FOREST PLANNING USING PSO WITH A PRIORITY REPRESENTATIONP.W. Brooks and W.D. Potter

Institute for Artificial Intelligence, University of Georgia, USA

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.

Nature-Inspired Optimization

Forest Planning

Daniel Pickett Forest – 73 stands with access roads,

ponds, and streams

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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

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

3 1 2 - - - - - - - 2

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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

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

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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

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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

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PSO – Experiment Setup

= 2 = 2 = 4 = -4 Inertia = 1.0 and 0.8 Popsize = 100, 500, and 1000 Trials = 5

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Results (smaller error is better)

NIO: GA DPSO RO EO

Harvest 6.5M 35M5,500,391

10M

inertia popsize PR best

1.0 100 7.3M

1.0 500 6.5M

1.0 1000 5.8M

0.8 100 8.5M

0.8 5005,500,330

0.8 1000 7M

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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

Nature-Inspired Optimization

Questions?Nature-Inspired Optimization

Thank You!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

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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

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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

Nature-Inspired Optimization