1. Wan-Yu Liu Aletheia University New Taipei City, Taiwan 1 A Cultural Algorithm for Spatial Forest Resource Planning Chun-Cheng Lin National Chiao Tung University Hsinchu, Taiwan

2. 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 on adjacent 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 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 3 1 2 6 4 5 6 7 8 9 10 11 12 13 2- dementional plane 1 2 8 adjacency relation age harvested age 13 polygons

4. 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 period to 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

5. 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] 5

6. 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  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

7. 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. 7 beliefs population variation acceptance influence adjust selection performance function two spaces of a cultural algorithm

8. population space belief space normative matrix leader selection performance function crossover, repairing, exploration (interchange, sequencing, simple mutation), balancing accept the best individual accept those individuals with fitness > ave. fitness normative influence Our CA approach 8 situational influence

9. Population space  A number of individuals (candidate solutions)  13 forestland polygons  3 partitions + 1 residual 9 1 2 6 4 5 6 7 8 9 10 11 12 13 Partition 2Partition 3Partition 1Residual x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 x7x7 x8x8 x9x9 x 10 x 11 x 12 x 13 belief space normative matrixleader selection performance function crossover, repairing, exploration (interchange, sequencing, simple mutation), balancing accept the best individual accept those individuals with fitness > ave. fitness normative influence situational influence population space as even as possible violated polygons Harvested at the 1st period fitness = total harvested volume

10. 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 possible 10 belief space normative matrixleader selection performance function crossover, repairing, exploration (interchange, sequencing, simple mutation), balancing accept the best individual accept those individuals with fitness > ave. fitness normative influence situational influence population space Partition i x1x1 x 10 x3x3 x9x9 x3x3 x7x7 x4x4 x 12 crossover repairing Residual x5x5 violate the adjacency constraint

11. 3 Exploration Operators on Population Space 11 xkxk 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 iPartition j move a gene to another partition xjxj xjxj Partition j

12. Acceptance Criteria 12

13. Update of the Belief Space 13 belief space normative matrixleader selection performance function crossover, repairing, exploration (interchange, sequencing, simple mutation), balancing accept the best individual accept those individuals with fitness > ave. fitness normative influence situational influence population space

14. Situational Influence 14 xjxj Partition i xjxj leader the concerned individual move gene x j to partition i belief space normative matrixleader selection performance function crossover, repairing, exploration (interchange, sequencing, simple mutation), balancing accept the best individual accept those individuals with fitness > ave. fitness normative influence situational influence population space

15. Normative influence 15 belief space normative matrixleader selection performance function crossover, repairing, exploration (interchange, sequencing, simple mutation), balancing accept the best individual accept those individuals with fitness > ave. fitness normative influence situational influence population space gigi Partition i gigi Belief #1 Belief #2 Partition i Belief #3 frequency f(g i ) = 2

16. Experimental Data 16

17. Experimental Results 17

18. Conclusion  This paper develops a cultural algorithm (CA) for a spatial forest resource planning problem under three constraints  Simulation shows that our proposed CA performs better than the previous simulated annealing (SA) approach.  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. 18

19. Thank you for your attention! 19