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Patrick De Causmaecker

Patrick De Causmaecker appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Artificial Intelligencemath.CODiscrete Mathematicsmath.NT

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Published work

8 published item(s)

preprint2026arXiv

Transforming Constraint Programs to Input for Local Search

Applying local search algorithms to combinatorial optimization problems is not an easy feat. Typically, human intervention is required to compile the constraints to input data for some metaheuristic algorithm. In this paper, we establish a link between symmetry properties of constraint optimization problems and local search neighborhoods, and we use this link to automatically generate neighborhoods from a constraint specification in the context of the IDP system. We evaluate the obtained neighborhoods for six classical optimization problems. The resulting observations support the viability of this technique.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

A multi-start local search algorithm for the Hamiltonian completion problem on undirected graphs

This paper proposes a local search algorithm for a specific combinatorial optimisation problem in graph theory: the Hamiltonian Completion Problem (HCP) on undirected graphs. In this problem, the objective is to add as few edges as possible to a given undirected graph in order to obtain a Hamiltonian graph. This problem has mainly been studied in the context of various specific kinds of undirected graphs (e.g. trees, unicyclic graphs and series-parallel graphs). The proposed algorithm, however, concentrates on solving HCP for general undirected graphs. It can be considered to belong to the category of matheuristics, because it integrates an exact linear time solution for trees into a local search algorithm for general graphs. This integration makes use of the close relation between HCP and the minimum path partition problem, which makes the algorithm equally useful for solving the latter problem. Furthermore, a benchmark set of problem instances is constructed for demonstrating the quality of the proposed algorithm. A comparison with state-of-the-art solvers indicates that the proposed algorithm is able to achieve high-quality results.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Characterization of neighborhood behaviours in a multi-neighborhood local search algorithm

We consider a multi-neighborhood local search algorithm with a large number of possible neighborhoods. Each neighborhood is accompanied by a weight value which represents the probability of being chosen at each iteration. These weights are fixed before the algorithm runs, and are considered as parameters of the algorithm. Given a set of instances, off-line tuning of the algorithm's parameters can be done by automated algorithm configuration tools (e.g., SMAC). However, the large number of neighborhoods can make the tuning expensive and difficult even when the number of parameters has been reduced by some intuition. In this work, we propose a systematic method to characterize each neighborhood's behaviours, representing them as a feature vector, and using cluster analysis to form similar groups of neighborhoods. The novelty of our characterization method is the ability of reflecting changes of behaviours according to hardness of different solution quality regions. We show that using neighborhood clusters instead of individual neighborhoods helps to reduce the parameter configuration space without misleading the search of the tuning procedure. Moreover, this method is problem-independent and potentially can be applied in similar contexts.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Intervals of Antichains and Their Decompositions

An antichain of subsets is a set of subsets such that no subset in the antichain is a proper subset of any other subset in the antichain. The Dedekind number counts the total number of antichains of subsets of an n-element set. This paper investigates the interval structure of the lattice of antichains. Several partitioning theorems and counting formulas for the size of intervals are derived.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Second International Nurse Rostering Competition (INRC-II) --- Problem Description and Rules ---

In this paper, we provide all information to participate to the Second International Nurse Rostering Competition (INRC-II). First, we describe the problem formulation, which, differently from INRC-I, is a multi-stage procedure. Second, we illustrate all the necessary infrastructure do be used together with the participant's solver, including the testbed, the file formats, and the validation/simulation tools. Finally, we state the rules of the competition. All update-to-date information about the competition is available at http://mobiz.vives.be/inrc2/.

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preprint2014arXiv

On the number of antichains of sets in a finite universe

Properties of intervals in the lattice of antichains of subsets of a universe of finite size are investigated. New objects and quantities in this lattice are defined. Expressions and numerical values are deduced for the number of connected antichains and the number of fully distinguishing antichains. The latter establish a connection with Stirling numbers of the second kind. Decomposition properties of intervals in the lattice of antichains are proven. A new operator allowing partitioning the full lattice in intervals derived from lower dimensional sub-lattices is introduced. Special posets underlying an interval of antichains are defined. The poset allows the derivation of a powerful formula for the size of an interval. This formula allows computing intervals in the six dimensional space. Combinatorial coefficients allowing another decomposition of the full lattice are defined. In some specific cases, related to connected components in graphs, these coefficients can be efficiently computed. This formula allows computing the size of the lattice of order 8 efficiently. This size is the number of Dedekind of order 8, the largest one known so far.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Partitioning in the space of antimonotonic functions

This paper studies partitions in the space of antimonotonic boolean functions on sets of n elements. The antimonotonic functions are the antichains of the partially ordered set of subsets. We analyse and characterise a natural partial ordering on this set. We study the inter- vals according to this ordering. We show how intervals of antimonotonic functions, and a fortiori the whole space of antimonotonic functions can be partitioned as disjoint unions of certain classes of intervals. These in- tervals are uniquely determined by antimonotonic functions on smaller sets. This leads to recursive enumeration algorithms and new recursion relations. Using various decompositions, we derive new recursion formu- lae for the number of antimonotonic functions and hence for the number of monotonic functions (i.e. the Dedekind number).

0 citations0 reviewsNo code linkedOpen access