Combinatorial Optimization Problems in Multimedia Delivery

2018 ◽  
pp. 67-92
Author(s):  
Tibor Szkaliczki
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Multimedia Systems ◽  
Multimedia Data ◽  
Discrete Mathematics ◽  
Resource Assignment ◽  
Multimedia Delivery ◽  
Combinatorial Optimization Problems ◽  
Problems And Solutions

The amount of multimedia data (video, audio, images, animation, etc.) delivered through the Internet is continuously increasing. There is a wide range of application possibilities of optimization methods in the multimedia systems such as adapting multimedia objects, replication of multimedia elements, resource assignment, etc. This chapter introduces selected combinatorial optimization problems arising during the operation of multimedia delivery systems. The efficient solution of the problems considered can enhance significantly the performance of the servers and improve the quality of the provided services. This chapter provides an overview of the algorithms that can be used in multimedia delivery. Both heuristics and adaptation of well-known combinatorial optimization algorithms can be applied to solve the problems concerned. The approaches are related to typical problems and solutions in discrete mathematics such as facility location problem, knapsack problem, monotonic optimization, linear programming, evolutionary algorithms, etc.

Analyses of Simple Hybrid Algorithms for the Vertex Cover Problem

2009 ◽  
Vol 17 (1) ◽  
pp. 3-19 ◽  
Author(s):  
Tobias Friedrich ◽  
Jun He ◽  
Nils Hebbinghaus ◽  
Frank Neumann ◽  
Carsten Witt
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Hybrid Methods ◽  
Vertex Cover ◽  
Optimization Methods ◽  
Theoretical Understanding ◽  
Combinatorial Optimization Problems ◽  
Vertex Cover Problem ◽  
The Subject ◽  
Cover Problem

Hybrid methods are very popular for solving problems from combinatorial optimization. In contrast, the theoretical understanding of the interplay of different optimization methods is rare. In this paper, we make a first step into the rigorous analysis of such combinations for combinatorial optimization problems. The subject of our analyses is the vertex cover problem for which several approximation algorithms have been proposed. We point out specific instances where solutions can (or cannot) be improved by the search process of a simple evolutionary algorithm in expected polynomial time.

scholarly journals An Analysis of a KNN Perturbation Operator: An Application to the Binarization of Continuous Metaheuristics

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 225
Author(s):  
José García ◽  
Gino Astorga ◽  
Víctor Yepes
Keyword(s):  
Transfer Functions ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Set Covering ◽  
Covering Problem ◽  
Perturbation Operator ◽  
K Nearest Neighbors ◽  
Combinatorial Optimization Problems ◽  
Box Plots ◽  
Metaheuristic Techniques

The optimization methods and, in particular, metaheuristics must be constantly improved to reduce execution times, improve the results, and thus be able to address broader instances. In particular, addressing combinatorial optimization problems is critical in the areas of operational research and engineering. In this work, a perturbation operator is proposed which uses the k-nearest neighbors technique, and this is studied with the aim of improving the diversification and intensification properties of metaheuristic algorithms in their binary version. Random operators are designed to study the contribution of the perturbation operator. To verify the proposal, large instances of the well-known set covering problem are studied. Box plots, convergence charts, and the Wilcoxon statistical test are used to determine the operator contribution. Furthermore, a comparison is made using metaheuristic techniques that use general binarization mechanisms such as transfer functions or db-scan as binarization methods. The results obtained indicate that the KNN perturbation operator improves significantly the results.

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