Improving the Asymmetric TSP by Considering Graph Structure

Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based on general graph properties. We experimentally show that such implied propagators bring robustness to pathological instances and highlight the fact that graph structure can significantly improve search heuristics behavior. Finally, we show that our approach outperforms current state of the art results.Comment: Technical repor

Applications of matching theory in constraint programming

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Revisiting the tree Constraint

International audienceThis paper revisits the tree constraint introduced in [2] which partitions the nodes of a n-nodes, m-arcs directed graph into a set of node-disjoint anti-arborescences for which only certain nodes can be tree roots. We introduce a new filtering algorithm that enforces generalized arc-consistency in O(n + m) time while the original filtering algorithm reaches O(nm) time. This result allows to tackle larger scale problems involving graph partitioning

Extension and evaluation of the global cardinality constraints functionality of the Gecode open source toolkit

Ο Προγραμματισμός με Περιορισμούς είναι μια μεθοδολογία της Τεχνητής Νοημοσύνης που αποσκοπεί να επιλύσει πραγματικά προβλήματα με αποτελεσματικό τρόπο. Σε αυ- τή την διπλωματική εργασία, επεκτείνουμε τον επιλυτή προβλημάτων ικανοποίησης περιορισμών ανοιχτού κώδικα Gecode, συνεισφέροντας στις δυνατότητές του σχετικά με Καθολικούς Περιορισμούς, συγκεκριμένα περιορισμούς Global Cardinality. Ένας Global Cardinality περιορισμός περιορίζει τον αριθμό εμφάνισης τιμών μέσα σε μια συλλογή μεταβλητών, ώστε να βρίσκεται μεταξύ συγκεκριμένων ορίων. Αναπτύσσουμε τον περιορισμό Global Cardinality With Costs, ο οποίος είναι παρόμοιος του Global Cardinality και επιπλέον συσχετίζει ένα κόστος με κάθε ανάθεση τιμής σε μεταβλητή, ενώ ταυτόχρονα απαιτεί το άθροισμα των κοστών να μην ξεπερνάει ένα όριο. Στη συνέχεια προσθέτουμε τον περιορισμό Symmetric Global Cardinality, ο οποίος ορίζεται πάνω σε μεταβλητές που αφορούν σύνολα, δίνοντας επιπλέον περιορισμούς γύρω από τον πληθικό αριθμό του κάθε συνόλου, πέραν των περιορισμών που αφορούν τις τιμές. Ερευνούμε τη βελτιστοποίηση της επίδοσής τους, πειραματιζόμενοι με διάφορες εναλλακτικές επιλογές υλοποίησης, και τελικά τους συγκρίνουμε ώστε να ανακαλύψουμε κάτω από ποιές συνθήκες είναι ωφέλιμοι, σε σχέση με την αποσύνθεσή τους σε περισσότερους απλούστερους περιορισμούς.Constraint Programming is an Artificial Intelligence methodology that aims to solve real world problems in an efficient way. In this work, we extend the open source constraint solver Gecode by expanding its features concerning Global Constraints, specifically Global Cardinality Constraints. A Global Cardinality Constraint restricts the value occurrences among a collection of variables, to be between certain bounds. We develop the Global Cardinality Constraint With Costs, which is similar to the Global Cardinality Constraint and additionally associates a cost with each variable-value assignment, while further restricting the sum of the costs related to the assigned variable-value pairs to not exceed a given cost bound. Moreover, we add the Symmetric Global Cardinality Constraint, which is defined on Set variables and introduces additional restrictions on the cardinality of each set, aside from the value occurrences. We attempt to optimize their performance by experimenting with various different implementation choices, and finally we evaluate our constraints to discover under which conditions they are beneficial compared to decomposing them to multiple simpler ones

Distributed constraint satisfaction for coordinating and integrating a large-scale, heterogeneous enterprise

Market forces are continuously driving public and private organisations towards higher productivity, shorter process and production times, and fewer labour hours. To cope with these changes, organisations are adopting new organisational models of coordination and cooperation that increase their flexibility, consistency, efficiency, productivity and profit margins. In this thesis an organisational model of coordination and cooperation is examined using a real life example; the technical integration of a distributed large-scale project of an international physics collaboration. The distributed resource constraint project scheduling problem is modelled and solved with the methods of distributed constraint satisfaction. A distributed local search method, the distributed breakout algorithm (DisBO), is used as the basis for the coordination scheme. The efficiency of the local search method is improved by extending it with an incremental problem solving scheme with variable ordering. The scheme is implemented as central algorithm, incremental breakout algorithm (IncBO), and as distributed algorithm, distributed incremental breakout algorithm (DisIncBO). In both cases, strong performance gains are observed for solving underconstrained problems. Distributed local search algorithms are incomplete and lack a termination guarantee. When problems contain hard or unsolvable subproblems and are tightly or overconstrained, local search falls into infinite cycles without explanation. A scheme is developed that identifies hard or unsolvable subproblems and orders these to size. This scheme is based on the constraint weight information generated by the breakout algorithm during search. This information, combined with the graph structure, is used to derive a fail first variable order. Empirical results show that the derived variable order is 'perfect'. When it guides simple backtracking, exceptionally hard problems do not occur, and, when problems are unsolvable, the fail depth is always the shortest. Two hybrid algorithms, BOBT and BOBT-SUSP are developed. When the problem is unsolvable, BOBT returns the minimal subproblem within the search scope and BOBT-SUSP returns the smallest unsolvable subproblem using a powerful weight sum constraint. A distributed hybrid algorithm (DisBOBT) is developed that combines DisBO with DisBT. The distributed hybrid algorithm first attempts to solve the problem with DisBO. If no solution is available after a bounded number of breakouts, DisBO is terminated, and DisBT solves the problem. DisBT is guided by a distributed variable order that is derived from the constraint weight information and the graph structure. The variable order is incrementally established, every time the partial solution needs to be extended, the next variable within the order is identified. Empirical results show strong performance gains, especially when problems are overconstrained and contain small unsolvable subproblems

Exploiting Global Constraints for Search and Propagation

Résumé Cette thèse se concentre sur la Programmation par contraintes (PPC), qui est un paradigme émergent pour résoudre des problèmes complexes d’optimisation combinatoire. Les principales contributions tournent autour du filtrage des contraintes et de la recherche; les deux sont des composantes cl´e dans la résolution de problèmes complexes à travers la PPC. D’un côté, le filtrage des contraintes permet de réduire la taille de l’espace de recherche, d’autre part, la recherche définit la manière dont cet espace sera exploré. Les progrès sur ces sujets sont essentiels pour élargir l’applicabilité de CP à des problèmes réels. En ce qui concerne le filtrage des contraintes, les contributions sont les suivantes: premièrement, on propose une amélioration sur un algorithme existant de la version relaxée d’une contrainte commune qui apparaît souvent dans les problèmes d’affectation (soft gcc). L’algorithme proposé améliore en termes de complexité soit pour la cohérence, soit pour le filtrage et en termes de facilité d’implémentation. Deuxièmement, on introduit une nouvelle contrainte (soit dure soit relaxée) et les algorithmes de filtrage pour une sous-structure récurrente qui se produit dans les problèmes d’affectation des ressources hétérogènes (hierarchical gcc). Nous montrons des résultats encourageants par rapport à une d´écomposition équivalente basée sur gcc. En ce qui concerne la recherche, nous présentons tout d’abord les algorithmes pour compter le nombre de solutions pour deux importantes familles de contraintes: les contraintes sur les occurrences, par exemple, alldifferent, symmetric alldifferent et gcc, et les contraintes de séquence admissible, telles que regular. Ces algorithmes sont à la base d’une nouvelle famille d’heuristiques de recherche, centrées sur les contraintes et basées sur le d´énombrement. Ces heuristiques extraient des informations sur le nombre de solutions des contraintes, pour guider la recherche vers des parties de l’espace de recherche qui contiennent probablement un grand nombre de solutions. Les résultats expérimentaux sur huit différents problèmes montrent une performance impressionnante par rapport à l’état de l’art des heuristiques génériques. Enfin, nous expérimentons une forme forte, déjà connue, de filtrage qui est guidée par la recherche (quick shaving). Cette technique donne des résultats soit encourageants soit mauvais lorsqu’elle est appliquée aveuglément à tous les problèmes. Nous avons introduit un estimateur simple mais très efficace pour activer ou désactiver dynamiquement le quick shaving; de tests expérimentaux ont montré des résultats très prometteurs.----------Abstract This thesis focuses on Constraint Programming (CP), that is an emergent paradigm to solve complex combinatorial optimization problems. The main contributions revolve around constraint filtering and search that are two main components of CP. On one side, constraint filtering allows to reduce the size of the search space, on the other, search defines how this space will be explored. Advances on these topics are crucial to broaden the applicability of CP to real-life problems. For what concerns constraint filtering, the contribution is twofold: we firstly propose an improvement on an existing algorithm of the relaxed version of a constraint that frequently appears in assignment problems (soft gcc). The algorithm proposed outperforms the previously known in terms of time-complexity both for the consistency check and for the filtering and in term of ease of implementiation. Secondly, we introduce a new constraint (both hard and soft version) and associated filtering algorithms for a recurrent sub-structure that occurs in assignment problems with heterogeneous resources (hierarchical gcc). We show promising results when compared to an equivalent decomposition based on gcc. For what concerns search, we introduce algorithms to count the number of solutions for two important families of constraints: occurrence counting constraints, such as alldifferent, symmetric alldifferent and gcc, and sequencing constraints, such as regular. These algorithms are the building blocks of a new family of search heuristics, called constraint-centered counting-based heuristics. They extract information about the number of solutions the individual constraints admit, to guide search towards parts of the search space that are likely to contain a high number of solutions. Experimental results on eight different problems show an impressive performance compared to other generic state-of-the-art heuristics. Finally, we experiment on an already known strong form of constraint filtering that is heuristically guided by the search (quick shaving). This technique gives mixed results when applied blindly to any problem. We introduced a simple yet very effective estimator to dynamically disable quick shaving and showed experimentally very promising results

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing