AI-powered heuristics for heavy industry mathematical optimization

The UKRI AI Centre for Doctoral Training (CDT) in Decision Making for Complex Systems is a joint CDT between The University of Manchester and the University of Cambridge. The CDT provides funding for four years of advanced studies towards a PhD. The first year consists of a taught program at Manchester that will cover the fundamentals of Machine Learning. This year is followed by three years of research at either at Manchester or Cambridge. Please note the research element of the PhD will take place at the host institution of the supervisor listed for each project.

The new state-of-the art Transformer Neural Networks [1] has recently revolutionized the world of generative Artificial Intelligence (AI). This technology is behind the most famous and successful Large Language Models (LLMs) such as GPT 3/4 (OpenAI) [2, 3], BERT/PaLM 2 (Google) [4, 5], LLaMA (Meta) [6] and other generative models (GM). These LLMs are the main engine of the popular well-known AI assistants like ChatGPT (OpenAI) and Bard (Google), that had demonstrated the potential of these kinds of models. GMs have been used recently to produce feasible solutions to combinatorial optimization problems [7].

Many optimization problems arising in industry are combinatorial in nature and involve sequencing, scheduling, cutting or packing. For example, the scheduling of production lines in heavy industry is a challenge faced every day in many companies and with a critical impact in their daily results. Due to its complexity and available time constraints, the use of classical mathematical techniques like integer linear programming is infeasible. Nowadays this scheduling is often solved by means of hand-crafted and carefully tuned heuristics and meta-heuristics [8], including local search and constructive heuristic methods such as GRASP. Although these optimization techniques have been used for many years, they still suffer from issues such as the difficulty to properly tune their parameters [9], the necessity to develop a tailored algorithm for each problem/project [10], very limited number of solution evaluations due to time requirements [11] and it is difficult to add learning to them [12]. It is often the case that a different instance of the same problem must be solved every week, day or hour, thus there is a large corpus of data available of previous instances and already evaluated solutions.

This project proposes to explore the possibility of using a transformer-based architecture as a scheduling method for production facilities, inspired by the state-of-the-art LLMs. This architecture would learn from historical data (e.g., schedules) and would be able to generate new schedules in a similar way to how they are currently generating text, implicitly learning the scheduling rules from the data. Candidates will explore cutting-edge technologies from academia but with an strong link with industry, facing a real world problem and applying cutting-edge technologies to solve it. 

This project aims to adapt such LLM/GM methods to the task of generating solutions to industrial combinatorial optimization problems. The main research questions that the project aims to answer are:

• How to adapt these LLM/GM methods to generate feasible high-quality solutions for complex combinatorial optimization problems arising in industry.
• How to efficiently train such a system, reusing as much available data as possible and minimising the amount of new data required?
• How to efficiently update the system in an online manner with the data generated by solving each new instance?
• Can such an AI system outperform the state-of-the-art heuristics used in industry on its own or does it need to be complemented with other optimization methods?

This project is co-funded by ArcelorMittal.

Entry requirements

Applicants should have, or expect to achieve, at least a 2.1 honours degree or a master’s (or international equivalent) in a relevant science or engineering related discipline.

How to Apply

As the CDT has only recently been awarded we strongly encourage you to contact the supervisor of the project you are interested in with your CV and supporting documents. You will have a chance to meet with prospective supervisors prior to submitting an application – further details will be provided.

Equality, diversity and inclusion is fundamental to the success of The University of Manchester, and is at the heart of all of our activities. We know that diversity strengthens our research community, leading to enhanced research creativity, productivity and quality, and societal and economic impact.

We actively encourage applicants from diverse career paths and backgrounds and from all sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation and transgender status.

We also support applications from those returning from a career break or other roles. We consider offering flexible study arrangements (including part-time: 50%, 60% or 80%, depending on the project/funder).

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