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

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.

[1]  P. Wolfe.  Note on a method of conjugate subgradients for minimizing nondifferentiable functions , 1974 .

[2]  Jean-Louis Goffin,et al.  On convergence rates of subgradient optimization methods , 1977, Math. Program..

[3]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[4]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[5]  Alan Frieze,et al.  An Algorithm for Solving 3-Dimensional Assignment Problems with Application to Scheduling a Teaching Practice , 1981 .

[6]  Jesfis Peral,et al.  Heuristics -- intelligent search strategies for computer problem solving , 1984 .

[7]  K. Kiwiel.  Methods of Descent for Nondifferentiable Optimization , 1985 .

[8]  Naum Zuselevich Shor,et al.  Minimization Methods for Non-Differentiable Functions , 1985, Springer Series in Computational Mathematics.

[9]  Egon Balas,et al.  Facets of the three-index assignment polytope , 1989, Discret. Appl. Math..

[10]  Egon Balas,et al.  An Algorithm for the Three-Index Assignment Problem , 1991, Oper. Res..

[11]  Y. Bar-Shalom,et al.  An S-dimensional assignment algorithm for track initiation , 1992, [Proceedings 1992] IEEE International Conference on Systems Engineering.

[12]  Dimitri P. Bertsekas,et al.  A forward/reverse auction algorithm for asymmetric assignment problems , 1992, Comput. Optim. Appl..

[13]  Y. Crama,et al.  Approximation algorithms for three-dimensional assignment problems with triangle inequalities , 1992 .

[14]  Jochem Zowe,et al.  A Version of the Bundle Idea for Minimizing a Nonsmooth Function: Conceptual Idea, Convergence Analysis, Numerical Results , 1992, SIAM J. Optim..

[15]  Y. Bar-Shalom,et al.  A new algorithm for the generalized multidimensional assignment problem , 1992, [Proceedings] 1992 IEEE International Conference on Systems, Man, and Cybernetics.

[16]  Panos M. Pardalos,et al.  Topics in parallel computing in mathematical programming , 1993, Applied discrete mathematics and theoretical computer science.

[17]  J. Hiriart-Urruty,et al.  Convex analysis and minimization algorithms , 1993 .

[18]  Aubrey B. Poore,et al.  A Lagrangian Relaxation Algorithm for Multidimensional Assignment Problems Arising from Multitarget Tracking , 1993, SIAM J. Optim..

[19]  C. Reeves.  Modern heuristic techniques for combinatorial problems , 1993 .

[20]  Aubrey B. Poore,et al.  Multidimensional Assignments and Multitarget Tracking , 1993, Partitioning Data Sets.

[21]  Aubrey B. Poore,et al.  Partitioning Multiple Data Sets: Multidimensional Assignments and Lagrangian Relaxation , 1993, Quadratic Assignment and Related Problems.

[22]  Panos M. Pardalos,et al.  A Greedy Randomized Adaptive Search Procedure for the Quadratic Assignment Problem , 1993, Quadratic Assignment and Related Problems.

[23]  Frits C. R. Spieksma,et al.  Approximation Algorithms for Multi-Dimensional Assignment Problems with Decomposable Costs , 1994, Discret. Appl. Math..

[24]  Aubrey B. Poore,et al.  A Numerical Study of Some Data Association Problems Arising in Multitarget Tracking , 1994 .

[25]  Aubrey B. Poore,et al.  Multidimensional assignment formulation of data association problems arising from multitarget and multisensor tracking , 1994, Comput. Optim. Appl..

[26]  Mauricio G. C. Resende,et al.  A Greedy Randomized Adaptive Search Procedure for Maximum Independent Set , 1994, Oper. Res..

[27]  Aubrey B. Poore,et al.  New class of Lagrangian-relaxation-based algorithms for fast data association in multiple hypothesis tracking applications , 1995, Defense, Security, and Sensing.

[28]  Alexander J. Robertson.  A class of lagrangian relaxation algorithms for the multidimensional assignment problem , 1995 .

[29]  Panos M. Pardalos,et al.  A Parallel Grasp Implementation for the Quadratic Assignment Problem , 1995 .