zone

Spatial Elements of the Landscape Parts Patches Blocks Owl Circle Forest Zone

Spatial Elements of the Landscape Forest Zone Owl Circle

Spatial Elements of the Landscape Blocks

Spatial Elements of the Landscape Parts Patches

Objectives of the Harvest Scheduling Approach Given the complicated spatial requirements of the experiment, schedule management activities so that we maintain or increase nesting, roosting, and foraging habitat and maximize net present value Develop a managed forest with many of the structural elements found in a mid- to late-successional forests Maintain a Douglas-fir dominated forest Install a replicated experiment Maintain at least 40% of the forest in nesting, roosting, and foraging habitat Maximize net present value of the plan Provide databases and tools to support implementation of the plan

Problem Formulation Objective function(s): 1) maximize net present value 2) maximize nesting, roosting, and foraging habitat for spotted owls OR

Problem Formulation Constraint #1: Minimum volume per time period Constraint #2: Maximum volume per time period

Problem Formulation Constraint #3: Minimum net present value Constraint #4: Minimum harvest age

Problem Formulation Constraint #5: Minimum amount of nesting, roosting, foraging habitat Constraint #6: Minimum net revenue per experimental block, per entry

Problem Formulation Constraint #7: Clearcut re-entry period within a block is 30 years Constraint #8: Thinning re-entry period within a block is 15 years *

Problem Formulation Constraint #9: Timing of treatments within a block must be synchronized

Problem Formulation Constraint #10: Green-up (adjacency) constraints

Problem Formulation Constraint #11: Only 20% of patches in a block can be clearcut in a time period

Solution Method Threshold Accepting Monte Carlo neighborhood search Similar to Simulated Annealing, Initially described by Dueck and Scheuer (1990) Yet accepts every new proposed solution that is not much worse than the previous solution Solutions are as good as SA solutions [ Journal of Computational Physics 90: ]

Change Threshold Stop and report best solution No Yes Randomly choose unit and period to harvest, and check constraints Calculate ΔE (value of proposed new solution - current solution) ΔE > ( - current threshold) ? Current solution = Proposed new solution “Long time” no increase in best solution? Reached stopping criteria? Threshold Accepting

Interface to define the problem objectives and goals Software

User-defined prices and costs User-defined timing of treatments, harvest ages, green-up, etc. Software

Results Clearcut harvest patterns Maintain 40% NRFMaintain 45% NRF

Results Clearcut volume (thousand board feet) 40% 45%

Results Thinning volume (thousand board feet)

Results Nesting, roosting, foraging habitat Maintain 40% NRFMaintain 45% NRF 20 yrs 100 yrs

Results Net present value Maintain 40% NRF $12,900,000 Maintain 45% NRF $11,385,000 $ 1,515,000Difference: