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

2020 ◽  
Vol 28 (03) ◽  
pp. 421-441 ◽  
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.

A Determinant Elimination Method for Bottleneck Assignment and Generalized Assignment Problems

2012 ◽  
Vol 239-240 ◽  
pp. 1522-1527
Author(s):  
Wen Bo Wu ◽  
Yu Fu Jia ◽  
Hong Xing Sun
Keyword(s):  
Computational Complexity ◽  
Optimization Algorithm ◽  
Assignment Problem ◽  
Numerical Experiments ◽  
High Efficiency ◽  
Synthesis Method ◽  
Assignment Problems ◽  
Generalized Assignment ◽  
The Cost ◽  
Time And Space Complexity

The bottleneck assignment (BA) and the generalized assignment (GA) problems and their exact solutions are explored in this paper. Firstly, a determinant elimination (DE) method is proposed based on the discussion of the time and space complexity of the enumeration method for both BA and GA problems. The optimization algorithm to the pre-assignment problem is then discussed and the adjusting and transformation to the cost matrix is adopted to reduce the computational complexity of the DE method. Finally, a synthesis method for both BA and GA problems is presented. The numerical experiments are carried out and the results indicate that the proposed method is feasible and of high efficiency.

scholarly journals Topology-Aware Strategy for MPI-IO Operations in Clusters

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Weifeng Liu ◽  
Jie Zhou ◽  
Meng Guo
Keyword(s):  
Phase I ◽  
Execution Time ◽  
Assignment Problem ◽  
Optimal Assignment ◽  
Local Data ◽  
Two Phase ◽  
File Access ◽  
Linear Assignment Problem ◽  
Linear Assignment

This paper presents the topology-aware two-phase I/O (TATP), which optimizes the most popular collective MPI-IO implementation of ROMIO. In order to improve the hop-bytes metric during the file access, topology-aware two-phase I/O employs the Linear Assignment Problem (LAP) for finding an optimal assignment of file domain to aggregators, an aspect which is not considered in most two-phase I/O implementations. The distribution is based on the local data stored by each process, and its main purpose is to reduce the total hop-bytes of the I/O collective operation. Therefore, the global execution time can be improved. In most of the considered scenarios, topology-aware two-phase I/O obtains important improvements when compared with the original two-phase I/O implementations.

scholarly journals Decentralizing Coordination in Open Vehicle Fleets for Scalable and Dynamic Task Allocation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Marin Lujak ◽  
Stefano Giordani ◽  
Andrea Omicini ◽  
Sascha Ossowski
Keyword(s):  
Task Allocation ◽  
Assignment Problem ◽  
Individual Interest ◽  
Matching Problem ◽  
Assignment Problems ◽  
Dynamic Task ◽  
Side Constraints ◽  
Dynamic Task Allocation ◽  
Bottleneck Assignment Problem ◽  
Linear Assignment

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.

A negative dual rectangle cancellation algorithm for the linear assignment problem

2013 ◽  
Vol 65 (4) ◽  
pp. 673-678 ◽  
Author(s):  
Mohammad S. Sabbagh ◽  
Sayyed R. Mousavi ◽  
Yasin Zamani
Keyword(s):  
Assignment Problem ◽  
Linear Assignment Problem ◽  
Linear Assignment

Statistical Physics Algorithms That Converge

1994 ◽  
Vol 6 (3) ◽  
pp. 341-356 ◽  
Author(s):  
A. L. Yuille ◽  
J. J. Kosowsky
Keyword(s):  
Field Theory ◽  
Assignment Problem ◽  
Statistical Physics ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Mean Field Theory ◽  
Mean Field ◽  
Approximate Solutions ◽  
Linear Assignment Problem ◽  
Linear Assignment

In recent years there has been significant interest in adapting techniques from statistical physics, in particular mean field theory, to provide deterministic heuristic algorithms for obtaining approximate solutions to optimization problems. Although these algorithms have been shown experimentally to be successful there has been little theoretical analysis of them. In this paper we demonstrate connections between mean field theory methods and other approaches, in particular, barrier function and interior point methods. As an explicit example, we summarize our work on the linear assignment problem. In this previous work we defined a number of algorithms, including deterministic annealing, for solving the assignment problem. We proved convergence, gave bounds on the convergence times, and showed relations to other optimization algorithms.

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