Distributed Lagrangian Relaxation Protocol for the Over-constrained Generalized Mutual Assignment Problem

2011 ◽  
pp. 174-186 ◽  
Author(s):  
Kenta Hanada ◽  
Katsutoshi Hirayama
Keyword(s):  
Lagrangian Relaxation ◽  
Assignment Problem

Solution to the quadratic assignment problem using semi-lagrangian relaxation

2016 ◽  
Vol 27 (5) ◽  
pp. 1063-1072
Author(s):  
Huizhen Zhang ◽  
◽  
Cesar Beltran-Royo ◽  
Bo Wang ◽  
Liang Ma ◽  
...  
Keyword(s):  
Lagrangian Relaxation ◽  
Assignment Problem ◽  
Quadratic Assignment Problem ◽  
Quadratic Assignment

scholarly journals Continuous Time Formulation and Lagrangian Relaxation Algorithm for the Gate Assignment Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yuan Yuan ◽  
Ping Yan ◽  
Liqiang Zhao
Keyword(s):  
Lagrangian Relaxation ◽  
Continuous Time ◽  
Assignment Problem ◽  
Second Order ◽  
Walking Distance ◽  
Relaxation Algorithm ◽  
Second Order Cone ◽  
Time Formulation ◽  
Gate Assignment ◽  
Lagrangian Relaxation Algorithm

Gates are important operating facilities and resources in civil airports. It is a core task in the airport operation management to select reasonable gates for inbound and outbound flights. We present a continuous time formulation with second-order cone programming (SOCP) for the gate assignment problem which allocates flights to available gates to optimize both the transfer time of passengers and the robustness of the airport operations schedules. The problem is formulated as a mixed integer nonlinear program, and then, the quadratic objective that minimizes the walking distance of transferring passengers is linearized, and the objective that minimizes the variance of idle time at the gates is transformed to a second-order cone constraint with a linear objective function. Then, a Lagrangian relaxation algorithm is developed by exploiting the problem structure. Computational tests are carried out to illustrate the efficiency of the model and the algorithms. It is shown that the continuous time formulation is more efficient than the existing model, and the Lagrangian relaxation algorithm can obtain better solutions faster than a commercial solver.

The Pollyanna Problem

2014 ◽  
Vol 5 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Virginia M. Miori
Keyword(s):  
Lagrangian Relaxation ◽  
Assignment Problem ◽  
Nuclear Family ◽  
Multidimensional Assignment Problem ◽  
Initial Approach ◽  
Family And Work ◽  
Gift Exchanges

The assignment problem serves as the basis for a novel formulation and initial approach to assigning participants in holiday “Pollyanna” gift exchanges. This research presents the formalization of a typical heuristic assignment with constraints as commonly imposed by family and work dynamics. The constraints include restrictions on exchanging within the same nuclear family, restrictions on repeating that same exchanges as the previous year, balancing “good” gifts with “bad” gifts and restricting direct exchanges. A multidimensional assignment problem is formulated and reformulated employing Lagrangian Relaxation.

Lagrangian Relaxation Based Inter-Layer Signal Via Assignment for 3-D ICs

2009 ◽  
Vol E92-A (4) ◽  
pp. 1080-1087 ◽  
Author(s):  
Song CHEN ◽  
Liangwei GE ◽  
Mei-Fang CHIANG ◽  
Takeshi YOSHIMURA
Keyword(s):  
Lagrangian Relaxation
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