The bandpass problem: combinatorial optimization and library of problems

A combinatorial optimization problem, called the Bandpass Problem , is introduced. Given a rectangular matrix A of binary elements {0,1} and a positive integer B called the Bandpass Number , a set of B consecutive non-zero elements in any column is called a Bandpass. No two bandpasses in the same co...

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Vydané v:Journal of combinatorial optimization Ročník 18; číslo 2; s. 151 - 172
Hlavní autori: Babayev, Djangir A., Bell, George I., Nuriyev, Urfat G.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Boston Springer US 01.08.2009
Springer
Predmet:
Applied sciences
Combinatorics
Convex and Discrete Geometry
Exact sciences and technology
Flows in networks. Combinatorial problems
Mathematical Modeling and Industrial Mathematics
Mathematical programming
Mathematics
Mathematics and Statistics
Operational research and scientific management
Operational research. Management science
Operations Research/Decision Theory
Optimization
Theory of Computation
Binary integer programming model
Bandpass problem
NP-hard problem
Library of problems
Heuristic polynomial algorithms
Combinatorial optimization problem
Combinatorial problem
Optical telecommunication
Polynomial method
Combinatorial optimization
Modeling
Research library
Zero one programming
Optical transmission
Efficiency
Fast algorithm
Cost lowering
Permutation
Wavelength division multiplexing
Communication network
Rectangular matrix
Wavelength
Integer programming
Information flow
Heuristic method
NP hard problem
Telecommunication network
Problem solving
Passband
Optimal flow
ISSN:1382-6905, 1573-2886
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Popis
Shrnutí:A combinatorial optimization problem, called the Bandpass Problem , is introduced. Given a rectangular matrix A of binary elements {0,1} and a positive integer B called the Bandpass Number , a set of B consecutive non-zero elements in any column is called a Bandpass. No two bandpasses in the same column can have common rows. The Bandpass problem consists of finding an optimal permutation of rows of the matrix, which produces the maximum total number of bandpasses having the same given bandpass number in all columns. This combinatorial problem arises in considering the optimal packing of information flows on different wavelengths into groups to obtain the highest available cost reduction in design and operating the optical communication networks using wavelength division multiplexing technology. Integer programming models of two versions of the bandpass problems are developed. For a matrix A with three or more columns the Bandpass problem is proved to be NP-hard. For matrices with two or one column a polynomial algorithm solving the problem to optimality is presented. For the general case fast performing heuristic polynomial algorithms are presented, which provide near optimal solutions, acceptable for applications. High quality of the generated heuristic solutions has been confirmed in the extensive computational experiments. As an NP-hard combinatorial optimization problem with important applications the Bandpass problem offers a challenge for researchers to develop efficient computational solution methods. To encourage the further research a Library of Bandpass Problems has been developed. The Library is open to public and consists of 90 problems of different sizes (numbers of rows, columns and density of non-zero elements of matrix A and bandpass number  B ), half of them with known optimal solutions and the second half, without.
ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-008-9143-3