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 6 AYs is ~35 pax. We will go full F2F throughout this sem (except on the first and last weeks when Steven 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 Steven's seventh iteration. The first six iterations were reasonably good (5 of them) or average (1 of them). Steven 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). Hopefully the seventh iteration runs well again (last AY's 6th iteration was the Personal Best for the course feedback so the setup is working) :).
2. Teaching staffs:
   

   (Senior) Lecturer: Dr Steven Halim, the key man behind VisuAlgo that will be used with increasing importance in some of CS4234 lectures. Steven 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 Assistant (TA): Audrey Felicio Anwar (took CS4234 last AY, A), Steven runs one tutorial session and Audrey takes the other two tutorial sessions.

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

   Rating (out of 5.0)	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% ▲	Aug-Nov 17 (n=20/33) 60% ▲	Aug-Nov 16 (n=23/40) 58%
   Course feedback (SoC avg ~3.9)	4.3 ▼ (but as per target)	4.5 ▲ (PB)	4.1 ▼ (C-19+IOI20)	4.2 ▼ (> avg)	4.3 ▼	4.4 ▲	4.00
   Course difficulty (SoC avg ~3.8)	4.3 == (fail to reduce diff)	4.3 ▼	4.4 ▲ (C-19+IOI20)	4.2 ==	4.2 ▲	4.1 ▼	4.13
   Steven's teaching (SoC avg ~4.2)	4.5 == (more than target)	4.5 ▲	4.1 ▼ (C-19+IOI20)	4.7 ▲ (PB)	4.6 ==	4.6 ▲	4.53

Syllabus

For the sixth iteration of CS4234, Steven uses the following lesson plan (initially derived from Dr Seth Gilbert's version of S1 AY15/16 but has significantly branched out since then). Also in S1 AY 2022/23, Steven is trying to push more 'flipped classroom' components in CS4234:

• Part 1 (about 4 weeks): (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-Salesman-Problem (4 variants, one is available @ VisuAlgo),
     5. plus a few others in tutorial/PSes/mini projects
  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 4 weeks+1 recess week): 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 Algorithm, some have Max Flow Visualization @ 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): (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 Steven's past PhD Thesis about Optimization Algorithms (2004-2010): SLS Design and Tuning Problem
• Throughought this course:
  1. Lots of 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 modal 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 stevenhalim at gmail dot com. Relevant answers will be posted here to reach wider audiences.

Q: Will this course be graded using Bell curve?

A: Historically, with average of ~35 students in the past 6 AYs, Steven usually do not have to 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 Steven 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 Steven'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, Steven also recognizes the growing number of exchange students taking this course. SEP should have resumed for S1 AY 2022/23, thus Steven is expecting some Exchange students to join the class.

Q: How different will this year's (AY 2022/23) version be compared to last six years (2016 until last year) versions?

A: Last year, CS4234 course feedback rating reached its personal best (4.5 out of 5.0), i.e., the setup is already good. Therefore, most elements will be kept constant and only a small local changes will be implemented:

1. start with 5 easier problems in the first 2 PSes and then automatically go down to 4 (medium-hard) problems only in the middle two PSes when the school gets busier,
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, as recorded lecture),
3. (slightly) better proof presentation in lectures and tutorials (also to re-prepare Steven for CS3230 in Sem 2 AY 2022/23),
4. continue asking more proving questions in tests,
5. further reduce the competition level one notch compared to the last six iterations,
6. a bit more of basic stuffs delegated to VisuAlgo e-Lecture (to make this course more into flipped classroom),
7. continue refining the more interesting Graph Matching topics: Kuhn-Munkres and Edmonds' Matching Algorithm,
8. there will be two sessions (the first and the last) where Steven himself is the one who is away (IOI 2022/clash with week 1 and then the postponed ICPC World Finals 2021/clash with week 13).

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

A: The lecturer is 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 (no more stock at NUS Central Library co-op or maybe last few stocks at @ 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 is one other book that Steven use but this one is rare-and-hard-to-find: Stochastic Local Search: Foundations and Applications so just read the notes.

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Class Roster

Steven uses a small-scale gamification system in his version of CS4234 for extra study motivation.
The list of possible achievements are as follows: (achievements highlighted with red color/green color are already completed in the past/being given, respectively)

1. I Say Hi: Given to first 7 students who reply Steven's welcome email with at least one paragraph of reply (sent on Mon, 25 July 2022, 5.05pm); Any early feedback will always help Steven in refining the preparation of the next iteration of this course, especially voice any concern about the plan to go full 100% F2F for this course
2. Kiasu (#): Given to the first 7 students who solve all tasks of PS1-Prerequisites
3. This Course Is Not Hard (#): Given to the first 7 students who solve all tasks of PS2-NP-hard 1
4. Flows Like Water (#): Given to top 7 students who solve all tasks of PS3-NP-hard 2+Flows 1
5. It is a Match (#): Given to the first 7 students who solve all tasks of PS4-Flows 2+Matchings
6. Test Master (#): Given to the top 7 students who have Midterm Test scores ≥ 78 points (Update on 04 October 2022: VisuAlgo Online Quiz system is half-ready by Week 08, so it is used as optional exercise only for this S1 AY 22/23)
7. Active in Class: Given to the top 2-3 students per tutorial group who participated the most in our tutorial classes (Given on the last Week 13, these students will get full 5% tutorial participation points, the rest will fight for 4, 3, 2, 1% tutorial participation points)
8. Future Algorithm Researcher: Given to top 3 project groups who perform well in their mini project about SLS experiments on two (NP-)hard COPs
9. Nowhere to Hide (Reason): Given to students who already remembered by Steven (stopped by last lecture)
10. Kattis Mini Apprentice (Kattis profile link): Given to students who manage to get 500.0 or more Kattis points at open.kattis during the execution of CS4234 in S1 AY 2022/23 (closed by last lecture); doing PS1+2+3+4+Mini Project will only give you about ~100.0 Kattis points... so you must have done a lot more extra homework than necessary; PS: This is my account and this CS4234-specific page of Methods to Solve can help you get this achievement)