PhD Scholarship in AI-Driven Optimization at DTU Management
You will join a supportive and dynamic research team working at the intersection of machine learning and operations research. Your main task will be to design and implement ML-enhanced exact methods, particularly focusing on Column Generation (and Branch-and-Price), to improve scalability and convergence in solving complex optimization problems.
In collaboration with your supervisors and fellow researchers, you will contribute to the development of solvers for combinatorial optimization problems and apply them to real-world data from industrial partners.
As part of your PhD, you will take advanced courses to build and deepen your skills, implement and evaluate algorithms, and develop your ability to write and present scientific work.
We are a supportive team that will welcome you in a vibrant, interdisciplinary environment at one of Europe’s top technical universities – a university that values innovation, societal impact, and diversity. At DTU you will benefit from supportive policies for professional development, entrepreneurship, and work-life balance. We are located in Copenhagen, one of the world's most livable cities. The university offers an excellent quality of life, a safe and sustainable urban environment, and a vibrant cultural scene.
Research Area and Project Description
In the LeGO (Learning-Guided Optimization), we aim to develop next-generation heuristic and exact optimization methods enhanced by machine learning (ML). The overarching goal is to solve large-scale combinatorial optimization problems more efficiently, particularly in domains such as transportation planning and resource management, where better decision-making can benefit both society and the environment. In this PhD project, the primary focus will be on improving exact optimization methods, with a particular emphasis on column generation approaches.
Column generation is a powerful decomposition method for solving large-scale linear and mixed-integer programming problems. Rather than explicitly considering the full set of variables, it begins with a smaller, manageable subset and iteratively generates new variables (columns) that can improve the solution. This is achieved by solving a master problem in coordination with one or more subproblems, each responsible for generating promising variables based on the current master solution. The approach is particularly effective in applications like crew scheduling and vehicle routing, where the number of potential variables is vast, but only a small fraction is typically needed for an optimal solution.
Within the LeGO project, two key research directions will be pursued to enhance column generation using machine learning. The first line of research focuses on improving scalability by using Graph Neural Networks to identify and eliminate non-essential components of the problem, thereby reducing the size of the subproblems and accelerating the overall solution process. The second line targets the convergence issues often encountered in column generation by developing ML-based dual stabilization techniques. These techniques aim to predict and control the behavior of dual variables, reducing oscillations and improving the efficiency of the iterative process. Together, these innovations aim to make column generation more practical for solving real-world, large-scale optimization problems.
These innovations will be tested within a structured software framework across a suite of practically relevant optimization problems in public transport planning and airport operations. The broader project also includes research on heuristic methods, in particular Large Neighborhood Search (LNS), which will use the developed approaches to design smarter LNS destroy/repair strategies, enabling further performance improvements.
The PhD student will join a strong academic team at DTU Management’s Management Science division. The project is led by Professors Stefan Ropke and Richard Lusby and involves international collaboration with leading researchers in machine learning and optimization. The work will involve collaborative research in algorithm design, software development, and empirical studies, leading to publishable contributions and shared scientific progress in the operations research community.
LeGO is funded by the Independent Research Fund Denmark (DFF). Two PhD students and several senior researchers will contribute to the project, along with industry partners who will support the application and validation of the developed methods.
Responsibilities and qualifications
As part of the LeGO project, you will help develop the next generation of tools for combinatorial optimization. We are looking for a candidate who is motivated by both technical curiosity and making a real-world impact. Ideally, you:
- Have experience with AI models (e.g., graph neural networks, supervised learning, or reinforcement learning)
- Have experience developing algorithms for combinatorial optimization problems
- Have knowledge about decomposition methods for mixed integer linear programs
- Are motivated to contribute to a collaborative, interdisciplinary research environment
- Are eager to learn and explore new ideas at the intersection of ML and optimization
- Can program efficiently in one or more languages
- Communicate well in English, both orally and in writing
We value diverse perspectives and encourage applicants from all backgrounds to apply, even if you do not meet every single requirement.
You must have a two-year master's degree (120 ECTS points) or a similar degree with an academic level equivalent to a two-year master's degree.
Approval and Enrolment The scholarship for the PhD degree is subject to academic approval, and the candidate will be enrolled in one of the general degree programmes at DTU. For information about our enrolment requirements and the general planning of the PhD study programme, please see DTU's rules for the PhD education .
We offer
DTU is a leading technical university globally recognized for the excellence of its research, education, innovation and scientific advice. We offer a rewarding and challenging job in an international environment. We strive for academic excellence in an environment characterized by collegial respect and academic freedom tempered by responsibility.
Salary and appointment terms
The appointment will be based on the collective agreement with the Danish Confederation of Professional Associations. The allowance will be agreed upon with the relevant union. The period of employment is 3 years.
You can read more about career paths at DTU here http://www.dtu.dk/english/about/job-and-career/working-at-dtu/career-paths.
Further information
Further information may be obtained from Professor Stefan Røpke (ropkehjacksonmckinneykathy@harmon-clark.dknguyen.dkcruz-khan.dkdtu.dk ) or Associate Professor Richard Lusby (jenniferhallfreemantiffanywmoorermlu@ward.dkberger.dkdtu.dkjones-rodriguez.dk).
You can read more about DTU Managemtn at www.man.dtu.dk
If you are applying from abroad, you may find useful information on working in Denmark and at DTU at DTU – Moving to Denmark . Furthermore, you have the option of joining our monthly free seminar “PhD relocation to Denmark and startup “Zoom” seminar ” for all questions regarding the practical matters of moving to Denmark and working as a PhD at DTU.
Application procedure
Your complete online application must be submitted no later than 22 August 2025 (23:59 Danish time) .
Applications must be submitted as one PDF file containing all materials to be given consideration. To apply, please open the link "Apply now", fill out the online application form, and attach all your materials in English in one PDF file . The file must include:
- A letter motivating the application (cover letter)
- Curriculum vitae
- Grade transcripts and BSc/MSc diploma (in English) including official description of grading scale
- A research statement (2-3 pages) explaining your ideas and relevant literature.
You may apply prior to obtaining your master's degree but cannot begin before having received it.
Applications received after the deadline will not be considered.
All interested candidates irrespective of age, gender, disability, race, religion or ethnic background are encouraged to apply. As DTU works with research in critical technology, which is subject to special rules for security and export control, open-source background checks may be conducted on qualified candidates for the position.
***DTU Management** conducts excellent research in the intersection between management, technology and economics. We develop solutions in close cooperation with companies and public authorities. Our research aims at strengthening welfare, productivity, and sustainability within society. A key element is the role of technology and its interaction with industry and individuals. The department is divided into four divisions: Technology & Business Studies, Management Science, Climate & Energy Policy and Transportation Science. The department offers a wide range of courses and programs at bachelor, master and PhD level across DTU’s study pro-grams. The department has around 200 employees, with around half coming from abroad.*
Technology for people
DTU develops technology for people. With our international elite research and study programmes, we are helping to create a better world and to solve the global challenges formulated in the UN’s 17 Sustainable Development Goals. Hans Christian Ørsted founded DTU in 1829 with a clear mission to develop and create value using science and engineering to benefit society. That mission lives on today. DTU has 13,500 students and 6,000 employees. We work in an international atmosphere and have an inclusive, evolving, and informal working environment. DTU has campuses in all parts of Denmark and in Greenland, and we collaborate with the best universities around the world.