Many classical synchronization problems such as the assembly line crew scheduling problem (ALCS), some data association problems or multisensor tracking problems can be formulated as finding intra-column rearrangement...
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Many classical synchronization problems such as the assembly line crew scheduling problem (ALCS), some data association problems or multisensor tracking problems can be formulated as finding intra-column rearrangements for a single matrix repre-senting costs, distances, similarities or time requirements. In this paper, we consider an extension of these problems to the case of multiple matrices, reflecting various possible instances (scenarios). To approximate optimal rearrangements, we introduce the Block Swapping Algorithm (BSA) and a further customization of it that we call the customized Block Swapping Algorithm (Cust BSA). A numerical study shows that the two algorithms we propose - in particular Cust BSA - yield high-quality solutions and also deal efficiently with high-dimensional set-ups. (C) 2021 Elsevier B.V. All rights reserved.
The central problem in multitarget tracking is the data association problem of partitioning the observations into tracks in some optimal way so that an accurate estimate of the true tracks can be recovered. This work ...
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The central problem in multitarget tracking is the data association problem of partitioning the observations into tracks in some optimal way so that an accurate estimate of the true tracks can be recovered. This work considers what is perhaps the simplest multitarget tracking problem in a setting where the issues are easily delineated, i.e., straight lines in two-dimensional space-time with an error component introduced into the observations. A multidimensionalassignment problem is formulated using gating techniques to introduce sparsity into the problem and filtering techniques to generate tracks which are then used to score each assignment of a collection of observations to a filtered track. Problem complexity is further reduced by decomposing the problem into disjoint components, which can then be solved independently. A recursive Lagrangian relaxation algorithm is developed to obtain high quality suboptimal solutions in real-time. The algorithms are, however, applicable to a large class of sparse multidimensional assignment problems arising in general multitarget and multisensor tracking. Results of extensive numerical testing are presented for a case study to demonstrate the speed, robustness, and exceptional quality of the solutions.
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