We invite applications from highly motivated candidates for full-time PhD positions focused on developing advanced methodologies, including quantum-based approaches, for solving polynomial optimization problems with binary decision variables. The developed methodologies will be applied to challenging real-world problems arising in production planning, finance, energy, transportation, and tourism.
Binary Polynomial Optimization Problems (BPOP) are special classes of discrete optimization, which amount to optimizing a polynomial objective function of binary decision variables subject to a set of linear or polynomial constraints. Some applications of BPOP include portfolio optimization, projects selection, sustainable development, facilities location and vehicle routing problems. BPOP problems are known to be very challenging to solve due to the non-linear nature of their objective functions and the discrete nature of their decision variables. Indeed, even simple special cases of BPOP, such as the quadratic knapsack problem, the quadratic assignment problem, etc. are known to be strongly NP-hard.
The aim of this research project is to develop a host of innovating solution methodologies for solving BPOP. These methodologies will include heuristic, meta-heuristics and exact algorithms. Some of the techniques to be used include, but not limited to:
- Dynamic programming
- Cutting planes
- Polyhedral studies
- Quantum algorithms
- Hybrid-quantum algorithms
- Branch-and-cut
- Binary decision diagrams.
Applicants should have:
• A Masters degree in Operations Research, Computer Science, Mathematics, Quantum Computing, IndustrialEngineering, or a related field;
• Good programming skills (e.g., Python, C/C++, or similar);
• An interest in combinatorial optimization.
A knowledge of optimization algorithms, as well as quantum computing is an asset but not required.
The successful candidates will be jointly supervised by Leandro Coelho (Professor at Université Laval in Quebec City) and Franklin Djeumou Fomeni (Professor at the University of Quebec in Montreal, UQAM, Montreal). They will also have the opportunity to be affiliated with leading international research groups, including GERAD (www.gerad.ca), CIRRELT (www.cirrelt.ca) and CRI2GS (https://cri2gs.uqam.ca). The research environment is highlydynamic, collaborative, and supportive. The students will interact regularly with a vibrant community of graduate studentsand researchers, benefit from frequent seminars and workshops, and have opportunities to collaborate with internationally recognized experts. The environment combines strong methodological expertise with a collegial andengaging atmosphere.
The positions are fully funded and include a competitive stipend and tuition support. There will also be fundings to attend national and international conferences.
Degrees certificates, Academic transcripts, CV, Cover letter and contact info for two references.
Email all documents to djeumou_fomeni.franklin@uqam.ca / leandro.coelho@fsa.ulaval.ca
We are committed to fostering an equitable, diverse, and inclusive research environment where all members are respected, supported, and able to thrive. We welcome applications from all qualified candidates and particularly encourage applications from individuals from groups that have been historically underrepresented in science and engineering, including women, Indigenous Peoples, persons with disabilities, members of racialized communities, and individuals from diverse gender identities and sexual orientations.
We value diverse perspectives and recognize that different educational, cultural, and life experiences strengthen research and innovation. Selection will be based on applicants demonstrated potential, motivation, and achievements, taking into consideration the opportunities and resources that have been available to them throughout their academic and professional journeys.
Accommodation measures are available upon request throughout the recruitment and selection process. Candidates who require accommodations are encouraged to contact us in confidence.