MA306-7-AU-CO:
Combinatorial Optimisation
2016/17
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Postgraduate: Level 7
Current
15
-
Requisites for this module
(none)
(none)
(none)
(none)
(none)
DIP G20109 Optimisation and Data Analytics,
MSC G20312 Optimisation and Data Analytics
The module aims to provide an understanding at postgraduate level of combinatorial optimisation. It aims to understand the mathematical underpinnings of algorithms commonly used in the solution of mathematical programming models where some or all
of the variables are integer. The focus is on applying such algorithms to solve integer and mixed integer models.
Syllabus
- Modelling integer and mixed-integer programming problems (Assignment problem, Travelling Salesman problem, Set Covering problem, Knapsack problem etc.).
- Modelling logical statements and constraints using Binary variables.
- Special purpose algorithms and their applications.
- Polyhedral theory.
- Convex hull, strong valid inequalities and facets for structured problems.
- Duality and relaxation.
- General integer programming algorithms (Branch-and-Bound, Gomory’s Cutting Plan).
- Benders’ decomposition and reformulation.
- (probably) Unimodularity.
On completion of the module, students should be able to:
- formulate planning and scheduling problems as integer programs;
- describe feasible sets as polyhedra using facets, rays and vertices;
- generate valid inequalities for feasible sets;
- use linear programming relaxation and duality to generate upper bounds for integer programs' objective values;
- solve integer programs with cutting-plane algorithms;
- solve integer and mixed integer programs with Branch-and-Bound;
- apply Benders' decomposition algorithm to mixed integer programs.
No information available.
No information available.
No additional information available.
There are 5 lectures and two classes in every fortnight. There will be regular assessed material at postgraduate level which will be discussed in one of the fortnightly classes. In the Summer term 3 revision lectures are given.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Homework 1 |
|
|
| Coursework |
Homework 2 |
|
|
| Coursework |
Homework 3 |
|
|
| Coursework |
Homework 4 |
|
|
| Coursework |
Homework 5 |
|
|
| Exam |
Main exam: 120 minutes during Summer (Main Period)
|
Additional coursework information
Information about coursework deadlines can be found in the "Coursework Information" section of the Current Students, Useful Information Maths web pages: Coursework and Test Information
Exam format definitions
- Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
- In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
- In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
- In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary,
for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Dr Xinan Yang, email xyangk@essex.ac.uk, tel 01206 872787
Mrs Shauna Meyers - Graduate Administrator. email: smcnally (Non essex users should add @essex.ac.uk to create the full email address), Tel 01206 872704
No
No
No
No external examiner information available for this module.
Available via Moodle
Of 33 hours, 33 (100%) hours available to students:
0 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
Disclaimer: The University makes every effort to ensure that this information on its Module Directory is accurate and up-to-date. Exceptionally it can
be necessary to make changes, for example to programmes, modules, facilities or fees. Examples of such reasons might include a change of law or regulatory requirements,
industrial action, lack of demand, departure of key personnel, change in government policy, or withdrawal/reduction of funding. Changes to modules may for example consist
of variations to the content and method of delivery or assessment of modules and other services, to discontinue modules and other services and to merge or combine modules.
The University will endeavour to keep such changes to a minimum, and will also keep students informed appropriately by updating our programme specifications and module directory.
The full Procedures, Rules and Regulations of the University governing how it operates are set out in the Charter, Statutes and Ordinances and in the University Regulations, Policy and Procedures.