This paper summarizes the main existing approaches to propagate resource constraints in Constraint-Based scheduling and identifies some of their limitations for using them in an integrated planning and scheduling framework. We then describe two new algorithms to propagate resource constraints on discrete resources and reservoirs. Unlike most of the classical work in scheduling, our algorithms focus on the precedence relations between activities rather than on their absolute position in time. They are efficient even when the set of activities is not completely defined and when the time window of activities is large. These features explain why our algorithms are particularly suited for integrated planning and scheduling approaches. All our algorithms are illustrated with examples. Encouraging preliminary results are reported on pure scheduling problems.

The cutting plane method is an augmentative constrained optimization procedure that is often used with continuous-domain optimization techniques such as linear and convex programs. We investigate the viability of a similar idea within message passing -- which produces integral solutions -- in the context of two combinatorial problems: 1) For Traveling Salesman Problem (TSP), we propose a factor-graph based on Held-Karp formulation, with an exponential number of constraint factors, each of which has an exponential but sparse tabular form. 2) For graph-partitioning (a.k.a., community mining) using modularity optimization, we introduce a binary variable model with a large number of constraints that enforce formation of cliques. In both cases we are able to derive surprisingly simple message updates that lead to competitive solutions on benchmark instances. In particular for TSP we are able to find near-optimal solutions in the time that empirically grows with N^3, demonstrating that augmentation is practical and efficient.

The constraint satisfaction problem (CSP) is a computational problem in which one is to decide, given a set of constraints on variables, whether or not there is an assignment to the variables satisfying all of the constraints. This problem appears in many guises throughout computer science, for instance, in database theory, artificial intelligence, and the study of graph homomorphisms. One obtains a rich and natural family of problems by defining, for each relational structure B, the problem CSP(B) to be the case of the CSP where the relations used to specify constraints must come fromB. An increasing literature studies the algorithmic and complexity behavior of this problem family, focusing on finite and finite-like structures [1, 12, 2]; a primary research issue is to determine which such problems are polynomial-time tractable, and which are not. To this end of classifying problems, a so-called algebraic approach has been quite fruitful [5]. In short, this approach is founded on the facts that the complexity of a problem CSP(B) depends (up to polynomial-time reducibility) only on the set of relations that are primitive positive definable from B, and that this set of relations can be derived from the clone of polymorphisms ofB. Hence, the project of classifying all relational structures according to the complexity of CSP(B) can be formulated as a classification question on clones; 1 this permits the employment of algebraic notions and techniques in this project.

In this paper we present SUNNY: a simple and flexible algorithm that takes advantage of a portfolio of constraint solvers in order to compute -- without learning an explicit model -- a schedule of them for solving a given Constraint Satisfaction Problem (CSP). Motivated by the performance reached by SUNNY vs. different simulations of other state of the art approaches, we developed sunny-csp, an effective portfolio solver that exploits the underlying SUNNY algorithm in order to solve a given CSP. Empirical tests conducted on exhaustive benchmarks of MiniZinc models show that the actual performance of sunny-csp conforms to the predictions. This is encouraging both for improving the power of CSP portfolio solvers and for trying to export them to fields such as Answer Set Programming and Constraint Logic Programming.

Ordinal conditional functions (OCFs) provide a semantic domain for qualitative conditionals of the form "if A, then (normally) B" by ordering worlds according to their degree of surprise. Transferring the idea of maximum entropy to a more qualitative domain, c-representations of a knowledge base R consisting of a set of conditionals have been defined as OCFs satisfying in particular the property of conditional indifference. While c-representations for R can be specified as the solutions of a constraint satisfaction problem CR(R), it has been an open problem whether there may be different minimal c-representations induced by minimal solutions of CR(R). Another open question has been whether particular inequations in CR(R) may be sharpened by transforming them into equations without loosing any minimal solutions, taking different notions of minimality into account. In this paper, we answer both questions and discuss further aspects of OCF minimality.

Game Theory studies situations in which multiple agents having conflicting objectives have to reach a collective decision. The question of a compact representation language for agents utility function is of crucial importance since the classical representation of a $n$-players game is given by a $n$-dimensional matrix of exponential size for each player. In this paper we use the framework of Constraint Games in which CSP are used to represent utilities. Constraint Programming --including global constraints-- allows to easily give a compact and elegant model to many useful games. Constraint Games come in two flavors: Constraint Satisfaction Games and Constraint Optimization Games, the first one using satisfaction to define boolean utilities. In addition to multimatrix games, it is also possible to model more complex games where hard constraints forbid certain situations. In this paper we study complete search techniques and show that our solver using the compact representation of Constraint Games is faster than the classical game solver Gambit by one to two orders of magnitude.

We propose a timed and soft extension of Concurrent Constraint Programming. The time extension is based on the hypothesis of bounded asynchrony: the computation takes a bounded period of time and is measured by a discrete global clock. Action prefixing is then considered as the syntactic marker which distinguishes a time instant from the next one. Supported by soft constraints instead of crisp ones, tell and ask agents are now equipped with a preference (or consistency) threshold which is used to determine their success or suspension. In the paper we provide a language to describe the agents behavior, together with its operational and denotational semantics, for which we also prove the compositionality and correctness properties. After presenting a semantics using maximal parallelism of actions, we also describe a version for their interleaving on a single processor (with maximal parallelism for time elapsing). Coordinating agents that need to take decisions both on preference values and time events may benefit from this language. To appear in Theory and Practice of Logic Programming (TPLP).

We describe a constraint-based timetabling system that was developed for the dental school based at Cork University Hospital in Ireland. Dental school timetabling differs from other university course scheduling in that certain clinic sessions can be used by multiple courses at the same time, provided a limit on room capacity is satisfied. Solutions for the years 2010, 2011 and 2012 have been used in the dental school, replacing a manual timetabling process, which could no longer cope with increasing student numbers and resulting resource bottlenecks. The use of the automated system allowed the dental school to increase the number of students enrolled to the maximum possible given the available resources.

We describe a constraint-based timetabling system that was developed for the dental school based at Cork University Hospital in Ireland. This sy stem has been deployed since 2010. Dental school timetabling differs from other university course scheduling in that certain clinic sessions can be used by multiple courses at the same time, provided a limit on room capacity is satisfied. Starting from a constraint programming solution using a web interface, we have moved to a mixed integer programming-based solver to deal with multiple objective functions, along with a dedicated Java application, which provides a rich user interface. Solutions for the years 2010, 2011 and 2012 have been used in the dental school, replacing a manual timetabling process, which could no longer cope with increasing student numbers and resulting resource bottlenecks. The use of the automated system allowed the dental school to increase the number of students enrolled to the maximum possible given the available resources. It also provides the school with a valuable “what-if” analysis tool.

Recent research has shown that a single arbitrarily efficient solver can be significantly outperformed by a portfolio of possibly slower on-average solvers. The solver selection is usually done by means of (un)supervised learning techniques which exploit features extracted from the problem specification. In this paper we present an useful and flexible framework that is able to extract an extensive set of features from a Constraint (Satisfaction/Optimization) Problem defined in possibly different modeling languages: MiniZinc, FlatZinc or XCSP. We also report some empirical results showing that the performances that can be obtained using these features are effective and competitive with state of the art CSP portfolio techniques.