arXiv subjects

Willem-Jan van Hoeve

Publications and source records attributed to Willem-Jan van Hoeve.

5 recordsLinked to original sources

arXiv2026

Dantzig-Wolfe and Arc-Flow Reformulations: A Systematic Comparison

Dantzig-Wolfe reformulation is a widely used technique for obtaining stronger relaxations in the context of branch-and-bound methods for solving integer optimization problems. Arc-Flow reformulations are a lesser known technique related to dynamic programming that has experienced a resurgence as result of the recent popularization of decision diagrams as a tool for solving integer programs. Although these two reformulation techniques arose independently, the recently proposed solution paradigm known as column elimination has revealed that they are in fact closely connected. Building on a unified formulation and notation, this study clarifies the theoretical connections and computational trade-offs between these two reformulations. We first revisit the known fact that the LP relaxations of these two reformulations yield the same dual bound. We then dig deeper, establishing conditions under which valid inequalities in the original, Dantzig-Wolfe, or Arc-Flow spaces can be translated across reformulations without loss of strength, and reinterpreting iterative strengthening methods, such as decremental state-space relaxation and column elimination, through the lens of cutting planes. To assess the potential impact of these insights empirically, we benchmark both reformulations under identical conditions on the vehicle routing problem with time windows using state-of-the-art column- and cut-generation techniques. The results identify clear contrasts: the Arc-Flow reformulation benefits from faster convergence and performs best when subproblems are highly relaxed or low-dimensional, whereas the Dantzig-Wolfe reformulation is more efficient when the master problem remains compact. Overall, our study provides a unified perspective and practical guidelines for choosing between Dantzig-Wolfe and Arc-Flow reformulations in large-scale integer optimization.

math.OC↗

arXiv2026

Inverse Optimization Without Inverse Optimization: Direct Solution Prediction with Transformer Models

We present an end-to-end framework for generating solutions to combinatorial optimization problems with unknown components using transformer-based sequence-to-sequence neural networks. Our framework learns directly from past solutions and incorporates the known components, such as hard constraints, via a constraint reasoning module, yielding a constrained learning scheme. The trained model generates new solutions that are structurally similar to past solutions and are guaranteed to respect the known constraints. We apply our approach to three combinatorial optimization problems with unknown components: the knapsack problem with an unknown reward function, the bipartite matching problem with an unknown objective function, and the single-machine scheduling problem with release times and unknown precedence constraints, with the objective of minimizing average completion time. We demonstrate that transformer models have remarkably strong performance and often produce near-optimal solutions in a fraction of a second. They can be particularly effective in the presence of more complex underlying objective functions and unknown implicit constraints compared to an LSTM-based alternative and inverse optimization.

math.OC↗

arXiv2024

Memory-Efficient Sequential Pattern Mining with Hybrid Tries

This paper develops a memory-efficient approach for Sequential Pattern Mining (SPM), a fundamental topic in knowledge discovery that faces a well-known memory bottleneck for large data sets. Our methodology involves a novel hybrid trie data structure that exploits recurring patterns to compactly store the data set in memory; and a corresponding mining algorithm designed to effectively extract patterns from this compact representation. Numerical results on small to medium-sized real-life test instances show an average improvement of 85% in memory consumption and 49% in computation time compared to the state of the art. For large data sets, our algorithm stands out as the only capable SPM approach within 256GB of system memory, potentially saving 1.7TB in memory consumption.

cs.DB↗

arXiv2019

A Computational Comparison of Optimization Methods for the Golomb Ruler Problem

The Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is minimized. The Golomb ruler problem has applications in information theory, astronomy and communications, and it can be seen as a challenge for combinatorial optimization algorithms. Although constructing high quality rulers is well-studied, proving optimality is a far more challenging task. In this paper, we provide a computational comparison of different optimization paradigms, each using a different model (linear integer, constraint programming and quadratic integer) to certify that a given Golomb ruler is optimal. We propose several enhancements to improve the computational performance of each method by exploring bound tightening, valid inequalities, cutting planes and branching strategies. We conclude that a certain quadratic integer programming model solved through a Benders decomposition and strengthened by two types of valid inequalities performs the best in terms of solution time for small-sized Golomb ruler problem instances. On the other hand, a constraint programming model improved by range reduction and a particular branching strategy could have more potential to solve larger size instances due to its promising parallelization features.

math.OC↗

arXiv2018

Constraint-based Sequential Pattern Mining with Decision Diagrams

Constrained sequential pattern mining aims at identifying frequent patterns on a sequential database of items while observing constraints defined over the item attributes. We introduce novel techniques for constraint-based sequential pattern mining that rely on a multi-valued decision diagram representation of the database. Specifically, our representation can accommodate multiple item attributes and various constraint types, including a number of non-monotone constraints. To evaluate the applicability of our approach, we develop an MDD-based prefix-projection algorithm and compare its performance against a typical generate-and-check variant, as well as a state-of-the-art constraint-based sequential pattern mining algorithm. Results show that our approach is competitive with or superior to these other methods in terms of scalability and efficiency.

cs.LG↗