This paper presents a class of lower bounds for the Quadratic Semi-Assignment Problem (QSAP). These bounds are based on recent results on polynomially solvable cases, in particular we will consider the QSAPs whose quadratic cost coefficients define a reducible graph. The idea is to decompose the problem into several subproblems, each defined on a reducible subgraph. A Lagrangean decomposition technique is used to improve the results. Several lower bounds are computationally compared on several types of test problems.
Lower bounds for the quadratic semi-assignment problem / F., Malucelli; Pretolani, Daniele. - In: EUROPEAN JOURNAL OF OPERATIONAL RESEARCH. - ISSN 0377-2217. - STAMPA. - 83 (2):(1995), pp. 365-375. [10.1016/0377-2217(95)00013-G]
Lower bounds for the quadratic semi-assignment problem
PRETOLANI, Daniele
1995
Abstract
This paper presents a class of lower bounds for the Quadratic Semi-Assignment Problem (QSAP). These bounds are based on recent results on polynomially solvable cases, in particular we will consider the QSAPs whose quadratic cost coefficients define a reducible graph. The idea is to decompose the problem into several subproblems, each defined on a reducible subgraph. A Lagrangean decomposition technique is used to improve the results. Several lower bounds are computationally compared on several types of test problems.
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