A Cultural Algorithm for�Spatial Forest Resource Planning

Wan-Yu Liu

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Aletheia University

New Taipei City, Taiwan

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Chun-Cheng Lin

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National Chiao Tung University

Hsinchu, Taiwan

Spatial Forest Resource Planning

• Forests play many roles
• Production + Protection + Recreation

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• Forest resource planning
• Impact on water pollution, erosion,�landscape aesthetics, and biodiversity

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• Spatial forest resource planning
• Clearcutting of one forestland�may expose neighboring forestland to wind damage, bark injuries, drainage problems, and site class deterioration.
• The spatial constraints on minimum adjacency green-up age are imposed upon harvesting activities on�adjacent forest stands of harvest units.

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Spatial Forest Resource Planning Problem

• Plan a harvest schedule of the forestland
• Harvest forest polygons at different time periods
• Maximize the total harvested volume�over the planning harvest schedule
• Under three spatial constraints
• The minimum harvest age constraint
• The minimum adjacency green-up age constraint
• The even flow constraint

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2-dementional plane

adjacency relation

age

harvested age

13 polygons

Three Constraints

• The minimum harvest age constraint
• Harvest the polygons at age ≥ a minimum age threshold

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• The even flow constraint
• To balance the harvest volume of each period,� enforce the timber volume for each period� to be harvested as even as possible

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• The minimum adjacency green-up age constraint
• The harvest should be dispersed�for wildlife reasons
• A forest polygon must be recovered �before an adjacent unit is harvested.

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Related Works on this topic

• A variety of approaches to�different spatial forest resource planning problems
• Multiple solution harvest scheduling [Van Deusen, 1999]
• A mixed-integer formulation of the minimum patch size problem�[McDill, 2003]
• Using dynamic programming and overlapping subproblems to address adjacency in large harvest scheduling problems.�[Hoganson, 1998]
• Harvest scheduling with adjacency constraints: A simulated annealing approach. [Lockwood,1993]
• Analyzing cliques for imposing adjacency restrictions in forest models (tabu search) [A. Murray, 1999]
• Optimisation algorithms for spatially constrained forest planning (evolutionary program) [G. Liu, 2006]

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Evolutionary Computation for Spatial Forest Planning

• [Liu et al., 2006]
• Propose two approaches
• The evolutionary program (EP) approach
• The simulated annealing (SA) approach
• The EP approach is complicated� but worse than the SA approach

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• Objective of our work
• Propose a cultural algorithm (CA) approach,�which is a type of EP
• Our CA' performance is better than the previous SA approach

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Cultural Algorithm (CA)

• Cultural algorithm (CA)�is a class of evolutionary program�based on some theories from sociology and archaeology�that try to formulate cultural evolution.

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beliefs

population

variation

acceptance

influence

adjust

selection

performance

function

two spaces of a cultural algorithm

Our CA approach

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population space

selection

performance

function

crossover, repairing, exploration (interchange, sequencing, simple mutation), balancing

Population space

• A number of individuals (candidate solutions)
• 13 forestland polygons 🡪 3 partitions + 1 residual

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Partition 2

Partition 3

Partition 1

Residual

x₁

x₂

x₃

x₄

x₅

x₆

x₇

x₈

x₉

x₁₀

x₁₁

x₁₂

x₁₃

as even as possible

violated polygons

Harvested at

the 1st period

fitness

= total harvested volume

Operators on the Population Space

• Selection
• Chosen for reproduction by the roulette-wheel selection
• Crossover and repairing

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• Balancing
• Make the volume harvested at each period as even as possible

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Partition i

Partition i

x₃

x₇

x₁₀

x₄

x₁₂

Residual

x₅

3 Exploration Operators on Population Space

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x_k

Partition i

Partition i

swap two genes respectively from�two different time partitions

Partition j

swap the two partitions

Sequencing operator

Interchange operator

Simple mutation operator

Partition i

Partition j

move a gene to another partition

x_j

x_j

Partition j

Acceptance Criteria

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Update of the Belief Space

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Situational Influence

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x_j

Partition i

x_j

Partition i

leader

the concerned

individual

move gene x_j to partition i

Normative influence

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g_i

Partition i

g_i

Partition i

Belief #1

Belief #2

Partition i

Belief #3

frequency f(g_i) = 2

Experimental Data

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Experimental Results

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Conclusion

• This paper develops a cultural algorithm (CA)�for a spatial forest resource planning problem�under three constraints

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• Simulation shows that�our proposed CA�performs better than�the previous simulated annealing (SA) approach .

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• One of our most important contributions is that�our CA can be viewed�an improved version of evolutionary program�that outperforms the previous SA approach.

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Thank you for your attention!

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