The Optimization of the Bandpass Lengths in the Multi-Bandpass Problem
The Bandpass problem has applications to provide a cost reduction in design and operating telecommunication network. Given a binary matrix Am × n and a positive integer B called the Bandpass length, 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 general Bandpass Problem consists of finding an optimal permutation of rows of the matrix A that produces the maximum total number of bandpasses having the same given bandpass length B in all columns. The Multi- Bandpass problem includes different bandpass lengths Bj in each column j of the matrix A, where j = 1,2,…,n. In this paper, we propose an extended formulation for the Multi-Bandpass problem. A given Bj may not be always efficient bandpass lengths for the communication network. Therefore, it is important to find an optimal values of the bandpass lengths in the Multi-Bandpass problem. In this approach, the lengths in each destination are defined as z j and we present a model to find the optimal values of z j. Then, we calculate the approximate solution of this model using genetic algorithm for the problem instances which are presented in an online library.
KeywordsCombinatorial optimization Bandpass problem Telecommunication Genetic algorithm
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The work is supported by the Key Program of National Natural Science Foundation of China (Grant No. 70831005), also supported by “985” Program of Sichuan University (Innovative Research Base for Economic Development and Management), and also supported by Philosophy and Social Sciences Planning Project of Sichuan Province (Grant No. SC12BJ05).
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