A New Lagrangian Relaxation Based Algorithm for a Class ofMultidimensional Assignment Problems

  • Authors:
  • Aubrey B. Poore;Alexander J. Robertson, III

  • Affiliations:
  • Department of Mathematics, Colorado State University, Fort Collins, CO 80523. E-mail: poore@math.colostate.edu;BDM Federal, Inc., 3375 Mitchell Lane, Boulder, CO 80301. E-mail: aroberts@bdm.com

  • Venue:
  • Computational Optimization and Applications
  • Year:
  • 1997

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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.