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Advanced Optimization Algorithms Course Overview

Explore optimization algorithms in discrete and combinatorial settings. Learn to find the best solutions in a large set of items using graphs, matroids, and similar structures. Dive into project planning, facility location, and supply chain management. Embrace the challenge of combinatorial optimization by maximizing profit and enhancing decision-making. Join us to uncover the power of algorithms in achieving optimal results!

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Advanced Optimization Algorithms Course Overview

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  1. CS4234Optimization Algorithms Welcome!

  2. Optimization Algorithms http://www.comp.nus.edu.sg/~gilbert/CS4234 • Instructor: Seth Gilbert Office: COM2-323 Office hours: by appointment CS4234 Overview

  3. Optimization Algorithms Optimization: Find the minimum/maximum…

  4. Optimization Algorithms Optimization: Find the minimum/maximum: Discrete: a collection of items

  5. Optimization Algorithms Optimization: Find the minimum/maximum: Discrete: a collection of items Combinatorial: a collection of items generated by counting, combining, and enumerating.

  6. Optimization Algorithms Optimization: Find the minimum/maximum: Discrete: a collection of items Combinatorial: a collection of items generated by counting, combining, and enumerating. Examples: Graphs Matroids Similar structures…

  7. Combinatorial Optimization Find the “best” item in a large set of items: Problem Set of items Size Difficulty Searching List of integersLinear Easy Shortest paths All paths in a graph Exponential Easy Minimum spanning tree All spanning trees Exponential Easy Steiner tree All steiner trees Exponential Hard Travelling salesman All possible tours Exponential Hard Matching All possible matchings Exponential Easy Bipartite vertex cover All possible covers Exponential Easy Vertex cover All possible covers Exponential Hard Maximum clique All possible subsets Exponential Very Hard

  8. Combinatorial Optimization Find the “best” item in a large set of items: Problem Difficulty Maintain student records Easy Data compression Easy Program halting problem Impossible VLSI chip layout Hard Exam timetable scheduling Hard Job assignment problem Easy Computer deadlock problem Easy Finding patterns in a database Easy

  9. Combinatorial Optimization Operations Research: How to make better decisions (e.g., maximize profit) Project planning / critical path analysis Facility location: where to open stores / plants Floorplanning: layout of factory or computer chips Supply chain management Berth assignment problem (BAP): port management Assignment problems (e.g., weapon target assignment) Routing / transportation problems: buses, subways, trucking. Airline ticket pricing

  10. Optimization Algorithms Optimization: Find the minimum/maximum: Discrete: a collection of items Combinatorial: a collection of items generated by counting, combining, and enumerating. Continuous: given a function f(x), find the vector x that maximizes f(x).

  11. Optimization Algorithms

  12. “If you need your software to run twice as fast, hire better programmers. But if you need your software to run more than twice as fast, use a better algorithm.” -- Software Lead at Microsoft

  13. “... pleasure has probably been the main goal all along. But I hesitate to admit it, because computer scientists want to maintain their image as hard-working individuals who deserve high salaries... ” -- D. E. Knuth

  14. “... pleasure has probably been the main goal all along. But I hesitate to admit it, because computer scientists want to maintain their image as hard-working individuals who deserve high salaries... ” -- D. E. Knuth

  15. CS4234 : Optimization Algorithms Brand new class: • We can make this class what we want. • Talk to me about your goals, interests, etc.

  16. CS4234 : Optimization Algorithms Brand new class: • We can make this class what we want. • Talk to me about your goals, interests, etc. Where did this class come from? • CS5234: Combinatorial and Graph Algorithms • More general: all sorts of optimization (not only graphs). • More specific: just optimization

  17. Optimization Algorithms Target students: • Advanced (3rd or 4thyear) undergraduates • Interested in algorithms • Interested in tools for solving hard problems Prerequisites: • CS3230 (Analysis of Algorithms) • Mathematical fundamentals

  18. CS4234 Overview • Mid-term exam October 6 In class • Final exam November 25 Exams will be graded and returned.

  19. CS4234 Overview • Grading 40% Problem sets 25% Mid-term exam 35% Final exam • Problem sets • 5-6 sets (about every 1-2 weeks) • Focused on algorithm design and analysis.

  20. CS4234 Overview • Mini-Project Small project Idea: put together some of the different ideas we have used in the class. Time scale: last 2-3 weeks of the semester.

  21. CS4234 Overview • Released today/tomorrow Survey: On IVLE. What is your background? Not more than 10 minutes. PS1: Released tomorrow.

  22. CS4234 Overview • Problem set grading Simple scheme: 3 : excellent, perfect answer 2 : satisfactory, mostly right 1 : many mistakes / poorly written 0 : mostly wrong / not handed in -1 : utter nonsense

  23. CS4234 Overview • What to submit: Concise and precise answers: Solutions should be rigorous, containing all necessary detail, but no more. Algorithm descriptions consist of: 1. Summary of results/claims. 2. Description of algorithm in English. 3. Pseudocode, if helpful. 4. Worked example of algorithm. 5. Diagram / picture. 6. Proof of correctness and performance analysis.

  24. CS4234 Overview • How to draw pictures? By hand: Either submit hardcopy, or scan, or take a picture with your phone! Or use a tablet / iPad… Digitally: 1. xfig (ugh) 2. OmniGraffle (mac) 3. Powerpoint (hmmm) 4. ???

  25. CS4234 Overview • Policy on plagiarism: Do your work yourself: Your submission should be unique, unlike anything else submitted, on the web, etc. Discuss with other students: 1. Discuss general approach and techniques. 2. Do not take notes. 3. Spend 30 minutes on facebook (or equiv.). 4. Write up solution on your own. 5. List all collaborators. Do not search for solutions on the web: Use web to learn techniques and to review material from class.

  26. CS4234 Overview • Policy on plagiarism: Penalized severely: First offense: minimum of one letter grade lost on final grade for class (or referral to SoC disciplinary committee). Second offense: F for the class and/or referral to SoC. Do not copy/compare solutions!

  27. Textbooks Introduction to Algorithms • Cormen, Leiserson, Rivest, Stein • Recommended…

  28. Textbooks Algorithm Design • Kleinberg and Tardos • Recommended…

  29. CS4234 Overview • Topics (tentative, TBD) Introduction to combinatorial optimization Vertex cover, set cover, Steiner tree, TSP Flows and matching Maximum flow, bipartite matching Linear programming LPs, duality, relaxations, rounding Continuous optimizationGradient descent, meta-heuristics

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