A Lagrangian Relaxation Algorithm for Multidimensional Assignment Problems Arising from Multitarget Tracking

Poore, Aubrey P.; Rijavec, Nenad

doi:10.1137/0803027

Cited by 134 publications

(90 citation statements)

References 26 publications

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“…Some Lagrangian relaxation algorithms for the MAP have been developed by Poore and Rijavec [146] and Poore and Robertson [148]. These algorithms relax one or more constraints and derive a set of good Lagrangean multipliers, e.g.…”

Section: General Remarks and Applicationsmentioning

confidence: 99%

Linear Assignment Problems and Extensions

Burkard

Çela

1999

Handbook of Combinatorial Optimization

255

150

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This paper aims at describing the state of the art on linear assignment problems (LAPs). Besides sum LAPs it discusses also problems with other objective functions like the bottleneck LAP, the lexicographic LAP, and the more general algebraic LAP. We consider different aspects of assignment problems, starting with the assignment polytope and the relationship between assignment and matching problems, and focusing then on deterministic and randomized algorithms, parallel approaches, and the asymptotic behaviour. Further, we describe different applications of assignment problems, ranging from the well know personnel assignment or assignment of jobs to parallel machines, to less known applications, e.g. tracking of moving objects in the space. Finally, planar and axial three-dimensional assignment problems are considered, and polyhedral results, as well as algorithms for these problems or their special cases are discussed. The paper will appear in the Handbook of Combinatorial Optimization to be published by Kluwer Academic Publishers, P. Pardalos and D.-Z. Du, eds.

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Section: General Remarks and Applicationsmentioning

confidence: 99%

Linear Assignment Problems and Extensions

Burkard

Çela

1999

Handbook of Combinatorial Optimization

255

150

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“…While finding the optimal assignment for S > 2 is an NPhard problem [46], a number of near-optimal modifications with polynomial complexity have been proposed [47]. Lagrangian relaxation-based techniques [48] have been proposed to find suboptimal solutions for applications that require realtime performance. In [49], impelled from the success of randomized heuristic methods, Bozdogan and Efe investigated a different stochastic approach, namely, the biologically inspired ant colony optimization to solve the NP hard S-D assignment problem for tracking multiple ground targets.…”

Section: Bayesian Approachesmentioning

confidence: 99%

A Survey of Motion-Based Multitarget Tracking Methods

Qiu¹,

Zhang²,

Lü³

et al. 2015

PIER B

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Abstract-Multitarget tracking (MTT) in surveillance system is extremely challenging, due to uncertain data association, maneuverable target motion, dense clutter disturbance, and real-time processing requirements. A good many methods have been proposed to cope with these challenges. However, no up-to-date survey is available in the literature that can help to select suitable tracking algorithm for practical problem. This paper provides a comprehensive review of the state-of-the-art motion-based MTT techniques, classifies existing methods into two groups, i.e., the detect-beforetrack (DBT) scheme and the track-before-detect (TBD) scheme. The DBT scheme is employed to achieve robust and tractable tracking performance when the signal-noise-ratio (SNR) is strong. The TBD scheme is used in the scenarios of low SNR, and it aims to cumulate target energy by multiple sensor frames. Furthermore, depending on the data association mechanism, the DBT methods can be classified into two categories, data association based approaches and finite set statistics (FISST) based approaches. And the TBD methods can be classified into non-Bayesian approaches and Bayesian approaches depending on the basis theory used for tracking. For each category, this paper provides the detailed descriptions of the representative algorithms, and examines their pros and cons. Finally, new trends for future research directions are offered.

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“…These correspondences make up a cubic assignment. The model can be formulated as the following 0-1 integer programming problem [1][2][3][4][5]: = 0, then worker i is either not assigned to job j or not assigned to machine k. In a deterministic environment, the 3D axial assignment problem is important in operations research. Applications of the 3D axial assignment problem arise in many areas, such as scheduling capital investments, addressing a rolling mill, military troop assignment, and satellite coverage optimisation [1,6].…”

Section: Introductionmentioning

confidence: 99%

Model and Algorithms of the Fuzzy Three-Dimensional Axial Assignment Problem With an Additional Constraint

Lin

2015

SAJIE

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This study constructs a practical fuzzy three-dimensional axial assignment model, and proposes two efficient algorithms to solve the model. In our case, the model is applied to team performance management in a company to promote the performance of all members in a team. Two algorithms, namely the index-based branch and bound (B&B) algorithm and the f-g trade-off algorithm, which is a hybrid of the trade-off and B&B concepts, are proposed. A numerical example is presented to illustrate these two algorithms. The computational results show that the proposed algorithms are sufficiently efficient and accurate. Two special cases are also discussed. OPSOMMING'n Praktiese, wasige, driedimensionele aksialetoekenningsmodel word voorgehou en twee doeltreffende algoritmes om die model op te los word voorgestel. Die model word toegepas op die spanprestasiebestuur in 'n maatskappy met die doel om die spanlede se vertoning te verbeter. Twee algoritmes, naamlik die indeksgebaseerde vertak-en-begrens algoritme en die f-g kompromie algoritme, word voorgestel. 'n Numeriese voorbeeld word ter illustrasie van die twee algoritmes voorgehou. Die resultate toon dat die voorgestelde algoritmes doeltreffend en akkuraat is. Twee spesiale gevalle word ook bespreek.

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A Lagrangian Relaxation Algorithm for Multidimensional Assignment Problems Arising from Multitarget Tracking

Cited by 134 publications

References 26 publications

Linear Assignment Problems and Extensions

Linear Assignment Problems and Extensions

A Survey of Motion-Based Multitarget Tracking Methods

Model and Algorithms of the Fuzzy Three-Dimensional Axial Assignment Problem With an Additional Constraint

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