panel. In order to capture the variation, multiple simulations were conducted, with parameters sampled
from the estimated prior distributions. The size (in
km2) of each parcel was used as conservation cost.
Contiguous candidate patches were generated
from the parcels by a region growing process, which
picks a random parcel as seed, and then iteratively
grows the patch up to a random size. This growth
process was biased to avoid complex boundaries.
Using this procedure 10,000 candidate patches were
generated for selection. To evaluate the objective
function, 100 random samples were generated from
the Dynamic Bayesian network. To avoid overfitting,
two thirds of those were used for optimization (as
done, for example by Sheldon et al. (2010) for a similar problem), and the quality of the solutions were
evaluated against the remaining one third. As noted
by Sheldon et al. (2010), the advantage of this procedure is that preprocessing can be used to drastically
speed up computation and bounds on the generalization error can be obtained. Further, instead of
using the algorithm described by Sviridenko (2004)
for solving the nonadaptive problem, a faster algorithm of Leskovec et al. (2007) was used that also carries theoretical guarantees.
The experiments mainly aimed to investigate two
questions: ( 1) How much better do optimized solutions perform compared to simple baselines? ( 2) How
much can be gained from dynamic optimization?
First, experiments were conducted on the static
reserve design problem. The budget was varied from
0 to 60 km2, and the optimized reserves were compared with random selection, as well as selecting
patches according to decreasing area. Figure 4 (left)
presents the results. Note that the optimized selection drastically outperforms the baselines. Figure 3
(bottom right) shows a solution obtained for a budget of 10 km2.
Then, our near-optimal policy for dynamic conservation planning was evaluated. The set of all patches
was randomly partitioned into 10 different subsets.
In the experiment, the budget that is made available
in each round was varied from 0 to 60 km2. Each
round, patches were opportunistically selected, either
by optimization, in decreasing order of area, or at
random. All experiments were repeated, and results
averaged, over 10 random trials. In order to estimate
the benefit of dynamic selection, results were compared against another baseline, where a fixed reserve
(having access to all patches and the entire budget)
was optimized a priori (approximately), and then, for
this fixed solution, patches were picked in the first
round in which they became available.
The expected number of persistent species (after 50
years) was estimated after ten rounds of selection.
The dynamically optimized solution outperforms the
baselines. Even after all ten rounds (that is, after all
patches were made available) the sequential solution
outperforms the a priori solution. The reason is that
the static a priori optimization is not aware of the per
round budget constraints, and therefore may not be
able to select some patches as they become available.
0 10 20 30 40 50 60
Figure 4. Simulation Results on the Conservation Planning Case Study.
Left: Performance (in terms of number of different species persistent at the end of the planning horizon) in the static reserve design problem for different selection methods as a function of the budget. Right: Performance on the dynamic reserve design problem, as a function
of planning rounds. See Golovin et al. (2011) for details.