The Combinatorial Optimization group investigates the structure and relationship between different problems, in order to design efficient and effective algorithms for solving them.

Combinatorial Optimization: finding an optimal solution from a finite set of solutions

Countless practical optimization problems are, in fact, combinatorial optimization problems: they have an optimal solution that needs to be found amongst a finite set of possible solutions. The aim of combinatorial optimization (CO) is to rapidly and efficiently find such an optimal solution.

CO is related to discrete mathematics, theoretical computer science, applied mathematics, operations research, algorithm theory and computational complexity theory and has important applications in several fields. These include scheduling, production planning, logistics, network design, communication and routing in networks, health care, artificial intelligence, machine learning, auction theory, and software engineering.

The Combinatorial Optimization (CO) group at Eindhoven University of Technology (TU/e) focuses on the analysis and solution of discrete algorithmic problems that are computationally difficult. The group investigates the structure of such problems, analyzes the relations between different problems, and uses this knowledge to design efficient and effective algorithms for solving them. We study both exact and heuristic algorithms. The Group is also interested in combinatorial optimization problems where the input is revealed only gradually, or where there is uncertainty in the parameters, leading to online, stochastic or robust solution methods.

Combinatorial Optimization develops theoretic results, for instance in graph theory and matroids, and apply these to real-world situations. Typical application areas are scheduling, production planning, logistics, network design, communication and routing in networks, and health care. The Group cooperates with KU Leuven, CWI (National Research Institute for Mathematics and Computer Science) and DIAMANT (Discrete, Interactive and Algorithmic Mathematics, Algebra and Number Theory, Dutch mathematics cluster).

Research focuses on:

• polyhedral techniques
• local search methods
• performance guarantee for approximation algorithms
• online route planning
• scheduling
• matroid structure and visualization
• network problems

The aim of combinatorial optimization (CO) is to rapidly and efficiently find such an optimal solution.