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

…… …… ……

Inst

ead

:M

ult

ivar

iate

Op

tim

izat

ion

alg

ori

thm

s(e

.g.

Sim

ula

ted

An

nea

lin

g)

…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)