Download Spatial Forest Resource Planning Using a Cultural Algorithm IEEE

A Cultural Algorithm for
Spatial Forest Resource Planning
Wan-Yu Liu
Chun-Cheng Lin
Aletheia University
New Taipei City, Taiwan
National Chiao Tung University
Hsinchu, Taiwan
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Spatial Forest Resource Planning

Forests play many roles


Forest resource planning


Production + Protection + Recreation
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.
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Spatial Forest Resource Planning Problem
age
2dementional
plane
13
polygons
adjacency
relation

4
6
5
7
12
13
22
1
1
6
10
8
9
harvested age
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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
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Three Constraints

The minimum harvest age constraint


The even flow constraint


Harvest the polygons at age  a minimum age threshold
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.
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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]
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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
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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.
adjust
beliefs
acceptance
selection
influence
performance
function
population
variation
two spaces of a cultural algorithm
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Our CA approach
belief space
leader
accept the best
individual
situational
influence
normative matrix
accept those individuals
with fitness > ave. fitness
population space
selection
normative
influence
performance
function
crossover, repairing, exploration (interchange,
sequencing, simple mutation), balancing
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Population space
A number of individuals (candidate solutions)


13 forestland polygons  3 partitions + 1 residual
Partition 1
Partition 2
Partition 3
Residual
fitness
= total harvested volume
x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13
Harvested at
the 1st period
as even as possible
violated polygons
belief space
leader normative matrix
2
accept the best
individual
situational accept those individuals
influence with fitness > ave. fitness
normative
influence
1
population space
selection
performance
function
6
10
8
9
crossover, repairing, exploration (interchange,
sequencing, simple mutation), balancing
4
6
5
7
12
13
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Operators on the Population Space

Selection


Chosen for reproduction by the roulette-wheel selection
Crossover and repairing
Partition i
belief space
x7 x10 x3 x4
leader normative matrix
accept the best
individual
crossover
Partition i
situational accept those individuals
influence with fitness > ave. fitness
normative
influence
Residual
population space
x10 x3 x1 x9 x5
repairing
violate the adjacency
constraint

Balancing

x12
selection
performance
function
crossover, repairing, exploration (interchange,
sequencing, simple mutation), balancing
Make the volume harvested at each period as even as possible
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3 Exploration Operators on Population Space
Sequencing operator
Partition i
Partition j
swap the two partitions
Interchange operator
Partition i
Partition j
xk
xj
swap two genes respectively from
two different time partitions
Simple mutation operator
Partition i
Partition j
xj
move a gene to another partition
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Acceptance Criteria

Original individual  fitness = E1
New individual  fitness E2

Accepted if 𝐸2 ≥ 𝐸1

Otherwise, accepted with the following
probability:
𝑒
where

𝑓1 𝑁
𝐸2 −𝐸1
𝐸1
/𝑓2 (𝑁)
N is the iteration number;
𝜅𝑁
) 𝑁
𝑁𝑚𝑎𝑥
𝜅𝑁 2
+
) ;
𝑁𝑚𝑎𝑥
 𝑓1
𝑁 = (1 +
 𝑓2
𝑁 = (1
 𝑁𝑚𝑎𝑥
𝜅
;
is the maximum iteration number;
is the convergence control parameter.
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Update of the Belief Space
belief space
leader normative matrix
accept the best
individual
situational accept those individuals
influence with fitness > ave. fitness
population space
selection
normative
influence
performance
function
crossover, repairing, exploration (interchange,
sequencing, simple mutation), balancing
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Situational Influence
belief space
leader
accept the best
individual
normative matrix
situational accept those individuals
influence with fitness > ave. fitness
normative
influence
population space
performance
function
selection
crossover, repairing, exploration (interchange,
sequencing, simple mutation), balancing
Partition i
leader
xj
Partition i
the concerned
individual
xj
move gene xj to partition i
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Normative influence
belief space
leader
Partition i
normative matrix
gi
Belief #1
accept the best
individual
situational accept those individuals
influence with fitness > ave. fitness
normative
influence
Partition i
Belief #2
population space
Partition i
performance
function
selection
gi
Belief #3
crossover, repairing, exploration (interchange,
sequencing, simple mutation), balancing

frequency f(gi) = 2
Use the roulette-wheel rule
for 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 𝑓(𝑔𝑖 )/

If an individual selects gene gx,
the individual adds gene gx in partition x.
𝑚
𝑗=1 𝑓(𝑔𝑖 )
.
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Experimental Data

An artificial problem instance.

(a) A 20 × 20 grid graph.

(b) Randomly remove 20 vertices from (a).

(c) Randomly shrink 80 edges in (b).
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Experimental Results
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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.
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Thank you for
your attention!
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