FORS 8450 • Advanced Forest Planning

Lecture 12

Tabu Search

Change in the Value of a Medium-Sized Forest when Considering Spatial Harvest Scheduling Constraints

Pete BettingerWise Batten, Jr.

Motivation for the Study

A relatively rare spatial / temporal combination of resources

1. University of Georgia graduate course "Advanced Forest Planning"

2. HATT: Heuristic Algorithm Teaching Tool

3. Motivated student

4. Curiosity about impacts of potential green-up and adjacency restrictions

Conifer plantations

Roads

Streams

Spatial Distribution of Pine Stands

Methods

Methods

Age Class Distribution

Methods

Growth and Yield Projections

10 management regimes (prescriptions) were developed for each stand.

SiMS 2003 (ForesTech International 2003) was used to model the prescriptions, providing NPV, harvest timing (thinning and clearcut), and potential revenues.

Logical management prescriptions were devised for each of the stands, given the goals of the landowner (a preference for thinnings and medium-length rotations).

The number of thinnings ranged from 0-2.

Stumpage prices, taxes, and costs for silvicultural activities (e.g., site preparation and planting) were derived from current local knowledge.

Methods

Forest Planning Problem

Time horizon: 40 yearsTime periods: 1 year

Objective:

Maximize the net present value of future activities on the forest.

Constraints:

(1) A maximum clearcut area per period.

(2) Adjacency restrictions for clearcuts (URM and ARM). Green-up periods assessed: 2-7 years

Methods

Forest Planning Problem

Types of spatial problems examined:

Unit restriction model (URM):

Green-up periods from 2-7 years

Area restriction model (ARM)

Green-up periods from 2-7 yearsMaximum clearcut sizes: 60, 120, 240 acres

Random feasiblesolution

Develop 1-optneighborhood

Select candidatemove

Updatesolution

Tabu ?

1-optiterationscomplete?

Bestsolution

?

Develop 2-optneighborhood

Select candidatemove

Updatesolution

Tabu ?

2-optiterationscomplete?

Doanotherloop?

Report bestsolution

Bestsolution

?

Yes Yes

YesYes

Yes

Yes

No No

NoNo

No No

Yes No

Methods

Tabu Search

1-opt moves

2-opt moves

Methods

Tabu Search Parameters

Aspiration criteria used.

Tabu state for 1-opt moves applied to Stand / Prescription choices.Tabu state for 1-opt moves: 550 iterations (assessed 50-650).

Tabu state for 2-opt moves applied to Stand / Stand swaps.Tabu state for 2-opt moves: 50 iterations (assessed 25-150).

50 independent runs of the heuristic were obtained for each type ofspatial planning problem assessed.

Methods

Linear Programming (LP) Solution

A relaxed version of the problem was solved using linear programming.

"Relaxed" = none of the spatial constraints are acknowledged.

One could view these results as the "upper bound" on any solution thatcould be generated with the spatial constraints.

Methods

Integer Programming (IP) Solutions

Three of the spatial problems using the Unit Restriction Model ofadjacency were solved using Integer programming.

One could view these results as the "optimal" solutions to those scenariosthat are assessed with the heuristic, since each will include the spatial constraints.

A direct comparison of the IP and heuristic results helps us understandhow well the heuristic performs for these types of problems.

Results

Unit Restriction Model

Change in NPV, as compared to "relaxed" LP solution:

Green-up Change in NPV(years)

234567

(%)

- 0.6- 1.0- 3.3- 7.6

- 13.3- 15.2

• $12 / acre to $283 / acre

Results

Area Restriction Model (240 acre maximum clearcut size)

Change in NPV, as compared to "relaxed" LP solution:

Green-up Change in NPV(years)

234567

(%)

- 0.1- 0.1- 0.1- 0.1- 0.1- 0.2

• $1.50 / acre to $3.50 / acre

Results

Area Restriction Model (120 acre maximum clearcut size)

Change in NPV, as compared to "relaxed" LP solution:

Green-up Change in NPV(years)

234567

(%)

- 0.1- 0.1- 0.2- 0.4- 0.4- 1.3

• $1.50 / acre to $24 per acre

Results

Area Restriction Model (60 acre maximum clearcut size)

Change in NPV, as compared to "relaxed" LP solution:

Green-up Change in NPV(years)

234567

(%)

- 0.1- 0.4- 1.0- 1.4- 2.5- 4.8

• $2 / acre to $90 per acre

Results

Performance

Computer: Pentium IV, 2.4 GHz CPU

URM solutions: 40 seconds each

ARM solutions: 1.5 to 2.0 minutes each

IP solution: 1 hour maximum

Results

Validation of the Heuristic Model

Solved the IP formulation of the URM model using LINDO 6.1.Pairwise adjacency constraints were used.

Constraints

1,1991,7832,333

Best solution,compared toIP solution

- 0.25 %- 0.10 %- 0.24 %

Average solution,

compared to IP solution

- 1.46 %- 2.68 %- 4.59 %

Percent ofsolutions within 1%

of IP solution

46266

Green-up period

2 years3 years4 years

Discussion

URM adjacency

Technically, the URM model should only be used when all of the standsare about the same size as the maximum clearcut area allowed.

Since they are not, the impacts are greater when using this model thanwhen using the ARM model.

Using this type of management model does not allow as much flexibilityin harvest design as when using the ARM model.

Discussion

Anticipatory Assessment of Impact

The notion that net present value declines as green-up periods increase, or as maximum allowable clearcut sizes decrease, is not new.

The level of impact is of interest, however, and should be assessedfor a variety of landowner size classes and ownership distributions.

Discussion

Drawbacks of the Heuristic

A number of runs of the heuristic may be necessary for one to feelconfident that they have developed a forest plan that could be close,in value, to the (perhaps unknown) global optimum solution.

Speed of processing is a function of the computer programming languageused and the potential speed of the computer's processor.

Conclusions

Impact of green-up period length

• A green-up period of 2-3 years did not seem to significantly affectthe NPV of the resulting forest plans.

• A longer green-up period (6-7 years) could reduce the NPV of the resulting forest plans 5-15%.

Impact of maximum clearcut size restrictions

• 240 acre maximum clearcut size does not affect NPV much at all.

• 60 acre maximum clearcut size may affect NPV more dramatically(up to 5%), depending on the green-up period assumed.

Conclusions

Value of using a heuristic over traditional integer programming

• Solutions can be generated for problems difficult or impossible to solvewith traditional integer programming.

• The heuristic method for assessing the impacts of green-up and adjacencyrestrictions worked very well - the best heuristic solution was within 0.25%(of net present value) of the integer programming solution.

Further Information

Study Results

Batten, W.H., Jr., P. Bettinger, and J. Zhu. 2005. The effects of spatial harvest scheduling constraints on the value of a medium-sized forest holding in the southeastern United States. Southern Journal of Applied Forestry. 29: 185-193.