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Assignment problem

About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the core-oriented linear assignment problem (LAP) with a dense cost matrix can be solved by first making this matrix sparse, i.e. the problem is solved on the core of the matrix.

63 citations

Journal ArticleDOI
TL;DR: In this paper, the authors apply optimal transport to the comparison of the graph of the data rather than the data itself, where each channel of the oscillatory data is interpreted as a discrete point cloud and the corresponding misfit function can be computed through the solution of series of linear sum assignment problem (LSAP), while, based on the adjoint state technique, its gradient can be calculated from the assignment solution of these LSAP.
Abstract: Optimal transport distance is an appealing tool to measure the discrepancy between datasets in the frame of inverse problems, for its ability to perform global comparisons and its convexity with respect to shifted patterns in the compared quantities. However, solving inverse problems might require to compare signed quantities, while the optimal transport theory has been developed for the comparison of probability measures. In this study we propose to circumvent this difficulty by applying optimal transport to the comparison of the graph of the data rather than the data itself. We investigate this approach in the frame of seismic imaging, where each channel of the oscillatory data is interpreted as a discrete point cloud. We demonstrate that the corresponding misfit function can be computed through the solution of series of linear sum assignment problem (LSAP), while, based on the adjoint state technique, its gradient can be computed from the assignment solution of these LSAP. We illustrate how this approach yields a convex misfit function in the frame of seismic imaging using the full waveform. We show how an efficient strategy, based on a specific LSAP solver, the auction algorithm, can be designed. We illustrate the interest of the approach on a realistic 2D visco-acoustic seismic imaging problem. The proposed strategy relaxes the constraint on the accuracy of the initial model, outperforming the conventional least-squares approach and a previously proposed optimal transport based approach. The computational time increases by only a few percents compared with the least-squares approach, opening the way to applications to 3D field data in the near future.

63 citations

Journal ArticleDOI
TL;DR: A metaheuristic algorithm for the multi-resource generalized assignment problem (MRGAP), which features a very large-scale neighborhood search, which is a mechanism of conducting the search with complex and powerful moves, where the resulting neighborhood is efficiently searched via the improvement graph.

63 citations

Book ChapterDOI
05 Sep 2004
TL;DR: The experimental results indicate that the use of local search procedures and the correlation between objectives play an essential role in the performance of the variants studied in this paper.
Abstract: Few applications of ACO algorithms to multiobjective problems have been presented so far and it is not clear how to design an effective ACO algorithms for such problems. In this article, we study the performance of several ACO variants for the biobjective Quadratic Assignment Problem that are based on two fundamentally different search strategies. The first strategy is based on dominance criteria, while the second one exploits different scalarizations of the objective function vector. Further variants differ in the use of multiple colonies, the use of local search, and the pheromone update strategy. The experimental results indicate that the use of local search procedures and the correlation between objectives play an essential role in the performance of the variants studied in this paper.

63 citations

Patent
Joel L. Wolf1
02 Sep 1988
TL;DR: In this article, the file assignment problem is partitioned into two sequential optimization problems, called the macro model and the micro model, and the output from the optimization is an "optimal" assignment of files to DASDs.
Abstract: A practical mathematical algorithm is used to solve the so-called "File Assignment Problem" (FAP). The FAP is partitioned into two sequential optimization problems, called the macro model and the micro model. The macro model is solved by a Non-Linear Programming Model (NLPM) and a Queuing Network Model (QNM). The NLPM takes as input detailed information on the computer system configuration and performance characteristics down through the DASD level, and, using the QNM as its objective function evaluator, determines the "optimal" DASD relative access rates as output. The micro model is solved by a Binary Linear Programming Model (BLPM), although the QNM is also involved to help determine the BLPM stopping criteria. The input to the micro model consists basically of the output from the macro model, together with statistics on the access rates of the various files in the computer system. The output from the optimization is an "optimal" assignment of files to DASDs. The micro model algorithm can be utilized in either an unlimited file movement mode or a limited file movement mode, the former being used when the computer system undergoes a major reconfiguration while the latter is used on a once per week basis. The BLPM is solved by a "neighborhood escape" type heuristic. The procedure provides a real-world, practical solution to the FAP resulting in significant increases in performance.

63 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202331
202298
2021303
2020339
2019342
2018326