MA306-7-AU-CO:
Combinatorial Optimisation
2023/24
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Postgraduate: Level 7
Current
Thursday 05 October 2023
Friday 15 December 2023
15
05 January 2024
Requisites for this module
(none)
(none)
(none)
(none)
(none)
DIP G20109 Optimisation and Data Analytics,
MSC G20312 Optimisation and Data Analytics,
MPHDG20048 Operational Research,
PHD G20048 Operational Research
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.
The aims of this module are:
- To equip the discerning and ambitious student with the necessary tools to approach problems of the optimisation type as arise in all sectors of human activity. These tools are explained and their mathematical justifications given to ensure that their outputs can be reliably used. The content relies on basic matrix algebra.
By the end of the module, students will be expected to:
- formulate planning and scheduling problems as integer programs;
- describe feasible sets as polyhedra using facets, extreme points and extreme rays;
- 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.
Indicative syllabus
Scope of integer and combinatorial programming: Modelling with integer variables.
Pre-processing: Balas' constraint disaggregation procedure.
Polyhedral theory: Valid inequalities; Facet constraints; Convex hull of integer solutions.
LP relaxation of integer programming problems.
General integer programming algorithms: Cutting plane, Branch and Bound algorithms.
Special purpose algorithms for Mixed Integer Programming: Benders decomposition.
Unimodularity.
Teaching in the School will be delivered using a range of face to face lectures, classes and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.
Fortnightly homework is given to students to work on in their own time. Model solutions are presented and discussed in class.
The above list is indicative of the essential reading for the course.
The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students.
Further reading can be obtained from this module's
reading list.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Assignment 1 |
|
|
| Coursework |
Assignment 2 |
|
|
| Exam |
Main exam: In-Person, Open Book (Restricted), 120 minutes during Summer (Main Period)
|
| Exam |
Reassessment Main exam: In-Person, Open Book (Restricted), 120 minutes during September (Reassessment Period)
|
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 Georgios Amanatidis, email: georgios.amanatidis@essex.ac.uk.
Dr Georgios Amanatidis
georgios.amanatidis@essex.ac.uk
No
No
No
Dr Yinghui Wei
University of Plymouth
Available via Moodle
Of 38 hours, 36 (94.7%) hours available to students:
2 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s), module, or event type.
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