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The quadratic assignment problem (QAP) is known as one of the most interesting and challenging problems in combinatorial optimization. This dissertation contributes to the theoretical, algorithmic and applicable understanding of quadratic assignment and its related problems.
The study includes four areas: (i) investigating the inherent relationship of the 3-dimensional assignment problem (3AP) to the quadratic assignment problem (QAP) and the quadratic 3-dimensional assignment problem (Q3AP); (ii) understanding the level-1 reformulation-linearization technique (RLT) formulation of the generalized quadratic assignment problem (GQAP) and comparing lower bounds from different RLT based models; (iii) modeling new applications of the multi-story space assignment problem (MSAP) and the crossdock door assignment problem (CDAP), and developing solution methods for an innovative assignment problem, the generalized quadratic 3-dimensional assignment problem (GQ3AP); and (iv) introducing the level-3 RLT formulation of the QAP for the first time and illustrating its great promise to provide superior lower bounds.
Solution methodologies studied in this work include the reformulation-linearization technique (RLT), Lagrangian dual procedure, and branch-and-bound enumeration. The methods devised herein effectively exploit the mathematical structure found within the RLT formulations. This consists of both theoretical and computational studies, including specially designed Lagrangian dual procedures that take advantage of the block-diagonal structures, and tradeoffs between linearization size and strength. Computational experiments were conducted by either implementing or extending the usefulness of existing algorithmic tools to solve application problems.