Abstract
The multidimensional assignment (MDA) problem is a combinatorial optimization problem arising in many applications, for instance multitarget tracking (MTT). The objective of an MDA problem of dimension <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> ∈ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> is to match groups of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> objects in such a way that each measurement is associated with at most one track and each track is associated with at most one measurement from each list, optimizing a certain objective function. It is well known that the MDA problem is NP-hard for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> ≥ 3. In this paper five new polynomial time heuristics to solve the MDA problem arising in MTT are presented. They are all based on the semi-greedy approach introduced in earlier research. Experimental results on the accuracy and speed of the proposed algorithms in MTT problems are provided.
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