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Case Study: Multi-objective Optimisation
1 Task
This case study is composed of two main tasks, problem solving (detailed in Section 2) and paper presentation
(detailed in Section 3), aiming at strengthening your understanding of multi-objective optimisation and appli cations of multi-objective optimisation algorithms. This case study will take 20% in your final mark of this
course (thus 20 points).
This is a group project. Each group should be composed of no more than four individuals. Each individual’s
mark depends on the correctness of the answers to the questions (cf. Section 2) and his/her performance in
group presentations (cf. Section 3).
2 Problem Solving (10 marks)
Context
An investor needs to select an appropriate portfolio from a set of investment options, aiming to minimize
investment risk degree (f1) and maximize investment return degree (f2). There are currently seven portfolio
options, with their corresponding f1 (risk) and f2 (return) values as follows:
A(1, 1), B(10, 9), C(5, 1), D(2, 3), E(8, 4), F(5, 5), G(7, 6)
Here, a lower f1 value indicates lower risk, and a higher f2 value indicates higher return. f1 and f2 are integers
∈ {1, . . . , 50}.
Question 1: Portfolio comparison. (2 marks)
(1.1) Comparing Portfolio F(5, 5) and Portfolio C(5, 1), which one is better? Analyse from the perspectives of
risk and return and provide reasoning. (1 mark)
(1.2) Comparing Portfolio G(7, 6) and Portfolio E(8, 4), which one is better? Analyse from the perspectives of
risk and return and provide reasoning. (1 mark)
Question 2: Identify all non-dominated solutions in the given seven portfolios. (1 mark)
Question 3: Investor preference matching. (2 marks)
There are currently two investors:
• The first investor is conservative, aiming to minimize investment risk (f1) and having lower requirements
for return (f2).
• The second investor is aggressive, willing to take higher risks (f1) and aiming solely to maximize investment
return (f2).
From the non-dominated solution set, select the most suitable portfolio for each investor and explain the rea soning.
Question 4: Investment portfolio selection based on preferences. (5 marks)
Assume that the investment portfolio options satisfy the formula f2 =
p 252 − (f1 − 25)2, where f1 (risk) is an
integer ∈ {1, . . . , 25}. There are three investors, each with different importance weights for risk and return as
follows:
1
• Investor 1: wf1 = 0.2, wf2 = 0.8 (more focused on return).
• Investor 2: wf1 = 0.5, wf2 = 0.5 (equal importance on risk and return).
• Investor 3: wf1 = 0.9, wf2 = 0.1 (more focused on risk).
Please design an appropriate method and implement the following tasks through programming:
(4.1) Generate the portfolio set: Based on the formula mentioned above, generate all possible investment port folio options, i.e., the set of (f1, f2). (1 mark)
(4.2) Design a scoring function: For each investor, design a scoring function in the form: Score = S(f1, f2, wf1
, wf2
)
where wf1
and wf2
are the weights for risk and return, respectively, and f1 and f2 are the risk and return values
of the portfolio. A larger score indicates a better matching. Explain the meaning of this scoring function. (1
mark)
(4.3) Calculate the score for each portfolio for the three investors based on the scoring function. (1 mark)
(4.4) Identify the highest-scoring portfolio for each investor and output the results. (1 mark)
(4.5) Result analysis and explanation: Analyse the highest-scoring portfolios for each investor and explain why
these portfolios align with their preferences. Discuss how changes in the weights wF 1 and wF 2 affect the final
portfolio selection. (1 mark)
3 Paper Reading and Presentation (10 marks)
A list of papers on applications of multi-objective optimisation is provided. Each group will select one of those
to read and present the paper orally with slides on 28 April 2025 (10am-1pm & 4:30pm-7:30pm). A paper can
only be selected by no more than one group (first come, first serve).
You are also encouraged to look for other papers on applications of multi-objective optimisation that are
not in the provided list. If such a case, please send the papers to the instructor of the course for approval first.
All individuals in the group should participate and contribute to the paper reading, slides preparation and
oral presentation.
3.1 Presentation slides
Please limit your slide count to approximately 8 to 12 slides. Below is an example structure/outline:
• Title page: information of the paper (title, publication, year), group members, contribution percentage1
.
• Background and motivation/impact of the work: What is the topic? Why it is important and should be
investigated.
• Challenges & why multi-objective optimisation methods: What are the challenges of tackling such prob lems? Why using multi-objective optimisation methods (thus the necessity)? What are the multiple
objectives?
• Contributions/claims/take-home messages of the work.
• Problem formulation/modelling: input, output, search space, objective(s), constraint(s), etc. Focusing on
core messages instead of explaining mathematical formulations in details. But mathematical formulations
(if any) should be provided on slides.
• Theoretical analysis and/or experimental studies & discussion: What are the theoretical analysis and/or
experimental studies that support the claims/contributions of the paper? How is the outcome? Any
insightful observation?
• Further work & limitations of the work.
• Your thoughts about the work: insights, criticism, etc.
1
Individual contribution to the presentation represented by a percentage ∈ {0%, 5%, 10%, 15%, . . . , 80%, 85%, 90%, 95%, 100%}.
Contributions of all individuals in a group sum to 100%. If an individual’s contribution is claimed to be 0, all members should
provide a written letter to support the claim. The contributions can not be revised after slides submission deadline.
2
3.2 Oral presentation
• All students should present orally.
• Note that those are normal lecture sessions, therefore all students should be present in both sessions
(10am-1pm & 4:30pm-7:30pm, 28 April 2025).
• We are going to randomly call on a group to present. A no-show results in 0 mark.
• Each group can present for no more than 10 minutes, followed by 6 minutes Q&A2
. Note that you will be
stopped when time’s up.
3.3 Evaluation
• All groups/individuals will be assessed according to the following criteria:
– Presentation slides (5 marks): correctness, clarity, conciseness, format, completeness. – This is group
assessment, score denoted as S
s
.
– Oral presentation + Q&A (5 marks): correctness, clarity, conciseness, completeness, understanding,
etc. – This is individual assessment, score denoted as S
o
.
• This is a group work. If you work individually, your score is (S
s + S
o
) × 0.9.
• Assuming a group of n students (n ∈ {2, 3, 4}), with group score S
s
for slides and individual score
S1
o
, . . . , Sn
o
for oral presentation and Q&A, and individual contribution C1, . . . , Cn, respectively. If Ci = 0,
then a student i’s score is.
If an individual’ total score of problem solving and presentation is above 20, then the overflow will be
counted as his/her bonus in the total mark of this course3
.
4 Submission
4.1 What to submit
Each student should submit a zip file named as casestudy-{groupnumber}.zip. Inside the zip, there should
be:
• A pdf file named as solutions.pdf for problem solving task detailed in Section 2.
• A pdf or pptx file named as presentation.pdf or presentation.pptx, respectively, to be used in the
oral presentation.
4.2 Where to submit
Upload your zip file via Moodle.
2The length of presentation and Q&A may be subject to change based on the number of groups.
3The formulas for calculating scores may be subject to change due to the actual group size and numbers.
3
4.3 Submission deadline
23:59 (Beijing time) April 27 (Sunday), 2025.
No further update or edit (even minor) is allowed after this deadline.
A group will get 0 as score for problem solving if any of the following cases happens:
• Plagiarism.
• Missed the deadline for submission.
A group will get 0 as score for presentation slides if any of the following cases happens:
• No show.
• Missed the deadline for submission.
An individual will get 0 as score for oral presentation if any of the following cases happens:
• No show.
• Not presentation or negligible/meaningless presentation (e.g., presenting paper title and members’ names).
4