1. MARXAN Strategic Conservation Planning by Falk Huettmann

2. 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 $

3. A typical Marxan application a): Area Network Site selection, e.g. MPA

4. A typical Marxan application b): Assessment of existing Area Network locations Species # Inside Outside Solutions A B Or, No Best Solution possible…

5. 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

6. 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 End Location A Location B Location C Location D Order of visit A,C,B,D B,A,C,D C,A,B,D … ? …Change of plans… …What If… (Spatial) Optimization Example: Traveling Salesman Problem

7. 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

8. A typical/traditional MPA application without MARXAN e): =>Scoring Number MPA Goal Score 1Biodiversity 1 High 2Economy 2 Medium 3Humans 3 Low 4Fish 1 Highest 5Habitats 2 Medium ……… Instead: Multivariate Optimization algorithms (e.g. Simulated Annealing) …10s or 1000s of stakeholders, spatial & dynamic goals…

9. 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

10. How Marxan works: Target Penalty Name of Layer PLUs 101 1000 Deep sea areas 53 5000 Albatross colonies 200 60 Fish habitat 302 100 Plankton diversity => find Optimum => show the best solution in GIS

11. How a Marxan solution can look like Scenario: 10% Ecological Services maintained for the Arctic (Huettmann & Hazlett 2010)

12. MPA certified

13. Optimization Problems applied elsewhere: -Operations Research -Trading, e.g. Carbon -Stockmarket -Banking -Storage -Traveling Salesman Problem -Political Decisions -Life…

14. Optimization: Simulated Annealing What is it ? “Annealing”: e.g. a hot liquid that cools Into crystals (Mathematical description of this process) Hot Cold

15. 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

16. Optimization: Simulated Annealing What is it ? Annealing: e.g. a hot liquid that cools into crystals, starting at a random location

17. Optimization: Simulated Annealing What is it ? Simulated Annealing: a mathematical process that “mimics” hot liquid that cools into crystals, starting at a random location

18. Optimization: Simulated Annealing Relevance of a Random Start Optimum is build additively, based on existing start and new & surrounding data

19. 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

20. 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

21. 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

22. Optimization: Simulated Annealing Why so good ?! http://4.bp.blogspot.com/_Hyi86mcXHNw/S IqveI8_1bI/AAAAAAAAAKs/LU6WJzOFo- M/s400/Simulated+Annealing.png

23. Beyond Annealing: Other algorithms & approaches (MARXAN example) -Scoring -Iterative Improvement -Greedy Heuristics -Richness Heuristics -Rarity Algorithms -Irreplacability

24. Finding the Optimum: A Point Optimum of “the data” e.g. a hyperdimensional cube/problem

25. 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

26. Finding the Optimum True optimum of the data (=best solution) Previous, local, optimum Optimum found within the Search Window

27. Finding the Optimum True optimum of the data (=best solution) Previous, local, optimum Size of the Search Window In TN & RF: Number of Trees settings…

28. Finding “the” Optimum: Always possible ? True optimum of the data (=best solution)

29. Finding the Optimum: Algorithms Derivatives Derivatives using bootstrapping or jackknifing (Neural Networks, CARTs) Simulated Annealing LP solver

30. 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 ? per 1 x unit ? y units Marginal Gain/Cost… =>Maximized Marginal Gain/Costs Cost Function, minimize “costs” =creates an obvious bias… (~unrealistic)