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