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Hugh Possingham, Ian Ball, and Sandy Andelman
tools for dealing with those complexities. To integrate all these issues in one
problem, let alone solve that problem, is difficult. In practice, the best approach
will be to build and solve specific problems for specific organizations and localities. For example, when we have some notion of the particular objectives and
financial dynamics of an agency or organization, we might attempt to build a
dynamic decision support tool. The most common type of problem will be to
determine, when an organisation has some existing capital and a variety of sites
are available for purchase, which, if any, should be acquired at any given point in
time. The problem-solving tool should be tailored to the problem at hand.
Discussion
In this chapter, we have considered the problem of reserve design from the
simplest possible formulation—the minimum set, presence-absence problem—to
more complex formulations, including explicit spatial constraints. There are many
variations and complexities that we have not discussed. For example, in all cases
we set biodiversity as a constraint and tried to minimize economic and other costs.
An alternative is to set an economic constraint. In this case, if there is fixed capital
available for reserve acquisition, or reserves can cover no more than a fixed
proportion of the region, the problem is to maximize long-term biodiversity
benefits. This problem has rarely been considered.
Regardless of how the problem is formulated or the type of algorithm used,
there are additional considerations. In practice, solving the reserve network design
problem requires more than just finding the very best solution. Flexibility to
explore alternative solutions is one important criterion, because optimality may
not be achievable, or its importance may diminish in practical problems (Cocklin
1989a; Andelman et al., 2000). Generally, conservation planners need to be able
to evaluate a range of reasonably good solutions (i.e., from an ecological perspective), in the context of other considerations, such as economics or political expediency. Speed of execution also is important, because it facilitates a much greater
level of interaction between the planner and the potential solution space. Solutions
can be examined and additional constraints added (e.g., the forced inclusion or
exclusion of some sites) before running the algorithm again. This can give planners and decision makers a range of good solutions to use in a broader decisionmaking or negotiation context (Cocklin 1989b; Pressey et al. 1996).
With respect to these criteria, the simple methods are useful. They are quick,
which makes it relatively easy for the user to change either the data set (as new
information becomes available, or to account for uncertainty) or the selection
criteria (to reflect different levels of risk tolerance, or different political or economic considerations), and then quickly reapply the method. For better answers,
simulated annealing is an appropriate method. Its use of an objective function with
penalties instead of constraints offers both flexibility and efficiency, although we
need to know more about how robust it is to variation in types of data or uncertainty. Integer Linear Programming methods, or optimization methods that work
Hugh Possingham, Ian Ball, and Sandy Andelman
tools for dealing with those complexities. To integrate all these issues in one
problem, let alone solve that problem, is difficult. In practice, the best approach
will be to build and solve specific problems for specific organizations and localities. For example, when we have some notion of the particular objectives and
financial dynamics of an agency or organization, we might attempt to build a
dynamic decision support tool. The most common type of problem will be to
determine, when an organisation has some existing capital and a variety of sites
are available for purchase, which, if any, should be acquired at any given point in
time. The problem-solving tool should be tailored to the problem at hand.
Discussion
In this chapter, we have considered the problem of reserve design from the
simplest possible formulation—the minimum set, presence-absence problem—to
more complex formulations, including explicit spatial constraints. There are many
variations and complexities that we have not discussed. For example, in all cases
we set biodiversity as a constraint and tried to minimize economic and other costs.
An alternative is to set an economic constraint. In this case, if there is fixed capital
available for reserve acquisition, or reserves can cover no more than a fixed
proportion of the region, the problem is to maximize long-term biodiversity
benefits. This problem has rarely been considered.
Regardless of how the problem is formulated or the type of algorithm used,
there are additional considerations. In practice, solving the reserve network design
problem requires more than just finding the very best solution. Flexibility to
explore alternative solutions is one important criterion, because optimality may
not be achievable, or its importance may diminish in practical problems (Cocklin
1989a; Andelman et al., 2000). Generally, conservation planners need to be able
to evaluate a range of reasonably good solutions (i.e., from an ecological perspective), in the context of other considerations, such as economics or political expediency. Speed of execution also is important, because it facilitates a much greater
level of interaction between the planner and the potential solution space. Solutions
can be examined and additional constraints added (e.g., the forced inclusion or
exclusion of some sites) before running the algorithm again. This can give planners and decision makers a range of good solutions to use in a broader decisionmaking or negotiation context (Cocklin 1989b; Pressey et al. 1996).
With respect to these criteria, the simple methods are useful. They are quick,
which makes it relatively easy for the user to change either the data set (as new
information becomes available, or to account for uncertainty) or the selection
criteria (to reflect different levels of risk tolerance, or different political or economic considerations), and then quickly reapply the method. For better answers,
simulated annealing is an appropriate method. Its use of an objective function with
penalties instead of constraints offers both flexibility and efficiency, although we
need to know more about how robust it is to variation in types of data or uncertainty. Integer Linear Programming methods, or optimization methods that work