I am delighted the Royal Society decided to fund a travel exchange to the Hong Kong University of Science and Technology under the Kan Tong Po Fellowship Scheme (apparently named after the co-founder of the Bank of East Asia).
In our project titled “Optimisation Methods for Public Transport Utilisation in Evacuation Planning”, we will consider emergency situations where a densely populated, urban area needs to be evacuated. In this setting, an efficient public transportation system is required to move people quickly, as road networks become congested. Surprisingly, literature on this topic is relatively sparse, and most research focussed on the role of buses for emergency evacuations.
Much looking forward to our work in Hong Kong!
Last week, I was invited to give a talk on “Robust Combinatorial Optimisation: Complexity and Approximability” within the GRK1855 at the wonderfully-named TU Dortmund University. Many thanks for the hospitality!
We also used the opportunity to discuss the idea of min-max-min robust optimisation (also referred to as K-adaptivity). I’m much looking forward to see where our cooperation will lead us to!
A new preprint is out, on “Compromise Solutions for Robust Combinatorial Optimization with Variable-Sized Uncertainty”. It uses a similar setting as our previous paper on variable-sized uncertainty, by assuming that only the shape of the uncertainty set is known, but not its size. But instead of finding a set of candidate robust solutions, we consider the problem of finding a single solution, that performs well over all possible uncertainty set sizes.
For min-max robustness, this problem can be solved quite efficiently by reformulating it as a single min-max problem for an uncertainty set of specific size. For min-max regret, however, things may get complicated, as the regret of a fixed solutions is a piecewise-linear function in the size of the uncertainty. We present general solution algorithms for this case, and consider the computational complexity for some classic combinatorial problems.
Here is the abstract:
In classic robust optimization, it is assumed that a set of possible parameter realizations, the uncertainty set, is modeled in a previous step and part of the input. As recent work has shown, finding the most suitable uncertainty set is in itself already a difficult task. We consider robust problems where the uncertainty set is not completely defined. Only the shape is known, but not its size. Such a setting is known as variable-sized uncertainty.
In this work we present an approach how to find a single robust solution, that performs well on average over all possible uncertainty set sizes. We demonstrate that this approach can be solved efficiently for min-max robust optimization, but is more involved in the case of min-max regret, where positive and negative complexity results for the selection problem, the minimum spanning tree problem, and the shortest path problem are provided. We introduce an iterative solution procedure, and evaluate its performance in an experimental comparison.
Just returned from Wroclaw, where we had an exciting time again discussing robust optimisation and enjoying most delicious pierogi. We had some breakthroughs, so I’m looking forward to discussing new preprints on our results soon.