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- W40832866 abstract "The Quadratic Assignment Problem (QAP) belongs to a class of combinatorial optimization problems with many practical application. However, only small instance (n < 20) of QAP have been solved to optimality in practice. QAP are normally solved using Branch and Bound, an exhaustive search method, which dynamically generates the search tree and searches as large parts of this as possible only implicitly through the use of bounds. A bounding procedure is described which extends the Hungarian method for the Linear Assignment Problem to QAP, operating on the four dimensional cost array of the objective fiuiction. The QAP is iteratively transformed in a series of equivalent RAP leading to an increasing sequence of lower bounds for the original problem. The values of the transformed objective function Z are the corresponding values of the old objective function Z shifted by some amount C. In the case that all entries of the transformed cost array are non-negative, then C is a lower bound for the initial QAP. If there exists a feasible solution X to the QAP, such that its value in the transformed problem is zero, then C is the optimal value of Z and X is an optimal solution for the original QAP. Several strategies are listed for determining C, or equivalently, transforming the cost array. The goal is the modification of the elements in the cost array so as to obtain new equivalent problems which bring the QAP closer to solution. Within the Branch and Bound method, the proposed bounding prosedure can be utilized as the auxiliary process for computing lower bounds." @default.
- W40832866 created "2016-06-24" @default.
- W40832866 creator A5001870811 @default.
- W40832866 date "2006-10-07" @default.
- W40832866 modified "2023-09-24" @default.
- W40832866 title "Penentuan Batas Bawah Pada Metoda Branch and Bound untuk Menyelesaikan Problema Penugasan Kuadratik" @default.
- W40832866 hasPublicationYear "2006" @default.
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