# Simultaneous aircraft sizing and multi-objective optimization considering off-design mission performance during early design
**Cai, Yu, Dushhyanth Rajaram, and Dimitri N. Mavris. Aerospace Science and Technology (2022): 107662.**

## 1)
Sec. 2 presents the formulation of both the on-design and off-design optimization problems;
Sec. 3 discusses the methods used in major disciplinary analyses performed in conceptual aircraft design;
Sec. 4 describes the mission profile and the tool to perform off-design mission performance evaluation;
Sec. 5 briefly describes the characteristics of NSGA-II, the optimization algorithm used in this paper;
Sec. 6 presents the optimization results along with discussions;
Sec. 7 draws the conclusion.

## 2) Section 2
This section describes the objectives considered for the on-design (single-mission) optimization and the off-design (multi-mission) optimization

In Sec. 2.1, the constraints considered for both optimization problems in Sec. 2.2, the set of aircraft-level design variables in Sec. 2.3, the necessity for down-selecting the design variables through screening in Sec. 2.4, the complete problem statement in Sec. 2.5, and finally, the reference vehicles’ data and the corresponding design variable ranges in Sec. 2.6.

## 3) Review
:::info
Aircraft sizing in conceptual design is to use point performance and mission performance requirements to obtain an initial estimate of the geometric scale, the propulsion characteristics, and the design gross weight, which are typically represented by the wing planform area, the rated sea-level static thrust, and the maximum takeoff weight(MTOW), respectively. Traditionally, this process yields a solution which satisfies the performance requirements is design mission. Although commercial aircraft are sized to fly design tasks, in real-world operations, various off-design tasks in aircraft operations with different payload and range combinations also have implications for optimization problems in aircraft design. Cai et al. solve a series of multi-objective design and multi-task optimization problems during the conceptual design phase of an aircraft across a range of size categories, taking into account both design and non-design tasks, using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). Most approaches that deal with multiple objectives solve a set of single-objective problems to compute the Pareto frontier. In such approaches, a weighted aggregation of the objectives defines a single-objective problem. Multiple such instances with different weights are solved to obtain the complete Pareto frontier. Success of such methods relies on strong assumptions such as convexity of the frontier, among others. Moreover, the distribution of points obtained on the frontier heavily relies on the series of single-objective optimization problems solved. Therefore, these methods are inappropriate candidates when an even distribution of points on the Pareto frontier is desired. On the other hand, the NSGA-II operates on a population of designs and successively refines it through meta-heuristic operators like crossover, mutation, and selection until the members in the evolved populations stop improving. The notion of improvement is handled through the concept of non-domination level. Therefore, NSGA-II is the most suitable method for this study. The primary goal of their work is to investigate the aforementioned issues through several multi-mission multi-objective sizing and optimization studies to assess the differences in top-level aircraft design parameters and off-design mission performance metrics among the Pareto optimal designs across a few size-classes, specifically, a Regional Jet (RJ), a Small Single-aisle Aircraft (SSA), and a Large Twin-aisle Aircraft (LTA). The objective function in this study is divided into two parts. For the on-design optimization, two mission-invariant objectives are considered: 1) the maximum ramp weight (MRW) and 2) the nominal takeoff field length(TOFL), computed at standard sea level conditions and at maximum takeoff weight. A third objective for the on-design optimization is the block fuel of the design mission, WBF,des , which is a good measurement of the direct operating cost when the aircraft flies the design mission. For the off-design optimization, the on-design objectives to minimize MRW and TOFL remain. A third objective to be minimized is payload fuel energy efficiency (PFEE). Aircraft Sizing and Off-Design Mission Analyzer (SODA), a MATLAB program developed by the authors, automatically generates additional input data specifying the range, payload, and/or fuel available of each off-design mission, based on the output of the vehicle sizing module. The authors generated 12 000 samples using SALib in Python and evaluated them in SODA in MATLAB. As expected, observe that given the range of the design variables, the set of most effective design variables primarily include the vehicle-level parameters (The thrust-to-weight ratio (TWR), the wing loading (WSR), and the design range capability (DESRNG)) and wing geometry parameters (wing aspect ratio (AR), wing average thickness-to-chord ratio (TCA), and wing quarter-chord sweep angle (SWEEP)). While ARVT does not have significant impact on any objective function, it has the most impact on the vertical tail height (VTH) which, as a constraint function, determines the design feasibility. According to result, for the on-design optimization, the single-objective optimal designs for MRW and PFEE0 have very similar performance, implying little trade-off between MRW and PFEE0. It is also observed that, for these two designs, the design mission is both weight and fuel constrained, resulting in the worst mission capability among all Pareto optimal designs. For off-design optimization, in the off-design optimization, the mission weighting has an impact on the shape of payload-range envelope of Pareto-optimal designs: the shape of feasible mission space enclosed by the envelope affects both PFEE1 and the mission coverage index (MCI). Results show that the mission weighting function has a strong impact on the Pareto optimal designs when off-design mission performance metrics such as the payload fuel energy efficiency and the mission coverage index are explicitly considered as objectives along with mission-invariant characteristics such as the maximum ramp weight and maximum takeoff field length at standard sea-level condition. When the long-and-heavy missions are given for higher weighting, increasing the design range capability and/or switching to fuel-constrained sizing modifies the shape of payload-range envelope and may increase the flight productivity with a penalty on the maximum ramp weight.
:::

**Questions**

1) "Aircraft sizing in conceptual design is to use point performance and mission performance requirements to obtain an initial estimate of the geometric scale, the propulsion characteristics, and the design gross weight, which are typically represented by the wing planform area, the rated sea-level static thrust, and the maximum takeoff weight(MTOW), respectively." The sentece is hard to understand. because of "is to use", "to obtain", and "of the geometric scale, the propulsion characteristics, and the design gross weight, which are typically represented by the wing planform area, the rated sea-level static thrust, and the maximum takeoff weight(MTOW), respectively.". Try changing the verb and remove unnecessary words to clearly convey what you want to say.

**Answer:**
When ~~doing~~ aircraft sizing in conceptual design, point performance and mission performance requirements ~~needed to~~ be clarified first. ~~According to~~ point performance and mission performance requirements, an initial estimate of the geometric scale, the propulsion characteristics, and the design gross weight can be determined. To represent these parameters, designers ~~will~~ use wing planform area, the rated sea-level static thrust, and the maximum takeoff weight(MTOW) for design analysis.

<font color="#f00">When determining aircraft size in conceptual design, point performance and mission performance requirements are needed to be clarified first. Based on point performance and mission performance requirements, an initial estimate of the geometric scale, the propulsion characteristics, and the design gross weight can be determined. To represent these parameters, designers use wing planform area, the rated sea-level static thrust, and the maximum takeoff weight(MTOW) for design analysis.</font>

2) What is the role of "respectively" in "Aircraft sizing in conceptual design is to use point performance and mission performance requirements to obtain an initial estimate of the geometric scale, the propulsion characteristics, and the design gross weight, which are typically represented by the wing planform area, the rated sea-level static thrust, and the maximum takeoff weight(MTOW), respectively."

"Each ~"

**Answer：**
Here "respectively" means one-to-one correspondence: the initial estimate of the geometric scale ~~corresponds to~~ the wing planform area, the propulsion characteristics correspond to the rated sea-level static thrust, and the design gross weight, corresponding to the maximum takeoff weight (MTOW ).

3) Remember that you should use past tense when you mention specific previous work. Change solve in "Cai et al. solve a series of multi-objective design and multi-task optimization problems during the conceptual design phase of an aircraft across a range of size categories, taking into account both design and non-design tasks, using the Non-dominated Sorting Genetic Algorithm II (NSGA-II)." to solved.

**Lijing - Well noted!**

4) 'TOFL' in "2) the nominal takeoff field length, TOFL, computed at standard sea level conditions and at maximum takeoff weight." should be inside of () to keep consistent notation.

**Lijing - Modified.**

5) What is 'des' in "A third objective for the on-design optimization is the block fuel of the design mission, WBF,des , which is a good measurement of the direct operating cost when the aircraft flies the design mission."

**Answer：**
I think "des" means destination. Block fuel is the total fuel required for the flight and is the sum of the Taxi fuel, the Trip fuel, the Contingency fuel, the Alternate fuel, the Final Reserve fuel, the Additional fuel and any Extra fuel carried. The Trip fuel is the required fuel quantity from brake release on takeoff at the departure aerodrome to the landing touchdown at the destination aerodrome.

<font color="#f00">Sorry, I am not actually asking what is 'des', I am pointing out how you wrote is wrong. You should write $W_{\text{BF, des}}$</font>

6) What is 'SALib' for and what methods does it provide? what sampling method is used in the paper?`

**Answer：**
SALib is an open source library for sensitivity analysis based on python. SALib provides a decoupled workflow, meaning that it does not directly interact with mathematical or computational models. SALib is responsible for generating model inputs using one of the sample functions, and Calculate the sensitivity index of the model output using one of the analyze functions. In this paper, the author used SALib’s implementation of Sobol’s method, which reports the individual effects of each design variable on each response.

<font color="#f00">Sobol is not a type of sampling method and sampling method is not applied to this study.</font>

7) What did you expect? in "As expected, observe that given the range of the design variables, the set of most effective design variables primarily include the vehicle-level parameters (The thrust-to-weight ratio (TWR), the wing loading (WSR), and the design range capability (DESRNG)) and wing geometry parameters (wing aspect ratio (AR), wing average thickness-to-chord ratio (TCA), and wing quarter-chord sweep angle (SWEEP))." and what is 'subject' of the sentece?

**Answer：**
I think the "subject" of this part is the optimization result after the author added the off-design mission. From table 6, it can be seen that the number of generation required when considering the off-design mission is significantly less than the generation that only considers the on-design mission. "As expected" indicates that the above design optimization is feasible as author's expectation.

<font color="#f00">Read your setence again.
From "As expected, observe that given the range of the design variables,", what is the subject in the form of S(subject)+V(verb)+O(object). 'observe' is a verb. 'that ~' is an object. What is the subject?</font>

8) What is 'ARVT'?

**Answer：**
I did not find direct definition of "ARVT" on the Internet. According to the message in table one, I guess "ARVT" means Aspect ratio in Vertical tail geometry. I will keep searching this.

<font color="#f00">The description of nomenclature regarding 'ARVT' is in the paper, page 10. I asked the question because you used the abbreviation without defining it. I already said several times that I don't want to point this out again and again. Please be careful and don't use the word you don't even know.</font>

9) There should be blank space after the period in "feasibility.According to result,"

**Lijing - Modified.**

10) What is 'PFEE0'?

**Answer：**
"PFEE" is a metric named payload fuel energy efficiency (PFEE) as a measure of flight productivity.
PFEE = Total payload carried × Great-circle distance/Fuel energy consumed

This work adopts the original definition of PFEE and modifies it based on the goal of the optimization problem in question. For the on-design optimization, minimizing the block fuel of the design mission is equivalent to minimizing the negative on-design PFEE, defined as
Wp =payload and R = range

<font color="#f00">So, next time, use math form PFEE$_{0}$ to represent that it is a math symbol.</font>

11) What does 'these two designs' in "It is also observed that, for these two designs, the design mission is both weight and fuel constrained, resulting in the worst mission capability among all Pareto optimal designs." indicate? You should be really careful and make clear connection when you use pronoun, such as "this", these", "it", and "that".

**Answer：**
'these two designs' means the single-objective optimal designs for MRW and PFEE0

12) 'I' should be a lower case 'i' after ',' in "For off-design optimization, In the off-design optimization, the mission weighting has an impact on the shape of payload-range envelope of Pareto-optimal designs: the shape of feasible mission space enclosed by the envelope affects both PFEE1 and the mission coverage index (MCI)."

**Lijing - Modified.**

13) Try not to use more than two nested phrases. e.g. "For off-design optimization, In the off-design optimization, "

**Lijing - Well noted!**

14) "Results show that the mission weighting function has a strong impact on the Pareto optimal designs when off-design mission performance metrics such as the payload fuel energy efficiency and the mission coverage index are explicitly considered as objectives along with mission-invariant characteristics such as the maximum ramp weight and maximum takeoff field length at standard sea-level condition." This is too long. Please split the sentence to make it readable.

**Answer：**
Results show that the mission weighting function has a strong impact on the Pareto optimal designs. ~~In this condition,~~ off-design mission performance metrics such as the payload fuel energy efficiency and the mission coverage index are explicitly considered as objectives along with mission-invariant characteristics (such as the maximum ramp weight and maximum takeoff field length at standard sea-level condition).

<font color="#f00">The off-design mission performance metrics are explicitly considered as objectives along with mission-invariant characteristics. For example, the payload fuel energy efficiency and the mission coverage index are explicitly considered as objectives along with the maximum ramp weight and maximum takeoff field length at standard sea-level condition.</font>

15) "When the long-and-heavy missions are given higher weighting, increasing the design range capability and/or switching to fuel-constrained sizing modifies the shape of payload-range envelope and may increase the flight productivity with a penalty on the maximum ramp weight." After 'given', there should be a preposition before 'higher'

**Lijing - Modified.**

**Additional assignment: read "https://en.wikipedia.org/wiki/Multi-objective_optimization" and make a note about priori and posteriori multi-objective optimization.**

**Note：**
Mmulti-objective optimization problem is an optimization problem that involves multiple objective functions. In mathematical terms, a multi-objective optimization problem can be formulated as
The vector-valued objective function is defined as

The most preferred results can be found using different philosophies. Multi-objective optimization methods can be divided into four classes:

1. In so-called no preference methods, no decision maker (DM) is expected to be available, but a neutral compromise solution is identified without preference information. The other classes are so-called a priori, a posteriori and interactive methods and they all involve preference information from the DM in different ways.
2. In a priori methods, preference information is first asked from the DM and then a solution best satisfying these preferences is found.
3. In a posteriori methods, a representative set of Pareto optimal solutions is first found and then the DM must choose one of them.
4. In interactive methods, the decision maker is allowed to iteratively search for the most preferred solution. In each iteration of the interactive method, the DM is shown Pareto optimal solution(s) and describes how the solution(s) could be improved. The information given by the decision maker is then taken into account while generating new Pareto optimal solution(s) for the DM to study in the next iteration. In this way, the DM learns about the feasibility of his/her wishes and can concentrate on solutions that are interesting to him/her. The DM may stop the search whenever he/she wants to.

I think that in the a priori approach, the DM first decides on the preferences ~~and then ranks according to the preferences~~. After that, single-objective optimization result solutions ~~are obtained one by one in order of preference and superimposed~~. Posterior methods are just the opposite. The posterior method involves DM, but first generates ``a set of Pareto optimal solutions``, and then DM selects one of them.

$$\omega_1 f_1 + \omega_2 f_2 $$
$f_1, f_2$: objective functions
$\omega_1, \omega_2$: preferences

priori approach: multi-objective optimization $\rightarrow$ single objective optimization methods

posterior approach: multi-objective optimization method (e.g. NSGA-II) Pareto front!!!