ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001
One of the significant improvements of the new proposed
redistricting algorithm is the availability of the parameter to show
the attitude to risk, a and level of confidence, X of the district
planner. These parameters act as observation parameter, which
aim to analyze the decision-making behavior of the decision
makers. Therefore, we have defined the decision makers based
on their attitude to risk into three different groups that are the
optimistic, moderate or pessimistic decision makers.
3.4 Optimization by Dynamic Programming
The redistricting problems are treated as similar to the knapsack
problem, which is maximization or minimization of a value. For
example, a thief robbing a safe finds it filled with N items of
various size and value but bag has only limited capacity (M). In
contrast, getting compact district plan means to calculate the
best combination of individual district for all district size up to
total district plan size. In other words, the district plan is a plan
that consists of many districts with different shape. Therefore,
the adopted implementation method in this research is Dynamic
Programming(DP) which is commonly used to solve the
knapsack problem. The method is chosen based on two main
reasons. First, DP takes time as the horizon and calculates the
least cost path in the interval. It is similar to the redistricting
process which ask for optimal compact district, so DP can build
a good model in a bottom-up technique to solve redistricting
problems. It allows for the breaking up of all problems into a
sequence of easier subproblems which are then evaluated by
stages and has the power to determine the optimal solution by
solving each of these stages optimality [11]. Second,
redistricting decisions is usually accompanied with many
complicated considerations, so these might be numerical
constraints or some constraints which were the experience of
the experts. These constraints are difficult to solve by nonlinear
programming or other methods but can be easily incorporated
and solved by the DP method. In addition, when integrate with
FMCDM, these constraints can even be systematically analyzed
and solved.
4. RESULTS AND ANALYSIS
The evaluation of the developed shape based redistricting
algorithm using forest blocking application as an prototype
focuses on the applications and limitations of incorporating an
enhanced compactness index based on multiple compactness
measurement into redistricting technique by using fuzzy multiple
criteria decision making. Overall performance of the developed
shape based redistricting algorithm is evaluated using statistical
tests. The statistical tests were applied on different conditions in
order to find out the performance of the developed shape based
redistricting algorithm under different circumstances. These tests
used for evaluation are referring to existing standard use to
define a district plan. For example, a plan’s compactness is
defined as the mean compactness of its districts used in Iowa
and in Michigan in United State for political redistricting [2].
Besides, other research mentioned that its least compact district
determines the compactness of a plan. Consequently, in this
study, statistical test that include Mean, Mean Deviation,
Maximum, Minimum and their Difference of compactness
indices for its districts is used to determine the compactness
evaluation of a district Plan.
There were three main areas of evaluations and tests was
carried out on the redistricting algorithm: (a) performance
evaluation and comparison on district plan produced with and
without the enhanced redistricting algorithm, (b) result and
analysis on the advance FMCDM component, (c) result and
analysis with respect the different input variable like interval to
calculate slope and also the restricted boundaries such as river
and license boundary using prototype. From the evaluation
process shown that the proposed method has the ability to
consider multiple criteria to ensure the compactness is within
optimality in producing district plan. Although there is a
necessary to have a precise understand on the shape optimal
rule or the linguistic terms’ definition of the most compact
district, the scheme able to produce a Enhanced Compactness
Index in order to represent the performance of the district within
the district plan. Besides, it is definitely going to give adequate
reflection of the district planner toward risk and their confidence
in their subjectivity assessment. In conclusion, the enhanced
redistricting algorithm really shows ability to shape based
redistricting scheme is going to give better performance to draw
or redraw district plan with optimal compactness.
The applicability of the methods is proven effective. An
Integrated Compactness Index had been successfully calculated
and incorporated into redistricting technique that discussed. This
compactness assessment index is more descriptive and able to
incorporate with natural feelings of district planners. Natural
feelings here may include their confidence and their attitude to
risk. The shape compactness information has been modeled
flexibly by utilizing the Fuzzy Multiple Criteria Decision Making
approach like Fuzzy AHP. The Fuzzy AHP approach allows the
integration of both Application Dependent and Application
Independent factors to be considered in the redistricting
application. The consideration of Application Dependent criteria
is compulsory whereby the consideration of Application
Independent criteria here is the more unique factors to ensure
the optimality of shape compactness. Besides, the integrated
shape-based redistricting technique is able to cope with
fuzziness in the compactness assessment index. The triangular
fuzzy number used to define the decision matrix and weight
matrix able to help to define the fuzziness of optimality of the
compactness.
The integration of multiple compactness measurement methods
in enhanced redistricting algorithm able to gather the strengths
of particular method and at the same time to reduce or minimize
the weaknesses or lacks of other method. Manipulating the
weight matrix that represents the importance of a particular
measurement accomplishes it. Then, these weight vectors will
then contribute to the enhanced compactness index, which will
incorporate into the redistricting process. A prototype is built
based on the conceptual design of the redistricting algorithm.
The prototype demonstrated the application of redistricting
algorithm developed. It also allowed the testing and evaluation
to be implemented. The prototype managed to demonstrate the
concept of the integration and the incorporation in the
redistricting algorithm. Later, overall performance of the
developed redistricting algorithm is evaluated using statistics
tests. The statistics tests are applied on different condition in
order to find out the performance of the developed shape based
redistricting algorithm under different circumstances. The
approach developed clearly has its advantages. These
advantages include (a) better modeling of the uncertainty and
imprecision associated with the fuzzy triangular number, (b)
Cognitively less demanding on the district planner, and (c)
adequate reflection of the district planner’s attitude towards risk
and their degrees of confidence in their subjective assessment.
Real experience in applying the approach in selecting the most
appropriate district plan in the prototype has reinforced these
findings. The incorporation of shape information sources has
enhanced the redistricting techniques by utilizing more sources
of information. As a result, the redistricting technique no longer
based on the application dependent information only. The
incorporation is proven to redraw district boundary effectively
when there is more than one criterion.
5. CONCLUSION
This research has contributed to the improvement of redistricting
