Abstract:A constraint network representation is presented for a combinatorial search problem: finding values for a set of variables subject to a set of constraints. A theory of consistency levels in such networks is formulated, which is related to problems of backtrack tree search efficiency. An algorithm is developed that can achieve any level of consistency desired, in order to preprocess the problem for subsequent backtrack search, or to function as an alternative to backtrack search by explicitly determining all so… Show more
“…It can be shown that the above consistency techniques are covered by a general notion of (strong) k-consistency [66]. Indeed, NC is equivalent to strong 1-consistency, AC to strong 2-consistency, and PC to strong 3-consistency.…”
Recent research has shown that the performance of a single, arbitrarily efficient algorithm can be significantly outperformed by using a portfolio of -possibly onaverage slower-algorithms. Within the Constraint Programming (CP) context, a portfolio solver can be seen as a particular constraint solver that exploits the synergy between the constituent solvers of its portfolio for predicting which is (or which are) the best solver(s) to run for solving a new, unseen instance.In this thesis we examine the benefits of portfolio solvers in CP. Despite portfolio approaches have been extensively studied for Boolean Satisfiability (SAT) problems, in the more general CP field these techniques have been only marginally studied and used. We conducted this work through the investigation, the analysis and the construction of several portfolio approaches for solving both satisfaction and optimization problems. We focused in particular on sequential approaches, i.e., single-threaded portfolio solvers always running on the same core.We started from a first empirical evaluation on portfolio approaches for solving Constraint Satisfaction Problems (CSPs), and then we improved on it by introducing new data, solvers, features, algorithms, and tools. Afterwards, we addressed the more general Constraint Optimization Problems (COPs) by implementing and testing a number of models for dealing with COP portfolio solvers. Finally, we have come full circle by developing sunny-cp: a sequential CP portfolio solver that turned out to be competitive also in the MiniZinc Challenge, the reference competition for CP solvers.iii iv
“…It can be shown that the above consistency techniques are covered by a general notion of (strong) k-consistency [66]. Indeed, NC is equivalent to strong 1-consistency, AC to strong 2-consistency, and PC to strong 3-consistency.…”
Recent research has shown that the performance of a single, arbitrarily efficient algorithm can be significantly outperformed by using a portfolio of -possibly onaverage slower-algorithms. Within the Constraint Programming (CP) context, a portfolio solver can be seen as a particular constraint solver that exploits the synergy between the constituent solvers of its portfolio for predicting which is (or which are) the best solver(s) to run for solving a new, unseen instance.In this thesis we examine the benefits of portfolio solvers in CP. Despite portfolio approaches have been extensively studied for Boolean Satisfiability (SAT) problems, in the more general CP field these techniques have been only marginally studied and used. We conducted this work through the investigation, the analysis and the construction of several portfolio approaches for solving both satisfaction and optimization problems. We focused in particular on sequential approaches, i.e., single-threaded portfolio solvers always running on the same core.We started from a first empirical evaluation on portfolio approaches for solving Constraint Satisfaction Problems (CSPs), and then we improved on it by introducing new data, solvers, features, algorithms, and tools. Afterwards, we addressed the more general Constraint Optimization Problems (COPs) by implementing and testing a number of models for dealing with COP portfolio solvers. Finally, we have come full circle by developing sunny-cp: a sequential CP portfolio solver that turned out to be competitive also in the MiniZinc Challenge, the reference competition for CP solvers.iii iv
“…All above mentioned consistency techniques are covered by a general notion of k-consistency [39] and strong k-consistency. A constraint graph is k-consistent if for every system of values for k − 1 variables satisfying all the constraints among these variables, there exist a value for arbitrary k-th variable such that the constraints among all k variables are satisfied.…”
We investigate the benefits that emerge when the fields of constraint programming and concurrency meet. On one hand, constraints can be use in concurrency theory to increase the conciseness and the expressive power of concurrent languages from a pragmatic point of view. On the other hand, problems modeled by using constraints can be solved faster and more efficiently using a concurrent system. We explore both directions providing two separate lines of contribution. Firstly we study the expressive power of a concurrent language, namely Constraint Handling Rules, that supports constraints as a primitive construct. We show what features of this language make it Turing powerful. Then we propose a framework to solve constraint problems that is intended to be deployed on a concurrent system. For the development of this framework we used the concurrent language Jolie following the Service Oriented paradigm. Based on this experience, we also propose an extension to Service Oriented Languages to overcome some of their limitations and to improve the development of concurrent applications. Needless to say, I am also in debt with my coauthors:
“…Path-consistency is equivalent to 3-consistency [88] which holds if for every consistent instantiation of two variables it is always possible to find an instantiation for any third variable such that the three variables together are consistent. 3-consistency can be generalised to k-consistency which holds if for any consistent instantiation of k − 1 variables there is always a consistent instantiation for any kth variable.…”
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