1. Nature-Inspired Optimization Forest Planning Using PSO with a priority representation P.W. Brooksand W.D. Potter Institute for Artificial Intelligence, University of Georgia, USA

2. Nature-Inspired Optimization Overview • Background: (NIO Project1) • PSO -- GA -- EO -- RO • Diagnosis – Configuration -- Planning – Route Finding • Forest Planning (aka Harvest Scheduling) • 73-Stand Daniel Pickett Forest • Particle Swarm Optimization • Priority Representation • Results • 1W.D. Potter, E. Drucker, P. Bettinger, F. Maier, D. Luper, M. Martin, M. Watkinson, G. Handy, and C. Hayes, “Diagnosis, Configuration, Planning, and Pathfinding: Experiments in Nature-Inspired Optimization”, in Natural Intelligence for Scheduling, Planning and Packing Problems, edited by Raymond Chiong, Springer-Verlag, Studies in Computational Intelligence (SCI), 2009.

3. Nature-Inspired Optimization Forest Planning Daniel Pickett Forest – 73 stands with access roads, ponds, and streams

4. Nature-Inspired Optimization Forest Planning • Even-flow harvest • Cutting occurs in one of three time periods • Each time period is 10 years in duration • A stand is only cut at most once • A plan may include un-cut stands • Adjacent cuts not allowed (same period) • Goal: achieve target harvest each period • Fitness: minimize plan error

5. Nature-Inspired Optimization Forest Planning • For this problem, the target is 34,467 mbf • Minimize • i is the harvest period • n is the number of harvest periods (i.e., 3) • Hi is the total harvest in period i • T is the target harvest • Representation: 73 integer array of periods

6. Nature-Inspired Optimization Particle Swarm Optimization (PSO) • Models behavior of large groups of animals such as flocks of birds • Individuals’ movement through search space is guided by • Population momentum • Individual velocity • Best local and global individual • Random influences • Continuous and discrete problem representations possible • A good general purpose algorithm

7. Nature-Inspired Optimization Particle Swarm Optimization (PSO) • Swarm of particles (potential solutions) • “Fly” through the search space • Local and Global knowledge influences search • Each particle has location & velocity • : velocity element, : location element, : inertia constant, /: random numbers, : particle best, : global best, : time step

8. Nature-Inspired Optimization PSO – Priority Representation • Particle is a set of priorities for assembling a plan • Use a 219-element array of priorities (73 stands x 3 periods) • : is the priority of cutting stand fl() in period • Stands range from 0 to 72, periods range from 0 to 2 • Sort particle elements (sort by priority) • Then assign stands to be cut in the highest priority period • Conflicts (assigned or adjacent) are skipped • Stands not assigned to any period are not cut

9. Nature-Inspired Optimization PSO – Priority Representation • Built-in constraint violation avoidance, but • Increased search space size (219 vs 73) • Real-valued priorities vs limited integer values • Longer processing time to generate a plan

10. Nature-Inspired Optimization PSO – Experiment Setup • = 2 • = 2 • = 4 • = -4 • Inertia = 1.0 and 0.8 • Popsize = 100, 500, and 1000 • Trials = 5

11. Nature-Inspired Optimization Results (smaller error is better)

12. Nature-Inspired Optimization Conclusion • The priority representation is an effective way to encode harvest schedules for PSO • Ordering of plan elements by priority allows a PSO to deal with some constrained problems without requiring repairs or penalties • Minimal impact occurs to PSO structure • Minimal domain knowledge is required in order to apply the priority representation

13. Nature-Inspired Optimization Questions?

14. Nature-Inspired Optimization Thank You!

15. Nature-Inspired Optimization Genetic Algorithm (GA) • Models Evolution by Natural Selection • Individuals (mates) are potential solutions • Driving force is selection pressure (mate selection) • Individuals mate to produce offspring (crossover) • Mutation of offspring increases genetic variation • Fitness function ranks individual fitness • Many variations are possible • Very powerful general purpose algorithm • Can be overly complicated to design

16. Nature-Inspired Optimization Extremal Optimization (EO) • Models tendency of systems to organize into non-equilibrium states • Based on the Bak-Sneppen Model • A single solution is evolved by changing the solution’s components • Each component must also be assigned a fitness • The worst component is randomly replaced • Useful for set covering and optimization problems • Component fitness may be difficult to calculate

17. Nature-Inspired Optimization Raindrop Method • Mimics the effect of falling rain • A random position on the search landscape is chosen (rain drop) • The chosen position’s value is randomly changed and all other positions are updated (water ripple) • Updates may cause invalid states, so repair is necessary • Recently developed algorithm • Useful for certain map coloring problems