Nature-Inspired Optimization
FOREST PLANNING USING
PSO WITH A PRIORITY
REPRESENTATION
P.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
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

Nature-Inspired Optimization
Forest Planning
For this problem, the target is 34,467 mbf
𝑛
2
 Minimize∶
𝐻
−
𝑇
𝑖=1
𝑖
 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
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

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

𝑽𝒊 𝒕 = 𝜶𝑽𝒊 𝒕 − 𝟏 + 𝒄𝟏(𝑷𝒊 − 𝑿𝒊 𝒕 − 𝟏) + 𝒄𝟐(𝑷𝒈 − 𝑿𝒊 𝒕 − 𝟏 )

𝑿𝒊 𝒕 = 𝑿𝒊 𝒕 − 𝟏 + 𝑽𝒊(𝒕)

𝑽𝒎𝒂𝒙 = 𝑪𝟏 + 𝑪𝟐

𝑽𝒎𝒊𝒏 = 𝟎 − (𝑪𝟏 + 𝑪𝟐)




𝑽𝒊: velocity element, 𝑿𝒊 : location element, 𝛼: inertia constant, 𝒄𝟏 / 𝒄𝟐 :
random numbers, 𝑷𝒊 : particle best, 𝑷𝒈 : global best, 𝒕 : time step
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)

𝑿𝒏 : is the priority of cutting stand fl( ) in period (𝑛 mod 3)






𝑛
3
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
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

Nature-Inspired Optimization
PSO – Experiment Setup
𝑪𝟏 = 2
 𝑪𝟐 = 2
 𝑽𝒎𝒂𝒙 = 4
 𝑽𝒎𝒊𝒏 = -4
 Inertia = 1.0 and 0.8
 Popsize = 100, 500, and 1000
 Trials = 5

Nature-Inspired Optimization
Results (smaller error is better)
NIO:
GA
DPSO
RO
EO
Harvest
6.5M
35M
5,500,391
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
500
5,500,330
0.8
1000
7M
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

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

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
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
