arXiv subjects

Joerg Kalcsics

Publications and source records attributed to Joerg Kalcsics.

3 recordsLinked to original sources

arXiv2023

Graph Reinforcement Learning for Operator Selection in the ALNS Metaheuristic

ALNS is a popular metaheuristic with renowned efficiency in solving combinatorial optimisation problems. However, despite 16 years of intensive research into ALNS, whether the embedded adaptive layer can efficiently select operators to improve the incumbent remains an open question. In this work, we formulate the choice of operators as a Markov Decision Process, and propose a practical approach based on Deep Reinforcement Learning and Graph Neural Networks. The results show that our proposed method achieves better performance than the classic ALNS adaptive layer due to the choice of operator being conditioned on the current solution. We also discuss important considerations such as the size of the operator portfolio and the impact of the choice of operator scales. Notably, our approach can also save significant time and labour costs for handcrafting problem-specific operator portfolios.

cs.LG↗

arXiv2019

Optimising portfolio diversification and dimensionality

A new framework for portfolio diversification is introduced which goes beyond the classical mean-variance approach and portfolio allocation strategies such as risk parity. It is based on a novel concept called portfolio dimensionality that connects diversification to the non-Gaussianity of portfolio returns and can typically be defined in terms of the ratio of risk measures which are homogenous functions of equal degree. The latter arises naturally due to our requirement that diversification measures should be leverage invariant. We introduce this new framework and argue the benefits relative to existing measures of diversification in the literature, before addressing the question of optimizing diversification or, equivalently, dimensionality. Maximising portfolio dimensionality leads to highly non-trivial optimization problems with objective functions which are typically non-convex and potentially have multiple local optima. Two complementary global optimization algorithms are thus presented. For problems of moderate size and more akin to asset allocation problems, a deterministic Branch and Bound algorithm is developed, whereas for problems of larger size a stochastic global optimization algorithm based on Gradient Langevin Dynamics is given. We demonstrate analytically and through numerical experiments that the framework reflects the desired properties often discussed in the literature.

q-fin.PM↗

arXiv2019

Mathematical models for stable matching problems with ties and incomplete lists

We present new integer linear programming (ILP) models for NP-hard optimisation problems in instances of the Stable Marriage problem with Ties and Incomplete lists (SMTI) and its many-to-one generalisation, the Hospitals / Residents problem with Ties (HRT). These models can be used to efficiently solve these optimisation problems when applied to (i) instances derived from real-world applications, and (ii) larger instances that are randomly-generated. In the case of SMTI, we consider instances arising from the pairing of children with adoptive families, where preferences are obtained from a quality measure of each possible pairing of child to family. In this case we seek a maximum weight stable matching. We present new algorithms for preprocessing instances of SMTI with ties on both sides, as well as new ILP models. Algorithms based on existing state-of-the-art models only solve 6 of our 22 real-world instances within an hour per instance, and our new models solve all 22 instances within a mean runtime of 60 seconds. For HRT, we consider instances derived from the problem of assigning junior doctors to foundation posts in Scottish hospitals. Here we seek a maximum size stable matching. We show how to extend our models for SMTI to the HRT case. For the real instances, we reduce the mean runtime from an average of 144 seconds when using state-of-the-art methods, to 3 seconds when using our new ILP-based algorithms. We also show that our models outperform considerably state-of-the-art models on larger randomly-generated instances of SMTI and HRT.

cs.DS↗