Johannes Thürauf – Optimization Online

An Integer Programming Approach to Compute Lower Bounds for Ramsey Numbers Using Circulant Graphs

Published: 2026/08/19

Branch and Cut Algorithms, Combinatorial Optimization, Integer Programming branch-and-cut, circulant graphs, combinatorial optimization, integer programming, ramsey numbers

The Ramsey number R(m,n) is the smallest order at which every red-blue edge coloring of a complete graph must contain a blue clique (a complete subgraph) of size m or a red clique of size n. Determining these numbers exactly is extremely hard, and even certifying a lower bound requires exhibiting an explicit coloring that … Read more

Robust Network Design for Potential-Based Flows with Controllable Elements

Published: 2026/06/19, Updated: 2026/07/07

(Mixed) Integer Nonlinear Programming, Bilevel Optimization, Robust Optimization bilevel optimization, mixed-integer nonlinear programming, potential-based flows, robust optimization, uncertainty

We study adjustable robust network design for potential-based flows with controllable elements under load uncertainty. The resulting problem combines discrete here-and-now expansion decisions with wait-and-see operational decisions governed by nonconvex flow constraints. Moreover, controllable elements introduce adjustable integer decisions, which are algorithmically challenging. We equivalently characterize robust feasibility and robust optimality of a fixed network … Read more