Postgraduate Course: Integer and Combinatorial Optimization (MATH11192)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Postgraduate)
||Availability||Available to all students
|Summary||In many optimization problems, the solution is found among a set of finite elements. However, exhaustive search is usually prohibitive and, thus, specialized mathematical techniques must be used to explore the solution space in an efficient way. This course will study exact and heuristic methods for solving several of the most important integer and combinatorial optimization problems.
In many optimization problems, the solution is found among a set of finite elements. Typical such problems are routing problems, matching problems or scheduling problems. However, the space search can be very large (combinatorial explosion) and, as a consequence, exhaustive search is usually prohibitive. Therefore, specialized mathematical techniques must be used to explore the solution space in an efficient way. In order to study these techniques, it is important to understand fundamental notions from integer programming and graphs theory (total unimodularity, matching, spanning tree, etc.) as well as general techniques (lagrangean relaxation, branch-and-cut, metaheuristics).
This course will study exact and heuristic methods for solving several of the most important integer and combinatorial optimization problems. We will first cover some basic notions in integer programming and graph theory. Later, they will be applied to the study of specific problems and solution algorithms.
1. Integer Programming. Total Unimodularity. Valid Inequalities and Preprocessing.
2. Solution Algorithms. Branch-and-Cut. Lagrangean Relaxation. Metaheuristics.
3. Matching Problems. The Assignment Problem.
4. Network Problems. Spanning Trees.
5. Covering Problems.
6. The Traveling Salesman Problem. Heuristics for the TSP.
7. Other Applications: Knapsack Problems, Scheduling Problems.
Information for Visiting Students
|Pre-requisites||Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.
|High Demand Course?
Course Delivery Information
|Academic year 2023/24, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 20,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||There will be two assessments, each worth 25% of the final mark. There will be one week for submitting each assessment. The first assessment will be published on Week 5 and the second on Week 10.
||Feedback in writing.
||Hours & Minutes
|Main Exam Diet S2 (April/May)||Integer and Combinatorial Optimization (MATH11192)||2:00|
On completion of this course, the student will be able to:
- Identify optimization problems which require integer variables.
- Formulate mathematical models for integer and combinatorial optimization problems.
- Identify and apply suitable solution techniques for integer and combinatorial optimization problems.
- Demonstrate an understanding of the theoretical results behind integer and combinatorial optimization, e.g., by proving unfamiliar results or applying them to unfamiliar problems.
|Combinatorial Optimization: Theory and Algorithms. B. Korte and J. Vygen. 5th edition. Springer (2012).|
Combinatorial Optimization. W. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver. Wiley (1998).
Integer and Combinatorial Optimization. G.L. Nemhauser and L.A. Wolsey. Wiley (1988).
Integer Programming. L.A. Wolsey. Wiley (1998).
|Graduate Attributes and Skills
|Keywords||ICO,Combinatorial Optimization,Integer Programming,Algorithms
|Course organiser||Dr Sergio Garcia Quiles
Tel: (0131 6)50 5038
|Course secretary||Miss Gemma Aitchison
Tel: (0131 6)50 9268