An adaptive CP method for TSP solving

M. Sellmann showed that CP-based Lagrangian relaxation gave good results but the interactions between the two techniques were quite dicult to understand. There are two main reasons for this: the best multipliers do not lead to the best ltering and each ltering disrupts the Lagrangian multiplier problem (LMP) to be solved. As the resolution of the TSP in CP is mainly based on a Lagrangian relaxation, we propose to study in detail these interactions for this particular problem. This article experimentally conrms the above statements and shows that it is very dicult to establish any relationship between ltering and the method used to solve the LMP in practice. Thus, it seems very dicult to select a priori the best method suited for a given instance. We propose to use a multi-armed bandit algorithm to nd the best possible method to use. The experimental results show the advantages of our approach

Efficient Operations On MDDs For Building Constraint Programming Models

International audienceWe propose improved algorithms for defining the most common operations on Multi-Valued Decision Diagrams (MDDs): creation, reduction, complement , intersection, union, difference, symmetric difference, complement of union and complement of intersection. Then, we show that with these algorithms and thanks to the recent development of an efficient algorithm establishing arc consistency for MDD based constraints (MDD4R), we can simply solve some problems by modeling them as a set of operations between MDDs. We apply our approach to the regular constraint and obtain competitive results with dedicated algorithms. We also experiment our technique on a large scale problem: the phrase generation problem and we show that our approach gives equivalent results to those of a specific algorithm computing a complex automaton

A note on arithmetic constraint propagation

We consider the resolution by constraint programming of large problems, i.e. involving millions of constraints, which mainly imply arithmetic constraints, like shortest path problems or other related problems. We show that a simple constraint programming model is not competitive with dedicated algorithms (or dedicated constraints). This mainly comes from the propagation mechanism, i.e. the ordering along which the constraints are revised. Thus, we propose a modification of this propagation mechanism integrating the main ideas of the dedicated algorithms. We give some experiments for the shortest path problem and more general problems which confirms the robustness of our approach. Last, we give some results showing that only a few variables are considered more than once during a propagation step

Beyond C<i>max</i>: an optimization-oriented framework for constraint-based scheduling

This paper presents a framework taking advantage of both the flexibility of constraint programming and the efficiency of operations research algorithms for solving scheduling problems under various objectives and constraints. Built upon a constraint programming engine, the framework allows the use of scheduling global constraints, and it offers, in addition, a modular and simplified way to perform optimality reasoning based on well-known scheduling relaxations. We present a first instantiation on the single machine problem with release dates and lateness minimization. Beyond the simplicity of use, the ptimizationoriented framework appears to be, from the experiments, effective for dealing with such a pure problem even without any ad-hoc heuristics

Beyond C<i>max</i>: an optimization-oriented framework for constraint-based scheduling

This paper presents a framework taking advantage of both the flexibility of constraint programming and the efficiency of operations research algorithms for solving scheduling problems under various objectives and constraints. Built upon a constraint programming engine, the framework allows the use of scheduling global constraints, and it offers, in addition, a modular and simplified way to perform optimality reasoning based on well-known scheduling relaxations. We present a first instantiation on the single machine problem with release dates and lateness minimization. Beyond the simplicity of use, the ptimizationoriented framework appears to be, from the experiments, effective for dealing with such a pure problem even without any ad-hoc heuristics

Introduction de contraintes structurelles pour la résolution du problème du voyageur de commerce

Plusieurs modèles basés sur la programmation par contraintes ont été proposés pour résoudre le problème du voyageur de commerce (TSP). Les plus efficaces, telle que la weighted circuit constraint (WCC), s'appuient prin-cipalement sur la relaxation lagrangienne du TSP, basée sur la recherche d'arbres recouvrants ou plus précisément de "one-trees". Le défaut de cette méthode est qu'elle n'inclut pas assez de contraintes structurelles et se base presque exclusivement sur les coûts des arêtes. L'objectif de cet article est de corriger ce défaut. Aussi, nous cherchons des motifs empêchant l'existence d'un cycle hamiltonien dans un graphe ou, à l'inverse, des motifs imposant que certaines arêtes soient dans l'ensemble de solutions du TSP. Nous proposons un propagateur basé sur la recherche de k-cutsets pour la contrainte de cycle hamiltonien. Sa combinaison avec la contrainte WCC permet d'obtenir, pour la résolution du TSP, des gains d'un ordre de magnitude pour le nombre de backtracks ainsi qu'une forte réduction du temps de calcul

Constraints First: A New MDD-based Model to Generate Sentences Under Constraints

This paper introduces a new approach to generating strongly constrained texts. We consider standardized sentence generation for the typical application of vision screening. To solve this problem, we formalize it as a discrete combinatorial optimization problem and utilize multivalued decision diagrams (MDD), a well-known data structure to deal with constraints. In our context, one key strength of MDD is to compute an exhaustive set of solutions without performing any search. Once the sentences are obtained, we apply a language model (GPT-2) to keep the best ones. We detail this for English and also for French where the agreement and conjugation rules are known to be more complex. Finally, with the help of GPT-2, we get hundreds of bona-fide candidate sentences. When compared with the few dozen sentences usually available in the well-known vision screening test (MNREAD), this brings a major breakthrough in the field of standardized sentence generation. Also, as it can be easily adapted for other languages, it has the potential to make the MNREAD test even more valuable and usable. More generally, this paper highlights MDD as a convincing alternative for constrained text generation, especially when the constraints are hard to satisfy, but also for many other prospects.Comment: To be published in Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence, IJCAI 202

Generating all Possible Palindromes from Ngram Corpora

International audienceWe address the problem of generating all possible palindromes from a corpus of Ngrams. Palin-dromes are texts that read the same both ways. Short palindromes (" race car ") usually carry precise , significant meanings. Long palindromes are often less meaningful, but even harder to generate. The palindrome generation problem has never been addressed, to our knowledge, from a strictly combinatorial point of view. The main difficulty is that generating palindromes require the simultaneous consideration of two interrelated levels in a sequence: the " character " and the " word " levels. Although the problem seems very combina-torial, we propose an elegant yet non-trivial graph structure that can be used to generate all possible palindromes from a given corpus of Ngrams, with a linear complexity. We illustrate our approach with short and long palindromes obtained from the Google Ngram corpus. We show how we can control the semantics, to some extent, by using arbitrary text corpora to bias the probabilities of certain sets of words. More generally this work addresses the issue of modelling human virtuosity from a combinatorial viewpoint, as a means to understand human creativity

Cardinality Reasoning for Bin-Packing Constraint: Application to a Tank Allocation Problem

International audienceFlow reasoning has been successfully used in CP for more than a decade. It was originally introduced by Régin in the well-known Alldifferent and Global Cardinality Constraint (GCC) available in most of the CP solvers. The BinPacking constraint was introduced by Shaw and mainly uses an independent knapsack reasoning in each bin to filter the possible bins for each item. This paper considers the use of a cardinal-ity/flow reasoning for improving the filtering of a bin-packing constraint. The idea is to use a GCC as a redundant constraint to the BinPacking that will count the number of items placed in each bin. The cardinality variables of the GCC are then dynamically updated during the propagation. The cardinality reasoning of the redundant GCC makes deductions that the bin-packing constraint cannot see since the placement of all items into every bin is considered at once rather than for each bin individually. This is particularly well suited when a minimum loading in each bin is specified in advance. We apply this idea on a Tank Allocation Problem (TAP). We detail our CP model and give experimental results on a real-life instance demonstrating the added value of the cardinality reasoning for the bin-packing constraint. This constraint enforces the relation L j = i (X i = j) · w i , ∀j. It makes the link between n weighted items (item i has a weight w i) and the m different capacitated bins in which they are to be put. Only the weights of the items are integers, the other arguments of the constraints are finite domain (f.d.) variables. Note that in this formulation, Lj is a variable which is bounded by the maximal capacity of the bin j. Without loss of generality we assume the item variables and their weights are sorted such that w i ≤ w i+1. Example: BinP acking([1, 4, 1, 2, 2], [2, 3, 3, 3, 4], [5, 7, 0, 3])