CS4234 - Optimisation Algorithms

Introduction

Overview (from Dr Seth Gilbert's version of S1 AY 2015/16 - many AYs ago): This course focuses on algorithms for solving optimization (American spelling) or optimisation (British spelling) problems, particularly focusing on combinatorial optimization. These types of problems are ubiquitous, with applications in a multitude of domains. They are used by companies to manage supply chains, retail chains to decide where and when to open new stores, and ports to manage incoming and outgoing cargo containers. In this course, we will cover a variety of powerful techniques for solving these types of problems.

Official description: This course covers common algorithmic techniques for solving optimisation problems, and introduces students to approaches for finding good-enough solutions to NP-hard problems. Topics covered include linear and integer programming, network flow algorithms, local search heuristics, approximation algorithms, and randomized algorithms. Through analysis and application of the techniques to a variety of canonical problems, students develop confidence to (i) appropriately model a given optimisation problem, (ii) apply appropriate algorithmic techniques to solve the problem, (iii) analyse the properties of the problem and candidate algorithms, such as time and space complexity, convergence, approximability, and optimality bound.

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Course Registration

CS4234 class size average in the past 7 AYs is ~36 pax. We will go full F2F throughout this sem (except on week 03 and 13 when Prof Halim is known to be away).

Useful information that has been used by current students to decide on whether they should register for CS4234 (see CS4234 in nusmods.com) in S1 AY21/22:

1. It is Prof Halim's eight iteration. From AY 2016/17 until the present, he has received teaching feedback ratings from 4.1 (average, just one iteration) to 4.7 (very good) out of a maximum of 5.0 for these offerings, with a running average rating of 4.504 (very good). Prof Halim did his PhD thesis around this topic more than one decade ago (2004-2010) and teaching the first iteration back in 2016 has refreshed his own knowledge of this topic. Back in 2017, VisuAlgo started to have some NP-hard/complete visualization topics created by the 2017 TA of this course (Muhammad Rais) and currently being extended by the 2023/24 FYP students (Ng Wee Han and Radian Krisno). Hopefully the eight iteration runs well again.
2. Teaching staffs:
   

   Associate Professor Steven Halim, the key man behind VisuAlgo that will be used with increasing importance in some of CS4234 lectures. Prof Halim is working towards fully flipping almost every modules that he teaches and there will be more flipped components (not all) in this course this semester... PS: His 'Dr' title was obtained after ~6 years working on (visualizations of local search algorithms on) NP-hard Combinatorial Optimization Problems (2004-2010)...

   Teaching Assistants (TAs): Past CS4234 students Lee Zheng Han (T1, 21 pax and T2, 16 pax) and Teoh Jun Jie (T3, 20 pax).
   Prof Halim does not run any tutorial session this time.

   Machines, e.g., VisuAlgo and Kattis will continue be used to help Prof Halim run this course...

   Rating (out of 5.0)	Aug-Nov 23 (n=30/57) ≥ 53%	Aug-Nov 22 (n=27/43) 63% ▼	Aug-Nov 21 (n=24/31) 77% ▲	Aug-Nov 20 (n=15/44) 34% ▼	Aug-Nov 19 (n=18/32) 56% ▼	Aug-Nov 18 (n=19/26) 73% ▲
   Course feedback (SoC avg ~3.8)	≥ 4.2 (target)	4.3 ▼	4.5 ▲ (PB)	4.1 ▼ (C-19+IOI20)	4.2 ▼ (> avg)	4.3 ▼
   Course difficulty (SoC avg ~3.8)	≤ 4.3 (ok let's limit to this)	4.3 ==	4.3 ▼	4.4 ▲ (C-19+IOI20)	4.2 ==	4.2 ▲
   Prof Halim's teaching (SoC avg ~4.1)	≥ 4.3 (target)	4.5 ==	4.5 ▲	4.1 ▼ (C-19+IOI20)	4.7 ▲ (PB)	4.6 ==

Syllabus

For this iteration of CS4234, Prof Halim uses the following lesson plan (initially derived from Associate Professor Seth Gilbert's version of S1 AY15/16 but has significantly branched out since then). Also in S1 AY 2023/24, Prof Halim is trying to push even more 'flipped classroom' components in CS4234:

• Part 1 (about 4 weeks: Wk01-04): (Combinatorial) Optimization Problems:
  1. Some NP-hard (Combinatorial) Optimization Problems. These are the ones to be officially discussed in lectures:
     1. Min-Vertex-Cover (2 variants, both are available @ VisuAlgo),
     2. Min-Set-Cover (not yet in VisuAlgo),
     3. Steiner-Tree (3 variants, the General-Steiner-Tree variant is available @ VisuAlgo),
     4. Traveling-Salesperson-Problem (4 variants, one is available @ VisuAlgo),
     5. plus a few others in tutorial/PSes/mini projects (Prof Halim has one FYP student who has completed CS4234 before working on a few more visualizations starting from Aug 2023)
  2. Current Approaches: Special Case(s), Small Instance/Parameterized Solution(s), Approximation Algorithm(s), and one more at Part 3 below
  3. Techniques Covered: (Clever) Brute Force/Complete Search, Dynamic Programming, Greedy Algorithm, Approximation Algorithm, Linear Programming, Integer Linear Programing (with relaxation)
• Part 2 (about 3 weeks+1 recess week: Wk05-07, plus the last Wk13): Network Flows and Matching:
  0. Problem Definition and Basic Algorithm: The Ford-Fulkerson Algorithm (faster analysis)
  1. Analysis of various Augmenting Path heuristics for Ford-Fulkerson Method, three variants have Max Flow Visualizations @ VisuAlgo
  2. The Push-Relabel Algorithm
  3. Graph Matching Algorithms, especially the Unweighted Bipartite Matching Visualization @ VisuAlgo
  4. Harder Graph Matching applications/algorithms: Kuhn-Munkres (not yet in VisuAlgo) and Edmonds' Matching Algorithms (in VisuAlgo; but still in raw form)
• Part 3 (about 4 weeks: Wk09-12): (Meta-)Heuristics/(Stochastic) Local Search:
  1. Techniques Covered: Gradient Descent/Hill Climbing, Simulated Annealing, Tabu Search, Iterated Local Search, etc
  2. A Trip to the Past: Discussing Prof Halim's past PhD Thesis about Optimization Algorithms (2004-2010): SLS Design and Tuning Problem
• Throughought this course:
  1. Many proofs :O (but we will skip some complicated one-time proofs in class if they become too dry but the details are in the lecture notes/tutorial reference answers)
  2. Implementation of (some of) these advanced optimization algorithms (via help of Online Judge) and their empirical analysis (especially for Part 3)

Course Registration Additional FAQ

If you have any important questions regarding this course, email dcssh at nus edu sg. Relevant answers will be posted here to reach wider audiences.

Q: Will this course be graded using Bell curve?

A: Historically, with average of ~36 students in the past 7 AYs, Prof Halim usually does not have to (strictly) follow Bell Curve system for CS4234...

Q: Will this course flocked by students who have (very) good CS3230 grades?

A: Experience from past AYs tell Prof Halim that the answer is not 100% true, but indeed many students from the earlier iterations have reasonably strong interest in algorithm (thus reasonably good CS3230 grades and also good grades on previous related algorithm modules).

Q: Will this course flocked by students who have taken CS3233?

A: In recent AYs, there is an increasing trend that a fraction of Prof Halim's past CS3233 students (strong experience with the implementation parts of this CS4234 course) are now taking CS4234 too (the reverse is actually rarer as CS4234 is coded as a level 4 course and CS3233 is coded as a level 3 course).

Q: Is this course suitable for (advanced) exchange students?

A: In recent AYs, Prof Halim also recognizes that there are always a few (suitable) Exchange students taking this course. With COVID becoming endemic, Prof Halim continues to expect a few (suitable) Exchange students to join the class.

Q: How different will this year's (AY 2023/24) version be compared to last seven years (2016 until last year) versions?

A: CS4234 course feedback rating is already at ≥ 4.3 in the last two AYs (SoC avg is 3.8), i.e., the setup is already good. Therefore, most elements will be kept constant and only a small local changes will be implemented:

1. Prof Halim reduces the weightage of the two-weeks Problem Sets (it is too difficult to fight ChatGPT/generative AI...) and replace the reduced weightage with a NEW VisuAlgo Online Quiz.
2. return of Push-Relabel algorithm (as there is no Public Holiday on Thursday this semester) -- slotted at the back of the semester (Week 13, now live , as recorded lecture, as Prof Halim is away again on Week 13 this time),
3. further reduce the competition level one notch compared to the last seven iterations,
4. a bit more of basic stuffs delegated to VisuAlgo e-Lecture (to make this course more into flipped classroom),
5. continue refining the more interesting Graph Matching topics: Kuhn-Munkres and Edmonds' Matching Algorithm,
6. there will be two weeks (Week 03+13) just one week where Prof Halim himself is the one who is away (IOI 2023 on Week 03 and the combo ICPC World Finals 2022+23 on Week 13).

Q: Will there be some form of coding in this course?

A: The lecturer is was a competitive programmer, has written a book (now two separate books) about it, and manages various programming competitions in SoC/Singapore/Worldwide :O. So yes, there will always be implementation side of the various optimization algorithms that we discuss in class. You will implement real algorithms to attack real NP-hard optimization problems throughout this course. See CPbook Methods to Solve, CS4234 related stuffs. Warning: Some of these (NP-)hard optimization problems discussed in class are time limit-critical... so students who can only code in Python will be at strong disadvantage at a few programming exercises. Java coder is still somewhat affected (but will 99% able to also solve the programming exercises with the same algorithm or different algorithm but similar time complexity). C++ coder is preferred.

Q: Do I have to buy any textbook for this course?

A: My Competitive Programming book: CP4, Book 2 (last few stock at NUS Central Library co-op or @ SIMCC e-Store (31.9 SGD nett, no shipping cost) and @ lulu.com (22.99 USD+shipping cost+10-14 days of shipping), or the e-book (PDF) version @ lulu.com) (actually for CS3233), can be a good book for about two-thirds of the course topics (especially the implementation side) of CS4234 (Pre-requisites topics, Network Flow, Graph Matching (including some of the rare ones), small or special-cases of NP-hard/complete problems). Introduction to Algorithms (by CLRS, the 3rd or new 4th edition, the typical textbook used in CS3230) or Algorithm Design (by Kleinberg and Tardos) are also recommended. There are two other books that Steven use: the rare-and-hard-to-find Stochastic Local Search: Foundations and Applications book and an optional The Golden Ticket book.

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