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A New Lagrangian Relaxation Based Algorithm for a Class of Multidimensional Assignment Problems

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Abstract

Large classes of data association problems in multiple targettracking applications involving both multiple and single sensorsystems can be formulated as multidimensional assignment problems.These NP-hard problems are large scale and sparse with noisyobjective function values, but must be solved in“real-time”. Lagrangian relaxation methods have proven to beparticularly effective in solving these problems to the noise levelin real-time, especially for dense scenarios and for multiple scansof data from multiple sensors. This work presents a new class ofconstructive Lagrangian relaxation algorithms that circumvent some ofthe deficiencies of previous methods. The results of severalnumerical studies demonstrate the efficiency and effectiveness of thenew algorithm class.

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Authors and Affiliations

  1. Department of Mathematics, Colorado State University, Fort Collins, CO, 80523

    Aubrey B. Poore

  2. BDM Federal, Inc., 3375 Mitchell Lane, Boulder, CO, 80301

    Alexander J. Robertson III

Authors
  1. Aubrey B. Poore
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  2. Alexander J. Robertson III
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Poore, A.B., Robertson III, A.J. A New Lagrangian Relaxation Based Algorithm for a Class of Multidimensional Assignment Problems. Computational Optimization and Applications 8, 129–150 (1997). https://doi.org/10.1023/A:1008669120497

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