Funded PhD position in Explanations Combinatorial Optimization

Organisation/Company KU LEUVEN Research Field Computer science & Informatics Researcher Profile First Stage Researcher (R1) Final date to receive applications 30 Sep 2026 - 23:59 (UTC) Country Belgium Type of Contract Temporary Job Status Full-time Offer Starting Date 1 Oct 2026 Is the job funded through the EU Research Framework Programme? Horizon Europe - ERC Reference Number BAP
- Is the Job related to staff position within a Research Infrastructure? No

The field of combinatorial optimization is concerned with developing generic tools that take a declarative problem description and automatically compute an optimal solution to it. Often, users specify their problem in a high‑level, human‑understandable formal language. This specification is first translated into a low‑level specification a solver understands and subsequently solved. Thanks to tremendous progress in solving technology, we can now solve a wide variety of NP‑hard (or worse) problems in practice.

Moreover, these tools are increasingly used in real‑life applications, including high‑value and life‑affecting decisions. Therefore, it is of utmost importance that they be completely reliable.

One of the central objectives of our research group is to develop methodologies and tools with which we can guarantee with 100% certainty that the right problem has been solved correctly. To achieve this ambitious objective, we will build on recent breakthroughs in proof logging, where solvers do not just output an answer, but also a machine‑verifiable proof (or certificate) of correctness.

However, a major limitation of current techniques is that correctness is not proven relative to the human‑understandable specification written by the user, but relative to the low-level translation that the solver receives, meaning that there is no guarantee that the solver is solving the original problem. The group is investigating end‑to‑end guarantees of correctness. When successful, this will have a major impact on the way combinatorial optimization software is developed, evaluated, and used: the proofs produced will enable (1) debugging, since proofs contain detailed information about where bugs occurred, (2) auditability, since proofs can be stored and checked by an independent third party, and even (3) rigorous evaluation of algorithmic improvements.

For some inspiration on this topic, see the CertiFOX project page: https://(Use the "Apply for this Job" box below)..

Another long‑standing objective is to develop methods by which we can explain the reasoning that leads to a certain decision made by combinatorial optimizer in a human‑understandable way. This can range from explaining why a problem has no solutions, to explaining why a solution is optimal, or why a problem has a unique solution and how a user could have seen this.

Explanations are crucial for building trust in declarative solutions and for future‑proofing our tools for new laws and regulations such as the GDPR, which requires that all AI with an impact on human lives needs to be accountable. Examples of such explanations in a puzzle domain can be found on the Zebra Tutor webpage .

The selected candidate should contribute to the second research line (on explanations).

• Investigate the relationship between proofs and explanations.
• Investigate explanations at different levels of abstraction.
• Develop more general explanation methods that can do without‑loss‑of‑generality reasoning.
• Develop methods in a solver that modify the solver process so that we can more easily extract explanations from its outputs.
• Develop domain‑specific explanation methods (for concrete applications).

• Hold (before start‑date of the position) a MSc degree in computer science or a closely related field (e.g., mathematics).
• Have a strong scientific curiosity.
• Be interested in declarative problem solving, combinatorial optimization, knowledge representation, and/or logic‑based methods in computer science.
• Good programming skills.
• Proficiency in English is required.

• Fully‑funded PhD position with an expected duration of 4 years.
• Position funded by a scholarship competitive with Belgian salaries.
• Travel budget sufficient to attend conferences, workshops, and summer schools.

The start is foreseen to be around the start of 2027, but this is negotiable.

For more information please contact Prof. dr. Bart Bogaerts, mail: