MARXAN
Strategic Conservation Planning
by Falk Huettmann
Decision-Support & Analysis Systems (in Space and Time)
How to manage
Where to manager
When to manage
What to manage …
=> Million $ Decisions
Use of computers to suggest best possible solution(s),
=> Make everybody “happy” and safe/make $
A typical Marxan application a): Area Network Site
selection, e.g. MPA
A typical Marxan application b): Assessment of existing
Area Network locations
Solutions
A
B
Species #
Inside Outside
Or,
No Best Solution
possible…
A typical Marxan application c): Optimization
Planning Units PLUs
Optimized for
(in time):
~x layers
1000s PLUs
Spatial arrangements
Weighting factors
Several solutions
Many scenarios
e.g. based on simulated annealing algorithm
(Spatial) Optimization Example:
Traveling Salesman Problem
Location C
Location A
End
Start
Location D
Location B
Order of visit
A,C,B,D
B,A,C,D
C,A,B,D
…?
…Change of plans…
…What If…
Often, can only be resolved through simulations…(no single mathematical solution)
=> Optimum is assumed, plain wrong, or never reached even…
Even small improvements do count
A typical Marxan application d):
Best Professional Conservation Practice
Principles of Conservation Planning:
-Efficiency
-Spatial arrangement: compactness and/or connectedness
-Flexibility
-Complementarity
-Representativeness
-Selection Frequency versus “Irreplaceability”
-Adequacy
-Optimisation, decision theory and mathematical programming
e.g. 10% of the area,
high altitude,
low biomass
Number
MPA Goal
Score
1
Biodiversity
1
High
2
Economy
2
Medium
3
Humans
3
Low
4
Fish
1
Highest
5
Habitats
2
Medium
…
…
…
Instead:
Multivariate Optimization algorithms
(e.g. Simulated Annealing)
A typical/traditional MPA application without MARXAN e):
=>Scoring
…10s or 1000s of stakeholders, spatial & dynamic goals…
How Marxan works:
http://en.wikipedia.org/wiki/Marxan
1. The total cost of the reserve network (required)
2. The penalty for not adequately representing conservation features (required)
3. The total reserve boundary length, multiplied by a modifier (optional)
4. The penalty for exceeding a preset cost threshold (optional
=> feed with (spatial) Data
How Marxan works:
Target
PLUs
101
53
200
302
Penalty
1000
5000
60
100
Name of Layer
Deep sea areas
Albatross colonies
Fish habitat
Plankton diversity
=> find Optimum
=> show the best solution in GIS
How a Marxan solution can look like
Scenario:
10% Ecological
Services
maintained for
the Arctic
(Huettmann & Hazlett 2010)
MPA certified
Optimization Problems applied elsewhere:
-Operations Research
-Trading, e.g. Carbon
-Stockmarket
-Banking
-Storage
-Traveling Salesman Problem
-Political Decisions
-Life…
Optimization: Simulated Annealing
What is it ?
“Annealing”:
e.g. a hot liquid that cools
Into crystals
(Mathematical description
of this process)
Hot
Cold
Optimization: Simulated Annealing
What is it ?
Annealing:
e.g. a hot liquid
that cools into
crystals, starting
at a random location
http://en.wikipedia.org/wiki/Simulated_annealing
Optimization: Simulated Annealing
What is it ?
Annealing:
e.g. a hot liquid
that cools into
crystals, starting
at a random location
Optimization: Simulated Annealing
What is it ?
Simulated Annealing:
a mathematical process
that “mimics” hot liquid
that cools into crystals,
starting at a random location
Optimization: Simulated Annealing
Relevance of a Random Start
Optimum is build additively,
based on existing start and
new & surrounding data
Optimization: Simulated Annealing
Relevance of the Random Start location
Simulated Annealing:
a mathematical process
that “mimics” hot liquid
that cools into crystals,
starting at a random location
 A different sample at each run
=> A different optimum
=> A different solution
Optimization: Simulated Annealing
Cooling algorithm
Simulated Annealing:
a mathematical process
that “mimics” hot liquid
that cools into crystals,
starting at a random location
A different sample size at each step
=>A different (local) optimum
=>A different solution
Optimization: Simulated Annealing
Cooling speed
Determines the amount of detail while
searching for the optimum
A different sample size at each step
=>A different (local) optimum
=>A different solution
Optimization: Simulated Annealing
Why so good ?!
http://4.bp.blogspot.com/_Hyi86mcXHNw/S
IqveI8_1bI/AAAAAAAAAKs/LU6WJzOFoM/s400/Simulated+Annealing.png
Beyond Annealing:
Other algorithms & approaches
(MARXAN example)
-Scoring
-Iterative Improvement
-Greedy Heuristics
-Richness Heuristics
-Rarity Algorithms
-Irreplacability
Finding the Optimum: A Point
Optimum of “the data”
e.g. a hyperdimensional
cube/problem
Finding the Optimum: A Polygon/Area
e.g. a feasible solution
within 2 value ranges (x,y) and
3 linear constraints imposed
A concept widely used in
Operations Research and
Microeconomics
Source: WIKI
Finding the Optimum
Previous, local, optimum
Optimum found
within the
Search Window
True optimum of the data
(=best solution)
Finding the Optimum
Previous, local, optimum
True optimum of the data
(=best solution)
Size of the
Search Window
In TN & RF: Number of Trees settings…
Finding “the” Optimum: Always possible ?
True optimum of the data
(=best solution)
Finding the Optimum: Algorithms
Derivatives
Derivatives using bootstrapping or
jackknifing
(Neural Networks, CARTs)
Simulated Annealing
LP solver
What is Optimization ?
Finding the “best”/optimal solution, taken all other
constraints (which can be thousands) into account
=> Often only an approximation
Measured how ?
What units ?
Derived how ?
=creates an obvious bias…
(~unrealistic)
? y units
Marginal Gain/Cost…
=>Maximized Marginal Gain/Costs
per 1 x unit
Cost Function,
minimize “costs”