Wan-Yu Liu

Aletheia University

New Taipei City, Taiwan

1

A Cultural Algorithm forSpatial Forest Resource

Planning

Chun-Cheng Lin

National Chiao Tung University

Hsinchu, Taiwan

Spatial Forest Resource Planning Forests play many roles

Production + Protection + Recreation

Forest resource planning Impact on water pollution, erosion,

landscape aesthetics, and biodiversity

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 onadjacent forest stands of harvest units.

2

3

Spatial Forest Resource Planning Problem

Plan a harvest schedule of the forestland Harvest forest polygons at different time periods

Maximize the total harvested volumeover the planning harvest schedule

Under three spatial constraints The minimum harvest age constraint

The minimum adjacency green-up age constraint

The even flow constraint

1

2

6

4

5

6

7

8

9

10

11

12

13

2-dementional

plane

1

2

8adjacency relation

age

harvested age

13 polygons

Three Constraints

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

The even flow constraint To balance the harvest volume of each period,

enforce the timber volume for each periodto be harvested as even as possible

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.

4

Related Works on this topic

A variety of approaches todifferent 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]

5

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 complicatedbut worse than the SA

approach

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

6

Cultural Algorithm (CA)

Cultural algorithm (CA)is a class of evolutionary programbased on some theories from sociology and archaeologythat try to formulate cultural evolution.

7

beliefs

population

variation

acceptance influence

adjust

selectionperformancefunction

two spaces of a cultural algorithm

population space

belief space

normative matrixleader

selection performancefunction

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

accept the bestindividual

accept those individualswith fitness > ave. fitness

normativeinfluence

Our CA approach

8

situationalinfluence

9

Population space

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

1

2

6

4

5

6

7

8

9

10

11

12

13

Partition 2 Partition 3Partition 1 Residual

x1 x2 x3 x4 x5x6 x7 x8 x9 x10 x11

x12 x13

belief space

normative matrixleader

selection performancefunction

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

accept the bestindividual

accept those individualswith fitness > ave. fitness

normativeinfluence

situationalinfluence

population space

as even as possible violated polygonsHarvested atthe 1st period

fitness= total harvested volume

Operators on the Population Space

Selection Chosen for reproduction by the roulette-wheel selection

Crossover and repairing

Balancing Make the volume harvested at each period as even as

possible10

belief space

normative matrixleader

selection performancefunction

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

accept the bestindividual

accept those individualswith fitness > ave. fitness

normativeinfluence

situationalinfluence

population space

Partition i

Partition i

x1x10 x3 x9

x3x7 x10 x4

x12

crossover

repairing

Residual

x5

violate the adjacencyconstraint

3 Exploration Operators on Population Space

11

xk

Partition i

Partition i

swap two genes respectively fromtwo 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

xj

xj

Partition j

Acceptance Criteria

Original individual fitness = E1

New individual fitness E2

Accepted if

Otherwise, accepted with the following probability:

where

N is the iteration number;

;

;

is the maximum iteration number;

is the convergence control parameter.

12

Update of the Belief Space

13

belief space

normative matrixleader

selection performancefunction

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

accept the bestindividual

accept those individualswith fitness > ave. fitness

normativeinfluence

situationalinfluence

population space

Situational Influence

14

xj

Partition i

xj

Partition i

leader

the concernedindividual

move gene xj to partition i

belief space

normative matrixleader

selection performancefunction

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

accept the bestindividual

accept those individualswith fitness > ave. fitness

normativeinfluence

situationalinfluence

population space

Normative influence

Use the roulette-wheel rulefor the mutation operator with normative influence. gi = the gene in partition i with the maximal frequency f(gi) for all the

individuals in the belief space.

The ratio of gi in the roulette wheel is .

If an individual selects gene gx,the individual adds gene gx in partition x.

15

belief space

normative matrixleader

selection performancefunction

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

accept the bestindividual

accept those individualswith fitness > ave. fitness

normativeinfluence

situationalinfluence

population space

gi

Partition i

gi

Partition i

Belief #1

Belief #2

Partition i

Belief #3

frequency f(gi) = 2

Experimental Data

An artificial problem instance. (a) A grid graph.

(b) Randomly remove 20 vertices from (a).

(c) Randomly shrink 80 edges in (b).

16

Experimental Results

17

18

Conclusion

This paper develops a cultural algorithm (CA)for a spatial forest resource planning problemunder three constraints

Simulation shows thatour proposed CAperforms better thanthe previous simulated annealing (SA) approach .

One of our most important contributions is thatour CA can be viewedan improved version of evolutionary programthat outperforms the previous SA approach.

19

Thank you for your attention!