This course is focusing on the problems and algorithms of combinatorial optimization (often called discrete optimization). Following the courses on linear algebra, graph theory, and basics of optimization, we show optimization techniques based on graphs, integer linear programming, heuristics, approximation algorithms and state space search methods. We focus on application of optimization, e.g. logistics, transportation, planning of human resources, scheduling in production lines, message routing and scheduling in parallel computers.
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Optimization, Discrete Mathematics, Logics and Graph Theory.
This timetable is for the czech version (B4M35KO) of the course. The timetable of the english version (BE4M35KO) is provided by prof. Hanzálek.
Week No. | Dates | Title | Notes | Handouts | Stream |
---|---|---|---|---|---|
1 | 19.2.-25.2. | Introduction of Basic Terms, Example Applications | https://rtime.felk.cvut.cz/~hanzalek/KO/Basic_e.pdf | Intro | |
2 | 26.2.-3.3. | Integer Linear Programming - Algorithms | https://rtime.felk.cvut.cz/~hanzalek/KO/ILP_e.pdf | ILP-I | |
3 | 4.3.-10.3. | Integer Linear Programming - Problem Formulations | https://rtime.felk.cvut.cz/~hanzalek/KO/ILP_e.pdf | ILP-II | |
4 | 11.3-17.3. | Shortest Paths | https://rtime.felk.cvut.cz/~hanzalek/KO/SPT_e.pdf | SP-I SP-II SP-III |
|
5 | 18.3.-24.3. | Problem Formulation by Shortest Paths | Theory test 1 | https://rtime.felk.cvut.cz/~hanzalek/KO/SPT_e.pdf | |
6 | 25.3.-31.3. | Flows and Cuts - Algorithms and Problem Formulation | https://rtime.felk.cvut.cz/~hanzalek/KO/Flows_e.pdf | Flows-I Flows-II Flows-III |
|
7 | 1.4.-7.4. | Bipartite Matching. Multi-commodity Network Flows | https://rtime.felk.cvut.cz/~hanzalek/KO/Flows_e.pdf | ||
8 | 8.4.-14.4. | Knapsack Problem, Pseudo-polynomial and Approximation Algorithms | https://rtime.felk.cvut.cz/~hanzalek/KO/knapsack_e.pdf | Knapsack-I | |
9 | 15.4.-21.4. | Traveling Salesman Problem and Approximation Algorithms | https://rtime.felk.cvut.cz/~hanzalek/KO/TSP_e.pdf | TSP-I | |
10 | 22.4.-28.4. | Mono-processor Scheduling | Theory test 2 | https://rtime.felk.cvut.cz/~hanzalek/KO/sched_e.pdf | Sched-I Sched-II Sched-III Sched-IV |
11 | 29.4.- 5.5. | Scheduling on Parallel Processors | https://rtime.felk.cvut.cz/~hanzalek/KO/sched_e.pdf | ||
12 | 6.5.-12.5. | Project Scheduling with Time Windows | https://rtime.felk.cvut.cz/~hanzalek/KO/sched_e.pdf | ||
13 | 13.5.-19.5. | No class on Tuesday | |||
14 | 20.5.-26.5. | Constraint Programming | https://rtime.felk.cvut.cz/~hanzalek/KO/cp_e.pdf | CP-I |
Materials by topic
Title | Handouts | Stream |
---|---|---|
Introduction | https://rtime.felk.cvut.cz/~hanzalek/KO/Basic_e.pdf | Intro |
Integer Linear Programming | https://rtime.felk.cvut.cz/~hanzalek/KO/ILP_e.pdf | ILP-I ILP-II |
Shortest paths | https://rtime.felk.cvut.cz/~hanzalek/KO/SPT_e.pdf | SP-I SP-II SP-III |
Network flows | https://rtime.felk.cvut.cz/~hanzalek/KO/Flows_e.pdf | Flows-I Flows-II Flows-III |
Knapsack | https://rtime.felk.cvut.cz/~hanzalek/KO/knapsack_e.pdf | Knapsack-I |
Traveling Salesman Problem | https://rtime.felk.cvut.cz/~hanzalek/KO/TSP_e.pdf | TSP-I |
Scheduling | https://rtime.felk.cvut.cz/~hanzalek/KO/sched_e.pdf | Sched-I Sched-II Sched-III Sched-IV |
Constraint Programming | https://rtime.felk.cvut.cz/~hanzalek/KO/cp_e.pdf | CP-I |
Students may receive a total of 100 points. The final exam is worth 50% of the grade, while the other 50% can be obtained during the semester.
The points are distributed according to the following table.
Category | Maximum points | ||
Semester | Homeworks (4 assignments) | 15 | |
Theoretical tests (two tests, 8 points each) | 16 | ||
Practical test | 8 | ||
Semester project | 11 | Minimum points | |
Total semester 1) | 50 | 30 | |
Final exam 2) | Written part | 40 | 20 |
Oral exam | 10 | 0 | |
Total | 100 | 50 |
1) To get an ungraded assessment the following requirements have to be met:
The last date of awarding the ungraded assessments is 23. 5. 2024 (Thursday) 23:59. If you fail to fulfill the requirements by then, you will also fail the entire class.
2) Only the students, who obtained the ungraded assessment are allowed to take the exam. The exam constitutes of the written part (40 points) and oral exam (10 points). To pass the written exam, it is necessary to get at least 20 points. The oral exam is mandatory.
All students write both theoretical tests and the practical test at given lecture/lab only. The exception is an illness (confirmed by a sick note from the doctor), planned educational leave like a summer school (confirmation must be provided to your lab teacher weeks in advance), or unforeseen severe events that must accepted by your lab teacher. The substitute terms are at the end of the semester (specific dates will be clarified).
Final grading scale:
Points | [0,50) | [50,60) | [60,70) | [70,80) | [80,90) | [90,100] |
---|---|---|---|---|---|---|
Grade | F | E | D | C | B | A |
The following applies only to students who got an ungraded assessment in the previous year (all other students have to undergo the course from scratch).
Although the assessments are not fully recognized, the students may opt-in to transfer some points from the previous year to the current one (they may also undergo the course from scratch to get a higher number of points). The following rules apply