CS4234 - Optimisation Algorithms

Introduction

Overview (from Dr Seth Gilbert's version of S1 AY 2015/16 - 3 years 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 module 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

The expected number of CS4234 students for Semester 1 (S1) AY18/19 is actually slightly larger than the past 3 AYs, which is 60 students. This is the initial number that Steven is working with when preparing this module albeit Steven has a feeling it will hover around 40+ after round 3B based on the enrollment data in the earlier rounds.

Useful information that has been used by current students to decide on whether they should register for CS4234 (see CS4234 in nusmods.com, no review though) in S1 AY18/19:

1. It is Steven's third iteration. The two iterations went relatively well and several known weaker spots from the first two iterations will be improved in the third iteration. Steven did his PhD thesis around this topic more than ~14 years ago (2004) and teaching the first iteration two years ago (2016) has refreshed his own knowledge of this topic. By 2017, VisuAlgo started to have some NP-hard/complete visualization topics created by the 2017 TA of this module (Muhammad Rais). Hopefully the third iteration will run at least equal or even better than the first two iterations :).
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... 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): Gan Wei Liang, IOI International Scientific Committee member 2018-2021, Champion of ICPC Manila Regional 2017, CS4234 alumni (S1 AY17/18, A+), Student Tutor Honour List AY16/17.
   Lab TA (Grader): Yohanes Yudhi Adhikusuma, PhD Candidate, NUS SoC, CS4234 alumni (S1 AY16/17, A-).
   Machines, e.g. Mooshak, VisuAlgo, and Kattis will continue be used to help Steven run this module...

   Rating (out of 5.0) (SoC avg ~4.1)	Aug-Nov 2018 (n=??/33) 70%+	Aug-Nov 2017 (n=20/33) 60%	Aug-Nov 2016 (n=23/40) 58%
   Module feedback	Target: 4.3+ (maintain)	4.4 ▲ (above avg)	4.00
   Module difficulty	Target: 4.1- (maintain)	4.1 ▼ (above avg :O)	4.13
   Steven's teaching	Target: 4.4+ (let's see)	4.6 ▲ (above avg)	4.53

Syllabus

For the third 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):

• Part 1 (about 4 weeks): (Combinatorial) Optimization Problems:
  1. Some NP-hard (Combinatorial) Optimization Problems: Min-Vertex-Cover (2 variants, both are available @ VisuAlgo), Max-Clique, Min-Set-Cover, Steiner-Tree (3 variants, the General-Steiner-Tree variant is available @ VisuAlgo), Traveling-Salesman-Problem (4 variants, one is available @ VisuAlgo), and a few others
  2. Current Approaches: Special Case(s), Small Instance/Parameterized Solution(s), Approximation Algorithm(s), and one more at Part 3
  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(+1 virtual) weeks): Network Flows and Matching:
  0. Problem Definition and Basic Algorithm: The Ford Fulkerson's Algorithm [will likely be turned into a flipped classroom]
  1. Analysis of various Augmenting Path heuristics for Ford Fulkerson's Algorithm, some have Max Flow Visualization @ VisuAlgo
  2. The Push-Relabel Algorithm
  3. Graph Matching Algorithms, especially the Bipartite and Non-Bipartite Unweighted Matching Visualization @ VisuAlgo
  4. NEW: More interesting Graph Matching applications/algorithms
• 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 module:
  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)
  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 module, email stevenhalim at gmail dot com. Relevant answers will be posted here to reach wider audiences.

Q: Will this module be graded using Bell curve?

A: Depending on whether the final class size is ≥ 40 or < 40.

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

A: From past 2 AYs, the answer is not 100% true, but indeed many students from the first two iterations have reasonably strong interest in algorithm (thus reasonably good CS3230 grades and also good grades on previous related algorithm modules).

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

A: In recent AYs, there is an increasing trend that many of Steven's past CS3233 students are now taking CS4234 too (the reverse is actually rarer as CS4234 is coded as a level 4 module and CS3233 is coded as a level 3 module).

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

A: In recent AYs, Steven also recognizes the growing number of exchange students taking this module. But take note that the pace of classes in NUS (Asian University) may be much faster than the pace in your home University...

Q: How different will this year's (AY18/19) version be compared to last two years (AY17/18 and AY16/17) versions?

A: The third iteration will continue to be a local improvement on the relatively successful first two iterations. He will only do these minor local changes: (slightly) less coding actually live demo coding, (slightly) better proof presentation, will ask more proving questions in tests, (slightly) less competitive than the first two iterations, (more basic stuffs delegated to VisuAlgo e-Lecture/flipped classroom), add new/harder/more interesting Graph Matching topics.

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

A: The lecturer is a competitive programmer, has written a book 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 module.

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

A: My Competitive Programming book, the CP3.18a edition (actually for CS3233) can be a good book for a small subset of the topics (especially the implementation side). But in CS4234, we will also discuss NP-hard problems that do not have efficient solutions (already covered a bit in CP3.18a edition and will continue to be expanded a bit more by CP4). Introduction to Algorithms (by CLRS, the typical textbook used in CS3230) and Algorithm Design (by Kleinberg and Tardos) are also recommended. Steven will also try to continue expanding Seth's initial LaTeX-style lecture summary that was already available for the Part 1 of the class but not yet available for Part 2-3 of the class.

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News Show All

Lesson Plan Hide Past Show Past

After exam, Bay Wei Heng, Muhammad Irham R B Z, Ng Yi Chong Raynold (students) will also going to compete in ICPC Asia Yangon 2018.

Lastly, on 13 December 2018, many CS4234 staffs/students will be involved in ICPC Asia Singapore 2018.

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. MPE: Given to students who got CS4234 via MPE (30 July 2018), i.e. the early birds...
2. Bid (Round): Given to students who bid CS4234 via CORS (late July-early August 2018) instead of MPE-ing it during early July 2018 (closed after round 3B; Master/PhD student do not have to bid but will be classified here anyway)
3. I Say Hi: Given to students who reply Steven's first proper welcome email regarding their reasons for taking CS4234 (sent on Tue, 14 August 2018, 11.42am); It will help Steven in planning the third iteration of this module (closed after the first lecture)
4. Kiasu (#): Given to the first 7 students who solve all subtasks of PS1-Art Gallery+
5. In FB: Given to students who are already in CS4234 FB group (closed after tutorial 01)
6. Spanning Tree Master (#): Given to the first 7 students who solve all subtasks of PS2-Rubble+
7. Mini Researcher (#): Given to only 4 students who have ≥ 90 points in PS3 (written)
8. Flows Like Water (#): Given to the first 7 students who solve all (different) tasks of PS4-Flows
9. Test Master (#): Given to the top 7 students who have the highest Midterm Test scores
10. Active in Class: Given to the top 3 students per tutorial group who participated the most in our first 9+ tutorial classes (Given on Week 12, these students will get full 5% tutorial participation points, the rest will fight for 4, 3, 2, 1% tutorial participation points)
11. Future Algorithm Researcher: Given to top 3 project groups who perform well in their mini project about SLS experiments on two (NP-)hard COPs
12. Nowhere to Hide (Reason): Given to students who already remembered by Steven (stopped by last lecture); These students can choose to hide their matric cards during CS4234 official assessments and Steven will allow them to do so