Sonet Network Design Problems

This paper presents a new method and a constraint-based objective function to solve two problems related to the design of optical telecommunication networks, namely the Synchronous Optical Network Ring Assignment Problem (SRAP) and the Intra-ring Synchronous Optical Network Design Problem (IDP). These network topology problems can be represented as a graph partitioning with capacity constraints as shown in previous works. We present here a new objective function and a new local search algorithm to solve these problems. Experiments conducted in Comet allow us to compare our method to previous ones and show that we obtain better results

Octagonal Domains for Continuous Constraints

International audienceDomains in Continuous Constraint Programming (CP) are generally represented with intervals whose $n$-ary Cartesian product (box) approximates the solution space. This paper proposes a new representation for continuous variable domains based on octagons. We generalize local consistency and split to this octagon representation, and we propose an octagonal-based branch and prune algorithm. Preliminary experimental results show promising performance improvements on several classical benchmarks

Learning sequential and parallel runtime distributions for randomized algorithms

In cloud systems, computation time can be rented by the hour and for a given number of processors. Thus, accurate predictions of the behaviour of both sequential and parallel algorithms has become an important issue, in particular in the case of costly methods such as randomized combinatorial optimization tools. In this work, our objective is to use machine learning to predict performance of sequential and parallel local search algorithms. In addition to classical features of the instances used by other machine learning tools, we consider data on the sequential runtime distributions of a local search method. This allows us to predict with a high accuracy the parallel computation time of a large class of instances, by learning the behaviour of the sequential version of the algorithm on a small number of instances. Experiments with three solvers on SAT and TSP instances indicate that our method works well, with a correlation coefficient of up to 0.85 for SAT instances and up to 0.95 for TSP instances

Un modèle markovien pour GSAT et WalkSAT résultats préliminaires

National audienceLes algorithmes GSAT et WalkSAT ont un comportement, bien connu expérimentalement, mais relativement peu étudié théoriquement. Nous étudions ici un modèle de GSAT et WalkSAT sous la forme de chaînes de Markov, modèle exact pour la partie gloutonne, approché pour la version avec random restart. Les résultats classiques sur les chaînes de Markov permettent d'en déduire deux nouvelles majorations de l'espérance du temps de calcul de WalkSAT sans random restart, en fonction des valeurs propres de la matrice de transition associée. Nous montrons expérimentalement sur de petites instances que cette borne permet de retrouver le paramétrage optimal observé dans la littérature. Nous donnons ensuite deux résultats sur l'espérance de GSAT ou Walk-SAT avec random restart en fonction du nombre d'itérations avant random restart (entre autres). Même si les résultats restent à approfondir, ce modèle donne une piste vers une étude théorique du paramétrage optimal et, au delà, du comportement de ces algorithmes

Modular Constraint Solver Cooperation via Abstract Interpretation

Cooperation among constraint solvers is difficult because different solving paradigms have different theoretical foundations. Recent works have shown that abstract interpretation can provide a unifying theory for various constraint solvers. In particular, it relies on abstract domains which capture constraint languages as ordered structures. The key insight of this paper is viewing cooperation schemes as abstract domains combinations. We propose a modular framework in which solvers and cooperation schemes can be seamlessly added and combined. This differs from existing approaches such as SMT where the cooperation scheme is usually fixed (e.g., Nelson-Oppen). We contribute to two new cooperation schemes: (i) interval propagators completion that allows abstract domains to exchange bound constraints, and (ii) delayed product which exchanges over-approximations of constraints between two abstract domains. Moreover, the delayed product is based on delayed goal of logic programming, and it shows that abstract domains can also capture control aspects of constraint solving. Finally, to achieve modularity, we propose the shared product to combine abstract domains and cooperation schemes. Our approach has been fully implemented, and we provide various examples on the flexible job shop scheduling problem. Under consideration for acceptance in TPLP.Comment: Paper presented at the 36th International Conference on Logic Programming (ICLP 2020), University Of Calabria, Rende (CS), Italy, September 2020, 17 pages. v2: Fix an example in Section 3.2 (improved closure

Prediction of Parallel Speed-ups for Las Vegas Algorithms

International audienceWe propose a probabilistic model for the parallel execution of Las Vegas algorithms, i.e. randomized algorithms whose runtime might vary from one execution to another, even with the same input. This model aims at predicting the parallel performances (i.e. speedups) by analysis the runtime distribution of the sequential runs of the algorithm. Then, we study in practice the case of a particular Las Vegas algorithm for combinatorial optimization on three classical problems, and compare the model with an actual parallel implementation up to 256 cores. We show that the prediction can be accurate, matching the actual speedups very well up to 100 parallel cores and then with a deviation of about 20% up to 256 cores

Contraintes sur des flux appliquées a la vérification de programmes audio

National audienceLa programmation par contraintes s'attaque en gé-néraì a desprobì emes statiques, sans notion de temps. Cependant, les méthodes de réduction de domaines pourraient par exemplê etre utiles dans desprobì emes portant sur des flux. C'est le cas de la vérification de programmes temps-réel, avec des variables dont les valeurs peuvent changer a chaque pas de temps. Dans cet article, nous nous intéressons a la vérification de domaines de variables (flux) dans le cadre d'un langage de diagrammes de blocs. Nous proposons une méthode de réduction de domaines de ces flux, pour encadrer finement les valeurs prises au cours du temps. En particulier, nous proposons un nouvel algorithme pour calculer un point fixe dans le cas des boucles temporelles. Nous présentons ensuite une application au langage FAUST, un langage fonctionnel temps réel pour le traitement audio et nous testons notre approche sur différents programmes FAUST standards. Abstract Constraint programming usually deals with static problems. However, domain reduction method could be useful in stream-based problems. This is the case in formal verification of real time programs for which variables can be assigned different values at every single time. In this paper, we focus on domain checking of stream variables in the context of block diagram languages. We propose a reduction algorithm for streams in order to tightly reduce their domains all over the time. Particularly , we propose a new technique to compute fix points of temporal loops. Finally, we apply our method to the FAUST language, which is a real time language for processing and generating audio streams. We also test some standards FAUST programs

Solution Sampling with Random Table Constraints

International audienceConstraint programming provides generic techniques to efficiently solve combinatorial problems. In this paper, we tackle the natural question of using constraint solvers to sample combinatorial problems in a generic way. We propose an algorithm, inspired from Meel's ApproxMC algorithm on SAT, to add hashing constraints to a CP model in order to split the search space into small cells. By uniformly sampling the solutions in one cell, we can generate random solutions without revamping the model of the problem. We ensure the randomness by introducing a new family of hashing constraints: randomly generated tables, which keeps the cost of the hashing process tractable. We implemented this solving method using the constraint solver Choco-solver. The quality of the randomness and the running time of our approach are experimentally compared to a random branching strategy. We show that our approach improves the randomness while being in the same order of magnitude in terms of running time. We also use our algorithm with an other, more powerful, set of hashing constraints: linear modular equalities. We experimentally show that the resulting sampling is uniform, at the cost of a longer running time

Revisiting Counting Solutions for the Global Cardinality Constraint

International audienceCounting solutions for a combinatorial problem has been identified as an important concern within the Artificial Intelligence field. It is indeed very helpful when exploring the structure of the solution space. In this context, this paper revisits the computation process to count solutions for the global cardinality constraint in the context of counting-based search. It first highlights an error and then presents a way to correct the upper bound on the number of solutions for this constraint