PhD on Structural (Mixed) Integer Programming in Combinatorial Optimization

at  TU Eindhoven

JOB DESCRIPTION

This projects seeks to investigate special instances of (mixed) integer programs ((M)IPs) with the intention of rendering them polynomial time solvable or establishing their hardness. Although traditionally known to be NP-hard, certain structured forms of (M)IPs exhibit properties that allow for efficiently finding solutions. Examples include block-structured (M)IPs, (M)IPs with a limited number of rows or columns, and (M)IPs whose constraint matrix is totally unimodular. Despite many recent advances in this field, numerous unresolved questions persist within this domain, and this project aims to solve some of them.
By solving such (M)IPs more efficiently, we further aim to design new algorithms for a broad spectrum of problems from combinatorial optimization. The relevance of (M)IPs spans across various applications where optimization plays a pivotal role. From supply chain management to resource allocation, encompassing fair division and voting rules among others, the ability to efficiently solve (M)IPs holds significant implications for operational efficiency, cost reduction, and decision-making processes. Moreover, recent developments in the field of machine learning have established a strong connection between these structures and neural networks, which we seek to fortify by developing robust algorithms tailored to these specific MIP classes.
The successful candidate for this Ph.D. position will work under the supervision of Alexandra Lassota in the group Combinatorial Optimization (https://www.tue.nl/en/research/research-groups/mathematics/statistics-probability-and-operations-research/combinatorial-optimization-1) of the department of Mathematics and Computer Science of TU/e. Your responsibilities include to perform scientific research on the topic of the above-mentioned project and to publish your results at international conferences and in international journals. For a small percentage of your time, you will be asked to assist with educational tasks (course support and supervision of students).

JOB REQUIREMENTS

• You have a bachelor and master degree in Mathematics or Computer Science.
• You have a strong background in Combinatorics and Complexity Theory.
• You have good communication skills.
• You are creative, ambitious, as well as self-motivated, proactive, and goal-oriented.
• You have a good command of the English language (knowledge of Dutch is not required).

ABOUT US

Eindhoven University of Technology is an internationally top-ranking university in the Netherlands that combines scientific curiosity with a hands-on attitude. Our spirit of collaboration translates into an open culture and a top-five position in collaborating with advanced industries. Fundamental knowledge enables us to design solutions for the highly complex problems of today and tomorrow.
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Please refer the Job description for details