The combinatorial optimization problem of multidimensional assignment has been treated with renewed interest because of its extensive application in target tracking, cooperative control, robotics and image processing. In this work we particularly concentrate on data association in multisensor-multitarget tracking algorithms, in which solving the multidimensional assignment is an essential step. Current algorithms generate good suboptimal solutions (with quantifiable accuracy) to these problems in pseudo polynomial time. However, in dense scenarios these methods can become inefficient because of the resulting dense candidate association tree. Also, in order to generate the top m (or ranked) solutions these algorithms need to solve a number of optimization problems, which increases the computational complexity significantly.
In this paper we develop a Randomized Heuristic Approach (RHA), in which, in each step, instead of choosing the best solution indicated by the heuristic, one of the solutions is chosen randomly depending on the "probability" associated with it. The resulting algorithm produces solutions that are as good as or better than those produced by Lagrange relaxation-based algorithms that have much higher computational complexity. This method also produces other ranked best solutions with no further computational requirement.