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3.0 The MARXAN AlgorithmOne of the more popular algorithms implemented in Marxan is the ‘simulated annealing’site optimization algorithm. In order to design an optimal reserve network, each planningunit is examined for the values it contains. The features within one planning unit may bevaluable alone but may not be the best choice overall—depending on the distribution andreplication of the other features in the wider planning area.During the simulated annealing procedure, an initial portfolio of planning units isselected. Planning units are then added and removed in an attempt to improve theefficiency of the portfolio. Early in the procedure, changes in the portfolio that do notimprove efficiency can be made in order to allow the possibility of finding a moreefficient overall portfolio. The requirement to accept only those changes that improveefficiency becomes stricter as the algorithm progresses through a set of iterations. Notethat for any set of conservation targets and goals, there may be many efficient andrepresentative portfolios that meet all conservation goals, but most of these networkswould have a number of planning units in common. Many runs of the algorithm are usedto find the most efficient portfolio and to calculate a measure of irreplaceability (usedhere to indicate the number of times a particular unit is chosen). In some cases,conservation targets are only found in limited sites – areas of high irreplaceability that arealways chosen in any representative portfolio. Additionally, areas of high irreplaceabilityalso include planning units, whose exclusion would require a proportionally largerconservation area network to achieve the same level of representation, resulting in a lossof portfolio efficiency.The algorithm attempts to minimize portfoliototal ‘cost’ whilst meeting conservation goalsin a spatially compact network of sites. Thisset of objectives constitutes the ‘objective costfunction’ and is made up of three user-defined‘costs’:Total Cost = ∑Unit Cost + ∑SpeciesPenalties + ∑Boundary Lengthwhere ‘Total Cost’ is the objective (to beminimized), ‘Unit Cost’ is a cost assigned toeach planning unit, ‘Species Penalties’ arecosts imposed for failing to meet biodiversitytarget goals, and ‘Boundary Length’ is a costdetermined by the total outer boundary lengthof the portfolio.Attempts are made to minimize the totalportfolio cost by selecting the fewest planningunits with the lowest total unit cost needed toTNC Protected Area Tools (PAT) Version 3.0The Nature Conservancy, August 200943