scholarly journals Towards a Closer Integration of Dynamic Programming and Constraint Programming

10.29007/gscn ◽  
2018 ◽  
Author(s):  
Steven Prestwich ◽  
Roberto Rossi ◽  
S. Armagan Tarim ◽  
Andrea Visentin
Keyword(s):  
Dynamic Programming ◽  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Constraint Satisfaction Problem ◽  
Network Interdiction ◽  
Global Constraints ◽  
Tree Search ◽  
Bilevel Optimisation

Three connections between Dynamic Programming (DP) and Constraint Programming (CP) have previously been explored in the literature: DP-based global constraints, DP- like memoisation during tree search to avoid recomputing results, and subsumption of both by bucket elimination. In this paper we propose a new connection: many discrete DP algorithms can be directly modelled and solved as a constraint satisfaction problem (CSP) without backtracking. This has applications including the design of monolithic CP models for bilevel optimisation. We show that constraint filtering can occur between leader and follower variables in such models, and demonstrate the method on network interdiction.

scholarly journals System Sizing with a Model-Based Approach: Application to the Optimization of a Power Transmission System

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Pierre-Alain Yvars ◽  
Laurent Zimmer
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Power Transmission ◽  
Constraint Satisfaction Problem ◽  
Transmission System ◽  
System Description ◽  
Model Based ◽  
Power Transmission System ◽  
Design Requirements ◽  
Interval Constraint

We test the relevance of a model-based approach for sizing and optimizing complex systems. Classically a model-based approach is characterized by a clear partition between the problem description and the solving process. In the case of a design problem, we show that the sizing task could be systematically characterized and therefore could lead to a declarative model combining both system description and design requirements. Once translated into a constraint satisfaction problem, the resulting model can be solved with interval constraint programming methods and algorithms. Our first contribution to this approach is to precisely characterize the sizing task in design. The resulting terminology enables us to easily and systematically express the problem as a constraint satisfaction problem (CSP) which combines in the same model the system description and the design requirements. We have tested the approach on the optimal sizing problem of a power transmission system. Previous authors have described this scalable case study. They provide a mathematical formulation of the problem and solve it with an evolutionary algorithm. Starting from their description, we apply our methodology to model the problem as a CSP and then solve it with interval constraint programming algorithms. Our solutions are more adequate both in computational time and in optimization results than those published in the literature on the same problem. Moreover the declarative nature of constraint programming makes modifications or extensions easier than with evolutionary programming. The explanation of these results is our second contribution to the approach. However some important modelling issues remain to address in order to capture more and more complex system specifications. Further research is presented at the end of this paper.

scholarly journals On the Subexponential-Time Complexity of CSP

2015 ◽  
Vol 52 ◽  
pp. 203-234 ◽  
Author(s):  
Ronald De Haan ◽  
Iyad Kanj ◽  
Stefan Szeider
Keyword(s):  
Constraint Satisfaction ◽  
Time Complexity ◽  
Constraint Satisfaction Problem ◽  
Structural Parameters ◽  
Constraint Satisfaction Problems ◽  
Global Constraints ◽  
Brute Force ◽  
Subexponential Time ◽  
Complete Problems ◽  
Np Complete

Not all NP-complete problems share the same practical hardness with respect to exact computation. Whereas some NP-complete problems are amenable to efficient computational methods, others are yet to show any such sign. It becomes a major challenge to develop a theoretical framework that is more fine-grained than the theory of NP-completeness, and that can explain the distinction between the exact complexities of various NP-complete problems. This distinction is highly relevant for constraint satisfaction problems under natural restrictions, where various shades of hardness can be observed in practice. Acknowledging the NP-hardness of such problems, one has to look beyond polynomial time computation. The theory of subexponential-time complexity provides such a framework, and has been enjoying increasing popularity in complexity theory. An instance of the constraint satisfaction problem with n variables over a domain of d values can be solved by brute-force in dn steps (omitting a polynomial factor). In this paper we study the existence of subexponential-time algorithms, that is, algorithms running in do(n) steps, for various natural restrictions of the constraint satisfaction problem. We consider both the constraint satisfaction problem in which all the constraints are given extensionally as tables, and that in which all the constraints are given intensionally in the form of global constraints. We provide tight characterizations of the subexponential-time complexity of the aforementioned problems with respect to several natural structural parameters, which allows us to draw a detailed landscape of the subexponential-time complexity of the constraint satisfaction problem. Our analysis provides fundamental results indicating whether and when one can significantly improve on the brute-force search approach for solving the constraint satisfaction problem.

Distributed Resource Allocation

2012 ◽  
Vol 4 (2) ◽  
pp. 49-62
Author(s):  
Kamal Moummadi ◽  
Rachida Abidar ◽  
Hicham Medromi
Keyword(s):  
Decision Support ◽  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Constraint Satisfaction Problem ◽  
Data Communication ◽  
Communication Technologies ◽  
Multi Agent System ◽  
Agent System ◽  
Distributed Resource Allocation ◽  
Multi Agent

The growth of technological capabilities of mobile devices, the evolution of wireless communication technologies, and the maturity of embedded systems contributed to expand the Machine to machine (M2M) concept. M2M refers to data communication between machines without human intervention. The objective of this paper is to present the grand schemes of a model to be used in an agricultural Decision support System. The authors start by explaining and justifying the need for a hybrid system that uses both Multi-Agent System (MAS) and Constraint Programming (CP) paradigms. Then, the authors propose an approach for Constraint Programming and Multi-Agent System mixing based on controller agent concept. The authors present concrete constraints and agents to be used in a distributed architecture based on the proposed approach for M2M services and agricultural decision support. The platform is built in Java using general interfaces of both MAS and Constraint Satisfaction Problem (CSP) platforms and the conception is made by agent UML (AUML).

scholarly journals Compact representation of constraints based on a new interpretation of the concept "tuple of a multi-place relation"

2020 ◽  
Vol 10 (4) ◽  
pp. 503-515
Author(s):  
A.A. Zuenko ◽  
◽  
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Global Constraints ◽  
Compact Representation ◽  
Production Rules ◽  
Memory Consumption ◽  
Traditional Concept ◽  
New Type ◽  
Points Of View ◽  
New Interpretation

The article discusses various points of view on the concept of "tuple of a multi-place relation" used in mathematics and information technology. Special attention is paid to an evolution of the concept “tuple” within Constraint Programming technology where the emergence of new interpretations for the concept “tuple” is related with attempts to design more “compact” table representation of qualitative relations comparing with typical relational tables. This “compact” representation can serve as a basis for accelerating qualitative constraint satisfaction procedures. In studied prototype-works, such varieties of table constraints as compressed-tables and smart-tables were proposed. In so doing, the concept of compressed- and smart- tuple substantially differs from traditional concept of tuple of a multi-place relation. However, the known table constraints types are not well suited for modeling and processing all types of quality relations, for example, there are inconveniences when modeling production rules. The article proposes a new type of table constraints – smart-tables of D-type and equivalent transformations rules allowing the initial constraint satisfaction problem to be effectively reduced. The application of the smart-tables of D-type allows in some cases to substantially reduce computer memory consumption comparing with application of the known types of table constraints. In particular, smart-tables of D-types are well suited for modeling production rules, some types of logical expirations and some types of global constraints.

scholarly journals Local Consistency and SAT-Solvers

2012 ◽  
Vol 43 ◽  
pp. 329-351 ◽  
Author(s):  
P. Jeavons ◽  
J. Petke
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Inference Rule ◽  
Constraint Satisfaction Problem ◽  
Constraint Satisfaction Problems ◽  
Fixed Size ◽  
Local Consistency ◽  
Sat Solvers ◽  
Clause Learning ◽  
Do So

Local consistency techniques such as k-consistency are a key component of specialised solvers for constraint satisfaction problems. In this paper we show that the power of using k-consistency techniques on a constraint satisfaction problem is precisely captured by using a particular inference rule, which we call negative-hyper-resolution, on the standard direct encoding of the problem into Boolean clauses. We also show that current clause-learning SAT-solvers will discover in expected polynomial time any inconsistency that can be deduced from a given set of clauses using negative-hyper-resolvents of a fixed size. We combine these two results to show that, without being explicitly designed to do so, current clause-learning SAT-solvers efficiently simulate k-consistency techniques, for all fixed values of k. We then give some experimental results to show that this feature allows clause-learning SAT-solvers to efficiently solve certain families of constraint problems which are challenging for conventional constraint-programming solvers.

scholarly journals Permutation groups with small orbit growth

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Manuel Bodirsky ◽  
Bertalan Bodor
Keyword(s):  
Automorphism Group ◽  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Permutation Groups ◽  
First Order ◽  
Finite Covers

Abstract Let K exp + \mathcal{K}_{{\operatorname{exp}}{+}} be the class of all structures 𝔄 such that the automorphism group of 𝔄 has at most c ⁢ n d ⁢ n cn^{dn} orbits in its componentwise action on the set of 𝑛-tuples with pairwise distinct entries, for some constants c , d c,d with d < 1 d<1 . We show that K exp + \mathcal{K}_{{\operatorname{exp}}{+}} is precisely the class of finite covers of first-order reducts of unary structures, and also that K exp + \mathcal{K}_{{\operatorname{exp}}{+}} is precisely the class of first-order reducts of finite covers of unary structures. It follows that the class of first-order reducts of finite covers of unary structures is closed under taking model companions and model-complete cores, which is an important property when studying the constraint satisfaction problem for structures from K exp + \mathcal{K}_{{\operatorname{exp}}{+}} . We also show that Thomas’ conjecture holds for K exp + \mathcal{K}_{{\operatorname{exp}}{+}} : all structures in K exp + \mathcal{K}_{{\operatorname{exp}}{+}} have finitely many first-order reducts up to first-order interdefinability.

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