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The quadratic assignment problem (QAP) is a well-known combinatorial optimization problem with a wide variety of applications, prominently including the facility location problem. The acknowledged difficulty of the QAP has made it the focus of many metaheuristic solution approaches. In this paper, we show the benefit of utilizing strategic diversification within the tabu search (TS) framework for the QAP, by incorporating several diversification and multistart TS variants. Computational results for an extensive and challenging set of QAP benchmark test problems demonstrate the ability of our TS variants to improve on a classic TS approach that is one of the principal and most extensively used methods for the QAP. We also show that our new procedures are highly competitive with the best recently introduced methods from the literature, including more complex hybrid approaches that incorporate the classic TS method as a subroutine. [ABSTRACT FROM AUTHOR]

Distance-increasing maps from binary vectors to permutations, namely DIMs, are useful for the construction of permutation arrays. While a simple mapping algorithm defining DIMs of even lengths is known, existing DIMs of odd lengths are defined either by recursively merging DIMs of shorter lengths or by complicated mapping algorithms. In this paper, simple mapping algorithms defining DIMs of all lengths are presented. [ABSTRACT FROM AUTHOR]

In this correspondence, the cycles of Tanner (3, 5) quasi-cyclic (QC) low-density parity-check (LDPC) codes are analyzed and their girth values are derived. The conditions for the existence of cycles of lengths 4, 6, 8, and 10 in Tanner (3, 5) QC LDPC codes of length 5p are expressed in terms of polynomial equations in a 15th root of unity of the prime field Fp. By checking the existence of solutions for these equations over Fp, the girths of Tanner (3, 5) QC LDPC codes are derived. [ABSTRACT FROM AUTHOR]