marxan strategic conservation planning by falk huettmann
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MARXANStrategic Conservation Planning
by Falk Huettmann
Decision-Support & Analysis Systems (in Space and Time)
How to manageWhere to managerWhen to manageWhat 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 existingArea Network locations
Species #Inside Outside
SolutionsA B
Or,No Best Solutionpossible…
A typical Marxan application c): Optimization
Planning Units PLUs
Optimized for(in time):~x layers1000s PLUsSpatial arrangementsWeighting factorsSeveral solutionsMany scenarios
e.g. based on simulated annealing algorithm
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
Start
EndLocation A
Location B
Location C
Location D
Order of visitA,C,B,DB,A,C,DC,A,B,D… ?…Change of plans……What If…
(Spatial) Optimization Example: Traveling Salesman Problem
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
A typical/traditional MPA application without MARXAN e): =>Scoring
NumberNumber MPA GoalMPA Goal ScoreScore
11 BiodiversiBiodiversityty
11 HighHigh
22 EconomyEconomy 22 MediuMediumm
33 HumansHumans 33 LowLow
44 FishFish 11 HighesHighestt
55 HabitatsHabitats 22 MediumMedium
…… …… ……
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…10s or 1000s of stakeholders, spatial & dynamic goals…
How Marxan works:
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
http://en.wikipedia.org/wiki/Marxan
How Marxan works:
Target Penalty Name of LayerPLUs101 1000 Deep sea areas102 5000 Albatross colonies 200 60 Fish habitat302 100 Plankton diversity
=> find Optimum
=> show the best solution in GIS
How a Marxan solution can look like
Scenario:10% Ecological
Servicesmaintained 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 coolsInto crystals(Mathematical description of this process) Hot
Cold
Optimization: Simulated Annealing
What is it ?
Annealing:e.g. a hot liquidthat cools intocrystals, startingat a random location
http://en.wikipedia.org/wiki/Simulated_annealing
Optimization: Simulated Annealing
What is it ?
Annealing:e.g. a hot liquidthat cools intocrystals, startingat a random location
Optimization: Simulated Annealing
What is it ?
Simulated Annealing:a mathematical processthat “mimics” hot liquidthat 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 processthat “mimics” hot liquidthat 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 processthat “mimics” hot liquidthat 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 whilesearching 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/SIqveI8_1bI/AAAAAAAAAKs/LU6WJzOFo-M/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 andMicroeconomics
Source: WIKI
Finding the Optimum
True optimum of the data (=best solution)Previous, local, optimum
Optimum foundwithin the Search Window
Finding the Optimum
True optimum of the data (=best solution)Previous, local, optimum
Size of theSearch 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 otherconstraints (which can be thousands) into account=> Often only an approximation
Measured how ? What units ? Derived how ?
per 1 x unit
? y unitsMarginal Gain/Cost…
=>Maximized Marginal Gain/Costs
Cost Function, minimize “costs”
=creates an obvious bias… (~unrealistic)