A shortest augmenting path algorithm for dense and sparse linear assignment problems

One of the major challenges in the coordination of large, open, collaborative, and commercial vehicle fleets is dynamic task allocation. Self-concerned individually rational vehicle drivers have both local and global objectives, which require coordination using some fair and efficient task allocation method. In this paper, we review the literature on scalable and dynamic task allocation focusing on deterministic and dynamic two-dimensional linear assignment problems. We focus on multiagent system representation of open vehicle fleets where dynamically appearing vehicles are represented by software agents that should be allocated to a set of dynamically appearing tasks. We give a comparison and critical analysis of recent research results focusing on centralized, distributed, and decentralized solution approaches. Moreover, we propose mathematical models for dynamic versions of the following assignment problems well known in combinatorial optimization: the assignment problem, bottleneck assignment problem, fair matching problem, dynamic minimum deviation assignment problem, Σk-assignment problem, the semiassignment problem, the assignment problem with side constraints, and the assignment problem while recognizing agent qualification; all while considering the main aspect of open vehicle fleets: random arrival of tasks and vehicles (agents) that may become available after assisting previous tasks or by participating in the fleet at times based on individual interest.

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White Matter Tract Segmentation as Multiple Linear Assignment Problems

Frontiers in Neuroscience ◽

10.3389/fnins.2017.00754 ◽

2018 ◽

Vol 11 ◽

Cited By ~ 9

Author(s):

Nusrat Sharmin ◽

Emanuele Olivetti ◽

Paolo Avesani

Keyword(s):

White Matter ◽

White Matter Tract ◽

Assignment Problems ◽

Linear Assignment

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Anatomically-Informed Multiple Linear Assignment Problems for White Matter Bundle Segmentation

2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019) ◽

10.1109/isbi.2019.8759174 ◽

2019 ◽

Cited By ~ 1

Author(s):

Giulia Berto ◽

Paolo Avesani ◽

Franco Pestilli ◽

Daniel Bullock ◽

Bradley Caron ◽

...

Keyword(s):

White Matter ◽

Assignment Problems ◽

Linear Assignment

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A Lexicographic Approach to Fuzzy Linear Assignment Problems with Different Types of Fuzzy Numbers

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488520500178 ◽

2020 ◽

Vol 28 (03) ◽

pp. 421-441 ◽

Cited By ~ 1

Author(s):

Boris Pérez-Cañedo ◽

Eduardo R. Concepción-Morales

Keyword(s):

Assignment Problem ◽

Fuzzy Numbers ◽

Multiple Criteria Decision Analysis ◽

Assignment Problems ◽

Solution Approach ◽

Linear Assignment Problem ◽

Different Types ◽

Standard Solution ◽

The Cost ◽

Linear Assignment

The fuzzy linear assignment problem (FLAP) is an extension of the classical linear assignment problem (LAP) to situations in which uncertainty in the cost coefficients is represented by fuzzy numbers. FLAP applications range from the assignment of workers to tasks to multiple-criteria decision analysis in fuzzy environments and many other engineering applications. Most FLAP formulations assume that all cost coefficients are fuzzy numbers of the same type (e.g. triangular, trapezoidal). The standard solution approach is the defuzzification of the cost coefficients, thus transforming the FLAP into a crisp LAP that can be solved by classical assignment algorithms such as the Hungarian method. It is known that defuzzification methods suffer from lack of discrimination when comparing fuzzy numbers which may lead to suboptimal assignments. The solution approach proposed in this paper is based on the theory of algebraic assignment problems and total orderings in the set of all fuzzy numbers, and it allows to solve FLAPs with different types of fuzzy numbers. More specifically, the FLAP is transformed into a lexicographic linear assignment problem (LLAP) which is solved in its place. We show, both theoretically and numerically, how this transformation overcomes the limitations present in existing approaches.

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