scholarly journals Minimizing Cost Travel in Multimodal Transport Using Advanced Relation Transitive Closure

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Rachid Oucheikh ◽  
Ismail Berrada ◽  
Lahcen Omari
Keyword(s):  
Binary Relation ◽  
Constraint Satisfaction ◽  
Operations Research ◽  
Transitive Closure ◽  
Constraint Satisfaction Problem ◽  
Cost Optimization ◽  
Binary Relations ◽  
Mathematical Background ◽  
Multimodal Transport ◽  
Binary Constraint

The optimization computation is an essential transversal branch of operations research which is primordial in many technical fields: transport, finance, networks, energy, learning, etc. In fact, it aims to minimize the resource consumption and maximize the generated profits. This work provides a new method for cost optimization which can be applied either on path optimization for graphs or on binary constraint reduction for Constraint Satisfaction Problem (CSP). It is about the computing of the “transitive closure of a given binary relation with respect to a property.” Thus, this paper introduces the mathematical background for the transitive closure of binary relations. Then, it gives the algorithms for computing the closure of a binary relation according to another one. The elaborated algorithms are shown to be polynomial. Since this technique is of great interest, we show its applications in some important industrial fields.

On transitive subrelations of binary relations

2011 ◽  
Vol 76 (4) ◽  
pp. 1429-1440 ◽  
Author(s):  
Christopher S. Hardin
Keyword(s):  
Binary Relation ◽  
Transitive Closure ◽  
Infinite Chain ◽  
Binary Relations ◽  
Transitive Relation

AbstractThe transitive closure of a binary relation R can be thought of as the best possible approximation of R “from above” by a transitive relation. We consider the question of approximating a relation from below by transitive relations. Our main result is that every thick relation (a relation whose complement contains no infinite chain) on a countable set has a transitive thick subrelation. This allows for a solution to a problem arising from previous work by the author and Alan Taylor. We also exhibit a thick relation on an uncountable set with no transitive thick subrelation.

scholarly journals Optimal haplotype reconstruction in half-sib families

10.29007/rpn1 ◽  
2018 ◽  
Author(s):  
Aurélie Favier ◽  
Jean-Michel Elsen ◽  
Simon de Givry ◽  
Andrés Legarra
Keyword(s):  
Constraint Satisfaction ◽  
Marker Assisted Selection ◽  
Genetic Improvement ◽  
Constraint Satisfaction Problem ◽  
Soft Constraints ◽  
Haplotype Reconstruction ◽  
Binary Constraint ◽  
Sib Families

In the goal of genetic improvement of livestock by marker assisted selection, we aim at reconstructing the haplotypes of sires from their offspring. We reformulate this problem into a weighted binary constraint satisfaction problem with only equality and disequality soft constraints. Our results show these problems have a small treewidth and can be solved optimally, improving haplotype reconstruction compared to previous approaches especially for small families (<10 descendants).

scholarly journals A Variable Depth Search Algorithm for Binary Constraint Satisfaction Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
N. Bouhmala
Keyword(s):  
Constraint Satisfaction ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Wide Spectrum ◽  
Constraint Satisfaction Problem ◽  
Practical Interest ◽  
Constraint Satisfaction Problems ◽  
Variable Depth ◽  
The Past ◽  
Binary Constraint

The constraint satisfaction problem (CSP) is a popular used paradigm to model a wide spectrum of optimization problems in artificial intelligence. This paper presents a fast metaheuristic for solving binary constraint satisfaction problems. The method can be classified as a variable depth search metaheuristic combining a greedy local search using a self-adaptive weighting strategy on the constraint weights. Several metaheuristics have been developed in the past using various penalty weight mechanisms on the constraints. What distinguishes the proposed metaheuristic from those developed in the past is the update ofkvariables during each iteration when moving from one assignment of values to another. The benchmark is based on hard random constraint satisfaction problems enjoying several features that make them of a great theoretical and practical interest. The results show that the proposed metaheuristic is capable of solving hard unsolved problems that still remain a challenge for both complete and incomplete methods. In addition, the proposed metaheuristic is remarkably faster than all existing solvers when tested on previously solved instances. Finally, its distinctive feature contrary to other metaheuristics is the absence of parameter tuning making it highly suitable in practical scenarios.

scholarly journals Galois Connections for Patterns: An Algebra of Labelled Graphs

2021 ◽  
pp. 125-150
Author(s):  
David A. Cohen ◽  
Martin C. Cooper ◽  
Peter G. Jeavons ◽  
Stanislav Živný
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Galois Connection ◽  
Language Classes ◽  
Finite Set ◽  
Binary Constraint ◽  
Tree Width ◽  
To Come ◽  
Forbidden Patterns ◽  
Near Unanimity

AbstractA pattern is a generic instance of a binary constraint satisfaction problem (CSP) in which the compatibility of certain pairs of variable-value assignments may be unspecified. The notion of forbidden pattern has led to the discovery of several novel tractable classes for the CSP. However, for this field to come of age it is time for a theoretical study of the algebra of patterns. We present a Galois connection between lattices composed of sets of forbidden patterns and sets of generic instances, and investigate its consequences. We then extend patterns to augmented patterns and exhibit a similar Galois connection. Augmented patterns are a more powerful language than flat (i.e. non-augmented) patterns, as we demonstrate by showing that, for any $$k \ge 1$$ k ≥ 1 , instances with tree-width bounded by k cannot be specified by forbidding a finite set of flat patterns but can be specified by a finite set of augmented patterns. A single finite set of augmented patterns can also describe the class of instances such that each instance has a weak near-unanimity polymorphism of arity k (thus covering all tractable language classes).We investigate the power of forbidding augmented patterns and discuss their potential for describing new tractable classes.

scholarly journals Binary Encodings of Non-binary Constraint Satisfaction Problems: Algorithms and Experimental Results

2005 ◽  
Vol 24 ◽  
pp. 641-684 ◽  
Author(s):  
N. Samaras ◽  
K. Stergiou
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Constraint Satisfaction Problems ◽  
Binary Representation ◽  
Binary Constraints ◽  
Arc Consistency ◽  
Binary Problem ◽  
Binary Constraint ◽  
Binary Problems ◽  
Standard Techniques

A non-binary Constraint Satisfaction Problem (CSP) can be solved directly using extended versions of binary techniques. Alternatively, the non-binary problem can be translated into an equivalent binary one. In this case, it is generally accepted that the translated problem can be solved by applying well-established techniques for binary CSPs. In this paper we evaluate the applicability of the latter approach. We demonstrate that the use of standard techniques for binary CSPs in the encodings of non-binary problems is problematic and results in models that are very rarely competitive with the non-binary representation. To overcome this, we propose specialized arc consistency and search algorithms for binary encodings, and we evaluate them theoretically and empirically. We consider three binary representations; the hidden variable encoding, the dual encoding, and the double encoding. Theoretical and empirical results show that, for certain classes of non-binary constraints, binary encodings are a competitive option, and in many cases, a better one than the non-binary representation.

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