Proof of Concept 1: MCDA in Aircraft Design
5.2 Selection of an Appropriate MCDA Method
Therefore, in order to explore the interrelationships among the interests of manufacturers, fuel-based emissions, the concerns of airliners, and the consideration of passenger comfort ex-plicitly, four design criteria: OEM, fuel mass, utilization/(block time), and passenger density, are selected to feed into the MCDA method. The other unselected design criteria of interest:
DOC, aircraft price, fuel cost, and TOM, are traced as aircraft performance measures during the optimization process. The five design variables are listed in Table 5.1. The constraints imposed in the aircraft design process are wing span, fuel mass, take-off field length, landing field length, take-off wing loading, and cruise thrust. The design variables, constraints, and design criteria for this simplistic aircraft design model are summarized in Table 5.2.
Table 5.2: Summary of Design Variables, Constraints, and Design Criteria in Aircraft Optimization Process
Units Values Design variables
Wing thickness-to-chord ratio − [0.1,0.2]
Wing aspect ratio − [8,12]
Wing reference area m2 [80,140]
Cruise Mach number − [0.70,0.84]
Fuselage diameter m [3.8,4.2]
Constraints
Wing span m ≤36
Fuel mass kg ≤Fuel tank volume
Take-off field length m ≤3000
Landing field length m ≤2000
Take-off wing loading kg/m2 ≤600
Cruise thrust N ≤0.9 Take-off thrust
Design criteria
OEM kg −
Fuel mass kg −
Utilization/(block time) − − Passenger density P ax/m2 −
5.2 Selection of an Appropriate MCDA Method
In this section, the selection of the most appropriate MCDA method for the aircraft design problem is presented, through the developed intelligent multi-criteria decision support system, as described in Chapter 3. The user guide can be found in Appendix A. The step by step method selection process is discussed in the following subsections.
Figure 5.4: Questions Related to Evaluation Criteria for Method Selection in Aircraft Design Process
Step 1: Define the Problem
As discussed in Section 5.1, the decision making problem in this simplistic aircraft design is to aggregate the four design criteria into one compound figure of merit using one appropriate MCDA method. The proposed intelligent multi-criteria decision support tool is employed to facilitate this decision making process.
Step 2: Define the Evaluation Criteria
In order to identify the most appropriate method, sixteen widely used MCDA methods are stud-ied and their characteristics are stored in the knowledge base. To compare the appropriateness of the methods with respect to the given problem, each method is evaluated based on the pro-posed twelve evaluation criteria. The twelve evaluation criteria can be captured by answering twelve questions relevant to the characteristics of the methods, as shown in Figure 5.4.
Step 3: Perform Initial Screening
In this step, infeasible MCDA methods are eliminated by three filtering questions. Considering that in this aircraft design problem, the compound figure of merit for the four design criteria aggregated by MCDA methods serves as an objective function in the optimization, scoring methods are more appropriate than classification methods. Meanwhile, all non-compensatory methods are excluded since compensation is allowed in the aircraft optimization process.
5.2 Selection of an Appropriate MCDA Method
Figure 5.5: MCDA Methods Ranking List with Scores in Aircraft Design Process
Step 4: Define the Preferences on Evaluation Criteria
Since DM may consider one criterion to be more important than another when selecting the most appropriate method, weighting factors are to be defined for each criterion to reflect the DM’s preference information. The DM’s preference information on the evaluation criteria can be defined using slide bars in our integrated user interface, with a subjective scale of 0 to 10, where 0 stands for extremely unimportant criterion and 10 represents extremely important.
Step 5: Calculate the Appropriateness Index
Essentially, AI is used to determine how the characteristics of a method match the characteristics of the given decision making problem. In this step, AI for each MCDA method is calculated by Equation 3.1, as described in Subsection 3.2.5.
Step 6: Evaluate the MCDA methods
Based on the calculation, AI of the MCDA methods are obtained and shown in Figure 5.5, where higher score represents more appropriateness of the method when solving the given problem.
Step 7: Choose the Most Suitable Method
In this example, as indicated in Figure 5.5, TOPSIS gets the highest score among the MCDA methods. In Subsection 3.2.5, it is shown that high value of AI indicates the method is more appropriate to solve a given decision problem. Therefore, TOPSIS is selected as the most appropriate method to solve the aircraft design problem. In the decision support system, the DM can simply click the name of the method and methodology instructions of TOPSIS will be displayed to guide the DM to solve the given problem, as illustrated in Figure 5.6.
Figure 5.6: Methodology Instructions for TOPSIS
Step 8: Conduct Sensitivity Analysis
Since different DMs often have different answers to the twelve questions, sensitivity analysis to the variation of input data should be performed on the MCDA method selection process.
In our integrated user interface, the DM can adjust the weights of each criterion by moving the slide bars. In this example, with the current input data, it can be seen from Figure 5.5 that SAW, PROMETHEE, and multiplicative weighting method, are ranked second by the multi-criteria decision support system. According to the methodology description in Chapter 2, PROMETHEE needs three threshold values for each criterion: indifference threshold, strict pref-erence threshold, and an intermediate value between indiffpref-erence and strict prefpref-erence threshold.
These extra twelve thresholds for the four design criteria increase the complexity of the aircraft design problem significantly. Moreover, these extra twelve threshold values are rather subjective and different DMs often have different threshold values. Besides, the difference between SAW and multiplicative weighting method is the multiplicative property of the weighting factors.
Therefore, considering that SAW is one widely used MCDA method, SAW is used in the aircraft design problem for the purpose of comparison.
5.2 Selection of an Appropriate MCDA Method
5.2.1 An Improved TOPSIS (ITOPSIS) Technique
TOPSIS technique is recommended by the multi-criteria decision support system as the most appropriate one to solve the aircraft design decision problem. In TOPSIS method, two ideal solutions are hypothesized: positive ideal solution which has all the best criteria values, and negative ideal solution which has all the worst criteria values. TOPSIS selects the alternative that is closest to the positive ideal solution and farthest from the negative ideal solution.
For the purpose of illustration, it can be imagined that TOPSIS puts the alternatives into a coordinate system. For example, if there are three criteria, it is a three-dimension coordinate system, as shown in Figure 5.7, where the green dot represents the positive ideal solution, and the red dot represents the negative ideal solution. TOPSIS ranks the alternatives based on the Euclidean distance to these two ideal solutions.
Figure 5.7: TOPSIS in Three Dimensions Coordinate System
However, in the original TOPSIS method, when an alternative is removed from or added to the candidate alternatives, the two hypothetical ideal solutions will probably change and the Euclidean distances to the two hypothetical ideal solutions will also change. Thus, the top-ranked alternative would possibly become inconsistent when the candidate alternatives are changed. It has been pointed out that the cause of rank inconsistency with TOPSIS lies in the calculation step of determining the two hypothetical ideal solutions [30].
In this study, an Improved TOPSIS (ITOPSIS) is utilized to aggregate the four design criteria into one compound figure of merit for optimization. The positive ideal solution and negative ideal solution are set beforehand in order to maintain the ranking consistency. In this aircraft design decision problem, two kinds of optimizations are conducted for each of the four design
Figure 5.8: An Improved TOPSIS (ITOPSIS) in Aircraft Design Decision Problem
criteria: minimization and maximization, as illustrated in Figure 5.8.
For instance, in order to find the ideal solutions for fuel mass, two kinds of optimizations for fuel mass are conducted: minimization and maximization. The minimum value of fuel mass serves as the positive ideal solution, while the maximum value of fuel mass serves as the negative ideal solution. The ideal solutions for the other three design criteria are searched in a similar way. These ideal solutions for the four design criteria are summarized in Table 5.3. It should be noted that utilization/(block time) ratio is a benefit criterion, and the other three design criteria are cost criteria.
Table 5.3: The Positive Ideal Solution and Negative Ideal Solution in ITOPSIS Ideal OEM Fuel mass Utilization/ Passenger density solutions (kg) (kg) (block time) (P ax/m2)
Positive 36943.4992 11766.8787 796.8551 1.2875 Negative 50521.0972 20864.0399 715.0679 1.4063