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Tuesday 3rd May 2022 to Tuesday 17th May 2022

The Newton Gateway to Mathematics has been implementing a number of short intensive training courses in mathematical areas of relevance to individuals in industry, business and government. We envisage that these courses will provide technical training in the subject matter with an emphasis on practical applications of mathematics.
In collaboration with NATCOR, the Newton Gateway to Mathematics hosted a training course on Optimisation for Industry for May 2022. This training course took place over 3 days in a hybrid teaching format through trained university lecturers from the NATCOR consortium of universities. The first day of the course, Tuesday 3rd May, took place physically at the Isaac Newton Institute, followed by two virtual sessions on Tuesday 10th and Tuesday 17th May 2022.



Optimisation is an Operational Research methodology that provides solutions to real-world decision problems across a wide range of application areas. Indeed, Optimisation has been successfully applied in many fields, e.g., Management Science, Statistics, Quantitative Finance, Computer Science, Engineering and the Physical Sciences. Optimisation models are now used routinely in industry, e.g., manufacturing, energy production and transport, in the public sector such as defence and healthcare, and in the services (especially finance).  The scope of this module was to cover key elements of Optimisation.
The course was delivered by experts in the field with strong publication records and experience in the design and deployment of these methods on real-world problems. The course was suitable for participants from a wide range of backgrounds, from those that were new to optimisation to those that already had some knowledge in optimisation but wanted to learn more about its applicability to decision-making.

Aims and Objectives

Optimisation is concerned with finding the “best” solution to a problem that has a large number of possible solutions.
In day one, the course started with a gentle introduction to the fundamentals of optimisation, with a particular focus on modelling (suitable) decision problems as linear programs, mixed-integer linear programs and nonlinear programs. It moved on to cover the implementation and resolution of these models with state-of-the-art solvers. Specific Python packages were presented.
In day two, we discussed optimisation under uncertainty, especially how to handle uncertain parameters in optimisation problems. Topics included two-stage stochastic optimisation using probability distributions of random parameters and robust optimisation, which is another popular modelling technique to deal with uncertain parameters without probabilistic information. Numerical case studies were introduced and implemented in Python.
In day three, the course gave an overview of modern heuristic optimisation techniques that are suitable for solving practical optimisation problems, where finding provably-optimal solutions is not computationally viable. Topics covered included local search, simulated annealing, genetic algorithms, hybrid algorithms and hyper-heuristics. We delivered an interesting demonstration of how Python can be used to implement heuristic algorithms for some optimisation problems and and showed that heuristic methods can allow good solutions to be found within a reasonable computation time. In the second half of day three, we focused on the role of optimisation in data science. We started with an introduction to supervised learning and we discussed how to formulate some of machine learning models. Numerical case studies were introduced and implemented in Python.
The aim was that on completion of the course, the participants will have an understanding of optimisation methods and their use to solve decision making problems. Participants became familiar with strengths and limitations of different optimisation approaches.  They also acquainted with some software tools for the rapid implementation and resolution of optimisation models including tools for prototyping heuristic algorithms.

Day 1 was led by Professor Guglielmo Lulli, Professor in Network Analytics at Lancaster University.
Day 2 was led by Dr Xuan Vinh Doan, Reader in the Operations Group at Warwick Business School.
Day 3 was led by Dr Nursen Aydin, Associate Professor of Operational Research at Warwick Business School in the morning, and Dr Ahmed Kheiri, Senior Lecturer in Management Science (Operations Research) at Lancaster University in the afternoon.


Knowledge of Python was desirable, participants had either practical programming experience and/or a numerate degree, but not necessarily in mathematical sciences.

Participants downloaded in advance the following Python packages: PuLP, Pyomo and Python-MIP.

Registration and Venue

Registration for this event is now closed.

The first session on Tuesday 3rd May took place at the Isaac Newton Institute and was followed by two virtual sessions on Tuesday 10th and Tuesday 17th May 2022.

In collaboration with: