2022/23 Undergraduate Module Catalogue

XJCO3910 Combinatorial Optimisation

10 creditsClass Size: 75

Module manager: Dr Sebastian Ordyniak
Email: s.ordyniak@leeds.ac.uk@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2022/23

Pre-requisites

XJCO2421	Numerical Computation
XJCO2711	Algorithms and Data Structures I
XJCO2721	Algorithms and Data Structures II

This module is not approved as a discovery module

Module summary

Solutions to many real world problems that arise in domains such as transport, manufacturing, supply chain management, telecommunications, financial decision making, healthcare logistics, planning and scheduling, can be obtained using techniques from the field of combinatorial optimisation. Combinatorial optimisation provides advanced analytical methods for decision making, where a set of feasible solutions is discrete and the task is to find the best one, with respect to some criteria. It is a well-established discipline with a powerful tool-kit that can be applied to solve real-world problems.In this module, we practice in formulating mathematical models using the techniques of linear programming and integer linear programming, learn how to distinguish between 'good' and 'bad' formulations and how the problems can be solved. One of the methods we study, the simplex method, is recognised as one of the 10 most influential algorithms of the 20th century.

Objectives

This module develops abstract modelling and problem solving skills and contributes to developing computer science professionals who are capable of handling real world problems using advanced analytical methods.

Learning outcomes
On successful completion of this module a student will have demonstrated the ability to:

- apply integer linear programming techniques to model combinatorial optimisation problems.

- select and apply appropriate methods for solving a combinatorial optimisation problem to find exact or heuristic solutions.

- articulate key concepts from the topic in a clear and rigorous manner.

Skills outcomes
Programming
Web development

Syllabus

This module covers the following 5 topic areas:

- Linear programming - simplex method, duality and the dual simplex method.

- Integer Linear Programming - modelling of combinatorial optimisation problems and logical conditions.

- Branch and bound algorithm - general methodology and implementation details.

- Network simplex algorithm - for minimum cost flows.

- Other solution approaches - construction and improvement heuristics.

Teaching methods

Delivery type	Number	Length hours	Student hours
Lecture	22	1.00	22.00
Tutorial	10	1.00	10.00
Private study hours			68.00
Total Contact hours			32.00
Total hours (100hr per 10 credits)			100.00

Private study

Taught session preparation: 10 hours;
Taught session follow-up: 10 hours;
Self-directed study: 13 hours;
assessment activities: 24 hours;

This module is re-assessed by exam only.

Opportunities for Formative Feedback

Coursework

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
In-course Assessment	Coursework 1	10.00
In-course Assessment	Coursework 2	10.00
Total percentage (Assessment Coursework)		20.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr	80.00
Total percentage (Assessment Exams)		80.00

This module is re-assessed by exam only.

Reading list

The reading list is available from the Library website

Last updated: 05/10/2022

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