arXiv subjects

David Van Bulck

Publications and source records attributed to David Van Bulck.

5 recordsLinked to original sources

arXiv2026

The Traveling Tournament Problem: An Overview

Over the past 25 years, the Traveling Tournament Problem (TTP) has become one of the most extensively studied optimization problems in sports scheduling. At its core, the TTP seeks to minimize the total travel distance incurred by teams that travel directly between opponents' venues during consecutive away games. The problem originated from the scheduling challenges faced by Major League Baseball, where it was identified as the central computational difficulty. This paper provides a comprehensive overview of the literature on the TTP. We review the principal problem variants and benchmark instances, and summarize the current state of the art in lower bounds, approximation guarantees, and exact and heuristic optimization algorithms. Moreover, we contribute to the continued development of the field by tracking and validating lower and upper bounds, while succeeding the repository originally established by Prof. Michael Trick as part of the RobinX sports timetabling project. Finally, we identify several open questions and outline promising directions for future research.

math.OC↗

arXiv2026

Novel neighborhood structures for incomplete round robin sports tournaments

The incomplete round robin sports tournament format, where each team plays the same number of games but faces only a subset of the other teams, is becoming increasingly popular in both youth and professional competitions. In contrast to conventional round robin tournaments, however, neighborhood structures for scheduling incomplete round robin tournaments have largely remained unexplored. We fill this gap by proposing two novel neighborhood structures and describe them in graph theory terms. One of them introduces a single new game followed by a minimal repair chain, while the other introduces possibly many new games but only affects a single round. The latter is shown to fully connect the solution space. We embed the neighborhoods in an adaptive late acceptance hill climbing algorithm and show that the proposed algorithm obtains high quality and new best solutions for several sets of instances from the literature, thereby empirically confirming the effectiveness of the proposed neighborhoods.

math.OC↗

arXiv2026

The incomplete Traveling Tournament Problem

We present a new problem called the incomplete Traveling Tournament problem, which introduces the well known Traveling Tournament Problem into the realm of incomplete round-robin tournaments. We focus on the case where teams can face each opponent at most once. We give a formal description of this problem and show that it is NP-hard. We first discuss how we can obtain lower bounds and how to strengthen them. Then, we propose two integer programming formulations and compare their LP-relaxations. We also propose a third formulation that assumes that home-away patterns of teams are fixed. We discuss how a recently proposed metaheuristic for incomplete round-robin scheduling can be tailored to our problem. In doing so, we present a novel neighborhood structure and show it fully connects the home-away pattern solution space. Finally, problem instances are proposed, for which we derive lower and upper bounds. We show that these instances are challenging, making the development of efficient algorithms for the incomplete Traveling Tournament problem an interesting direction for future research.

math.OC↗

arXiv2025

Quantum Optimization Benchmarking Library - The Intractable Decathlon

Through recent progress in hardware development, quantum computers have advanced to the point where benchmarking of (heuristic) quantum algorithms at scale is within reach. Particularly in combinatorial optimization - where most algorithms are heuristics - it is key to empirically analyze their performance on hardware and track progress towards quantum advantage. To this extent, we present ten optimization problem classes that are difficult for existing classical algorithms and can (mostly) be linked to practically relevant applications, with the goal to enable systematic, fair, and comparable benchmarks for quantum optimization methods. Further, we introduce the Quantum Optimization Benchmarking Library (QOBLIB) where the problem instances and solution track records can be found. The individual properties of the problem classes vary in terms of objective and variable type, coefficient ranges, and density. Crucially, they all become challenging for established classical methods already at system sizes ranging from less than 100 to, at most, an order of 100,000 decision variables, allowing to approach them with today's quantum computers. We reference the results from state-of-the-art solvers for instances from all problem classes and demonstrate exemplary baseline results obtained with quantum solvers for selected problems. The baseline results illustrate a standardized form to present benchmarking solutions, which has been designed to ensure comparability of the used methods, reproducibility of the respective results, and trackability of algorithmic and hardware improvements over time. We encourage the optimization community to explore the performance of available classical or quantum algorithms and hardware platforms with the benchmarking problem instances presented in this work toward demonstrating quantum advantage in optimization.

quant-ph↗

arXiv2024

Which algorithm to select in sports timetabling?

Any sports competition needs a timetable, specifying when and where teams meet each other. The recent International Timetabling Competition (ITC2021) on sports timetabling showed that, although it is possible to develop general algorithms, the performance of each algorithm varies considerably over the problem instances. This paper provides an instance space analysis for sports timetabling, resulting in powerful insights into the strengths and weaknesses of eight state-of-the-art algorithms. Based on machine learning techniques, we propose an algorithm selection system that predicts which algorithm is likely to perform best when given the characteristics of a sports timetabling problem instance. Furthermore, we identify which characteristics are important in making that prediction, providing insights in the performance of the algorithms, and suggestions to further improve them. Finally, we assess the empirical hardness of the instances. Our results are based on large computational experiments involving about 50 years of CPU time on more than 500 newly generated problem instances.

cs.AI↗