scholarly journals A heuristic approach to constraint optimization in timetabling

2002 ◽  
Vol 20 (1) ◽  
pp. 64 ◽  
Author(s):  
A. Chand
Keyword(s):  
Constraint Satisfaction ◽  
Query Language ◽  
Constraint Satisfaction Problem ◽  
Heuristic Method ◽  
Constraint Optimization ◽  
Examination Timetabling ◽  
Acceptable Solution ◽  
Timetabling Problem ◽  
Complete Problem ◽  
Np Complete

Timetabling is a difficult (NP-complete) problem and belongs to a general class of problems known as scheduling. Due to a variety of constraints typical in different timetabling environments, it has been difficult to develop a generic solution for timetabling. This paper is an attempt to define a generic computational model for examination timetabling for predefined constraints found in the problem, and proposes a heuristic method of developing an acceptable solution. The declarative nature of the developed constraints language (based on the structured query language) is utilized to construct constraints and specify the timetabling problem as a constraint satisfaction problem. A university examination timetabling problem is used to illustrate and test the model.

scholarly journals CSP DICHOTOMY FOR SPECIAL POLYADS

2013 ◽  
Vol 23 (05) ◽  
pp. 1151-1174 ◽  
Author(s):  
LIBOR BARTO ◽  
JAKUB BULÍN
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Np Complete ◽  
Bounded Width ◽  
Near Unanimity

For a digraph ℍ, the Constraint Satisfaction Problem with template ℍ, or CSP(ℍ), is the problem of deciding whether a given input digraph 𝔾 admits a homomorphism to ℍ. The CSP dichotomy conjecture of Feder and Vardi states that for any digraph ℍ, CSP(ℍ) is either in P or NP-complete. Barto, Kozik, Maróti and Niven (Proc. Amer. Math. Soc.137 (2009) 2921–2934) confirmed the conjecture for a class of oriented trees called special triads. We generalize this result, establishing the dichotomy for a class of oriented trees which we call special polyads. We prove that every tractable special polyad has bounded width and provide the description of special polyads of width 1. We also construct a tractable special polyad which neither has width 1 nor admits any near-unanimity polymorphism.

Formalising PFSQL queries using ŁΠ fuzzy logic

2011 ◽  
Vol 22 (3) ◽  
pp. 533-547 ◽  
Author(s):  
ALEKSANDAR PEROVIĆ ◽  
ALEKSANDAR TAKAČI ◽  
SRDJAN ŠKRBIĆ
Keyword(s):  
Fuzzy Logic ◽  
Constraint Satisfaction ◽  
Relational Databases ◽  
Query Language ◽  
Constraint Satisfaction Problem ◽  
Current Paper ◽  
Conservative Extension ◽  
Logic Formula ◽  
Structured Query Language

Using the concept of a generalised priority constraint satisfaction problem, we previously found a way to introduce priority queries into fuzzy relational databases. The results were PFSQL (Priority Fuzzy Structured Query Language) together with a database independent interpreter for it. In an effort to improve the performance of the resolution of PFSQL queries, the aim of the current paper is to formalise PFSQL queries by obtaining their interpretation in an existing fuzzy logic. We have found that the ŁΠ logic provides sufficient elements. The SELECT line of PFSQL queries is semantically a formula of some fuzzy logic, and we show that such formulas can be naturally expressed in a conservative extension of the ŁΠ logic. Furthermore, we prove a theorem that gives the PSPACE containment for the complexity of finding a model for a given ŁΠ logic formula.

scholarly journals Solving Weighted Constraint Satisfaction Problems with Memetic/Exact Hybrid Algorithms

2009 ◽  
Vol 35 ◽  
pp. 533-555 ◽  
Author(s):  
J. E. Gallardo ◽  
C. Cotta ◽  
A. J. Fernández
Keyword(s):  
Constraint Satisfaction ◽  
Large Scale ◽  
Constraint Satisfaction Problem ◽  
Heuristic Method ◽  
Optimal Solution ◽  
Constraint Satisfaction Problems ◽  
Still Life ◽  
Level Model ◽  
Weighted Constraint

A weighted constraint satisfaction problem (WCSP) is a constraint satisfaction problem in which preferences among solutions can be expressed. Bucket elimination is a complete technique commonly used to solve this kind of constraint satisfaction problem. When the memory required to apply bucket elimination is too high, a heuristic method based on it (denominated mini-buckets) can be used to calculate bounds for the optimal solution. Nevertheless, the curse of dimensionality makes these techniques impractical on large scale problems. In response to this situation, we present a memetic algorithm for WCSPs in which bucket elimination is used as a mechanism for recombining solutions, providing the best possible child from the parental set. Subsequently, a multi-level model in which this exact/metaheuristic hybrid is further hybridized with branch-and-bound techniques and mini-buckets is studied. As a case study, we have applied these algorithms to the resolution of the maximum density still life problem, a hard constraint optimization problem based on Conway's game of life. The resulting algorithm consistently finds optimal patterns for up to date solved instances in less time than current approaches. Moreover, it is shown that this proposal provides new best known solutions for very large instances.

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.

scholarly journals Fine-Grained Time Complexity of Constraint Satisfaction Problems

2021 ◽  
Vol 13 (1) ◽  
pp. 1-32
Author(s):  
Peter Jonsson ◽  
Victor Lagerkvist ◽  
Biman Roy
Keyword(s):  
Constraint Satisfaction ◽  
Time Complexity ◽  
Constraint Satisfaction Problem ◽  
Constraint Satisfaction Problems ◽  
Finite Domain ◽  
Infinite Domain ◽  
Worst Case ◽  
Fine Grained ◽  
Restricted Problems ◽  
Np Complete

We study the constraint satisfaction problem (CSP) parameterized by a constraint language Γ (CSPΓ) and how the choice of Γ affects its worst-case time complexity. Under the exponential-time hypothesis (ETH), we rule out the existence of subexponential algorithms for finite-domain NP-complete CSPΓ problems. This extends to certain infinite-domain CSPs and structurally restricted problems. For CSPs with finite domain D and where all unary relations are available, we identify a relation S D such that the time complexity of the NP-complete problem CSP({ S D }) is a lower bound for all NP-complete CSPs of this kind. We also prove that the time complexity of CSP({ S D }) strictly decreases when |D| increases (unless the ETH is false) and provide stronger complexity results in the special case when |D|=3.

scholarly journals TAYLOR TERMS, CONSTRAINT SATISFACTION AND THE COMPLEXITY OF POLYNOMIAL EQUATIONS OVER FINITE ALGEBRAS

2006 ◽  
Vol 16 (03) ◽  
pp. 563-581 ◽  
Author(s):  
BENOIT LAROSE ◽  
LÁSZLÓ ZÁDORI
Keyword(s):  
Polynomial Time ◽  
Constraint Satisfaction ◽  
Finite Algebra ◽  
Algorithmic Complexity ◽  
Polynomial Equations ◽  
Finite Algebras ◽  
Complete Problem ◽  
Np Complete ◽  
System Of Polynomial Equations

We study the algorithmic complexity of determining whether a system of polynomial equations over a finite algebra admits a solution. We characterize, within various families of algebras, which of them give rise to an NP-complete problem and which yield a problem solvable in polynomial time. In particular, we prove a dichotomy result which encompasses the cases of lattices, rings, modules, quasigroups and also generalizes a result of Goldmann and Russell for groups [15].

Dynamic Clustering Heuristic Method for Smart Grid Computing

2014 ◽  
Vol 607 ◽  
pp. 868-871
Author(s):  
Jeong Sig Kim ◽  
Jin Hong Kim
Keyword(s):  
Smart Grid ◽  
Grid Computing ◽  
Dynamic Scheduling ◽  
Fundamental Problem ◽  
Heuristic Method ◽  
Program Completion ◽  
Computing Systems ◽  
Complete Problem ◽  
Np Complete ◽  
Scheduling Heuristic

Efficient scheduling has appeared as a fundamental problem in smart grid computing systems. Since finding an optimal scheduling on the system to minimize the program completion time is a well-known NP-complete problem in general, researchers have resorted to devising efficient heuristics. In this paper, we present a dynamic scheduling heuristic which is appropriate for the system. The goal is realized with four general metrics and two additional restricted metrics, which not only take the communication cost, priority, mutex between jobs into account, but also consider the characteristic of the resource, such as the storage capability and the dynamic characteristic in smart grid computing.

scholarly journals Application of Heuristic Combinations in Hyper-Heuristic Framework for Exam Scheduling Problems

2020 ◽  
Vol 4 (4) ◽  
pp. 664-671
Author(s):  
Gabriella Icasia ◽  
Raras Tyasnurita ◽  
Etria Sepwardhani Purba
Keyword(s):  
Tabu Search ◽  
Large Scale ◽  
Search Algorithm ◽  
Heuristic Method ◽  
Combinatorial Problems ◽  
Hill Climbing ◽  
Tabu Search Algorithm ◽  
Scheduling Problems ◽  
Examination Timetabling ◽  
Timetabling Problem

Examination Timetabling Problem is one of the optimization and combinatorial problems. It is proved to be a non-deterministic polynomial (NP)-hard problem. On a large scale of data, the examination timetabling problem becomes a complex problem and takes time if it solved manually. Therefore, heuristics exist to provide reasonable enough solutions and meet the constraints of the problem. In this study, a real-world dataset of Examination Timetabling (Toronto dataset) is solved using a Hill-Climbing and Tabu Search algorithm. Different from the approach in the literature, Tabu Search is a meta-heuristic method, but we implemented a Tabu Search within the hyper-heuristic framework. The main objective of this study is to provide a better understanding of the application of Hill-Climbing and Tabu Search in hyper-heuristics to solve timetabling problems. The results of the experiments show that Hill-Climbing and Tabu Search succeeded in automating the timetabling process by reducing the penalty 18-65% from the initial solution. Besides, we tested the algorithms within 10,000-100,000 iterations, and the results were compared with a previous study. Most of the solutions generated from this experiment are better compared to the previous study that also used Tabu Search algorithm.

scholarly journals The Tractability of CSP Classes Defined by Forbidden Patterns

2012 ◽  
Vol 45 ◽  
pp. 47-78 ◽  
Author(s):  
D. A. Cohen ◽  
M. C. Cooper ◽  
P. Creed ◽  
D. Marx ◽  
A. Z. Salamon
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
The Novel ◽  
Considerable Effort ◽  
Relational Properties ◽  
Np Complete ◽  
Novel Concept ◽  
Forbidden Patterns ◽  
Special Case ◽  
Hybrid Properties

The constraint satisfaction problem (CSP) is a general problem central to computer science and artificial intelligence. Although the CSP is NP-hard in general, considerable effort has been spent on identifying tractable subclasses. The main two approaches consider structural properties (restrictions on the hypergraph of constraint scopes) and relational properties (restrictions on the language of constraint relations). Recently, some authors have considered hybrid properties that restrict the constraint hypergraph and the relations simultaneously. Our key contribution is the novel concept of a CSP pattern and classes of problems defined by forbidden patterns (which can be viewed as forbidding generic sub-problems). We describe the theoretical framework which can be used to reason about classes of problems defined by forbidden patterns. We show that this framework generalises certain known hybrid tractable classes. Although we are not close to obtaining a complete characterisation concerning the tractability of general forbidden patterns, we prove a dichotomy in a special case: classes of problems that arise when we can only forbid binary negative patterns (generic sub-problems in which only disallowed tuples are specified). In this case we show that all (finite sets of) forbidden patterns define either polynomial-time solvable or NP-complete classes of instances.

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