Treffer: The quadratic three-dimensional assignment problem : Exact and approximate solution methods
CoDE, IRIDIA, CP 194I6, Université Libre de Bruxelles, 1050 Brussels, Belgium
Computer Science, Darmstadt University of Technology, 64283 Darmstadt, Germany
Mathematics and Computer Science, High Point University, High Point, NC 27262, United States
Electrical and Computer Engineering, University of California, Davis, Davis, CA 95616, United States
Operations and Information Management, The Wharton School, University of Pennsylvania, Philadelphia, PA 19104-6340, United States
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This paper reports on algorithm development for solving the quadratic three-dimensional assignment problem (Q3AP). The Q3AP arises, for example, in the implementation of a hybrid ARQ (automatic repeat request) scheme for enriching diversity among multiple packet re-transmissions, by optimizing the mapping of data bits to modulation symbols. Typical practical problem sizes would be 8, 16, 32 and 64. We present an exact solution method based upon a reformulation linearization technique that is one of the best available for solving the quadratic assignment problem (QAP). Our current exact algorithm is useful for Q3AP instances of size 13 or smaller. We also investigate four stochastic local search algorithms that provide optimum or near optimum solutions for large and difficult QAP instances and adapt them for solving the Q3AP. The results of our experiments make it possible to get good solutions to signal mapping problems of size 8 and 16.