MA306-6-AU-CO:
Combinatorial Optimisation
2016/17
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Undergraduate: Level 6
Current
15
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Requisites for this module
MA114 and MA205
(none)
(none)
(none)
(none)
The module 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.
Available to Socrates /IP students spending all relevant terms at Essex.
The module runs at 3 hours per week in the Autumn term. There are 5 lectures and one class in every fortnight.
In the Summer term 3 revision lectures are given.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
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Homework 1 |
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Homework 2 |
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| Coursework |
Homework 3 |
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Homework 4 |
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| Coursework |
Homework 5 |
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| Exam |
Main exam: 120 minutes during Summer (Main Period)
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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
Miss Claire Watts, Department Manager, Tel. 01206 873040, email cmwatts@essex.ac.uk
Yes
Yes
No
No external examiner information available for this module.
Available via Moodle
Of 32 hours, 32 (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).
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