On the Complexity of a Column Generation Algorithm for Convex or Quasiconvex Feasibility Problems

1994 ◽  
pp. 182-191 ◽  
Author(s):  
Jean-Louis Goffin ◽  
Zhi-Quan Luo ◽  
Yinyu Ye
Keyword(s):  
Column Generation ◽  
Generation Algorithm

scholarly journals A HYBRID COLUMN GENERATION ALGORITHM BASED ON METAHEURISTIC OPTIMIZATION

Transport ◽  
2013 ◽  
Vol 31 (4) ◽  
pp. 389-407 ◽  
Author(s):  
Wenbin Hu ◽  
Bo Du ◽  
Ye Wu ◽  
Huangle Liang ◽  
Chao Peng ◽  
...  
Keyword(s):  
Column Generation ◽  
Time Windows ◽  
Path Selection ◽  
Optimization Strategy ◽  
Heuristic Solution ◽  
Generation Algorithm ◽  
Metaheuristic Optimization ◽  
Selection Strategies ◽  
Dual Variables ◽  
Labelling Algorithm

The exact solution and heuristic solution have their own strengths and weaknesses on solving the Vehicle Routing Problems with Time Windows (VRPTW). This paper proposes a hybrid Column Generation Algorithm with Metaheuristic Optimization (CGAMO) to overcome their weaknesses. Firstly, a Modified Labelling Algorithm (MLA) in the sub-problem of path searching is analysed. And a search strategy in CGAMO based on the demand of sub-problem is proposed to improve the searching efficiency. While putting the paths found in the sub-problem into the main problems of CGAMO, the iterations may fall into endless loops. To avoid this problem and keep the main problems in a reasonable size, two conditions on saving the old paths in the main problem are used. These conditions enlarge the number of constraints considered in the iterations to strengthen the limits of dual variables. Through analysing the sub-problem, we can find many useless paths that have no effect on the objective function. Secondly, in order to reduce the number of useless paths and improve the efficiency, this paper proposes a heuristic optimization strategy of CGAMO for dual variables. It is supposed to accelerate the solving speed from the view of on the dual problem. Finally, extensive experiments show that CGAMO achieves a better performance than other state-of-the-art methods on solving VRPTW. The comparative experiments also present the parameters sensitivity analysis, including the different effects of MLA in the different path selection strategies, the characteristics and the applicable scopes of the two pathkeeping conditions in the main problem.

A Note on “The Facility Location Problem with Limited Distances”

2020 ◽  
Vol 54 (6) ◽  
pp. 1439-1445
Author(s):  
Prahalad Venkateshan
Keyword(s):  
Facility Location ◽  
Column Generation ◽  
Location Problem ◽  
Facility Location Problem ◽  
Sum Of Squares ◽  
Generation Algorithm ◽  
Math Programming ◽  
Modified Algorithm

In this paper, it is shown that the polynomially bounded enumerative procedure to solve the facility location problem with limited distances, originally described by Drezner, Mehrez, and Wesolowsky [Drezner Z, Mehrez A, Wesolowsky GO (1991) The facility location problem with limited distances. Transportation Sci. 25(3):183–187.], and subsequently corrected by Aloise, Hansen, and Liberti [Aloise D, Hansen P, Liberti L (2012) An improved column generation algorithm for minimum sum-of-squares clustering. Math. Programming 131(1–2):195–220.], can still fail to optimally solve the problem. Conditions under which the procedures succeed are identified. A new modified algorithm is presented that solves the facility location problem with limited distances. It is further shown that the proposed correction is complete in that it does not require further corrections.

A column generation algorithm for the bus driver scheduling problem

2016 ◽  
Vol 50 (8) ◽  
pp. 1598-1615 ◽  
Author(s):  
Dung‐Ying Lin ◽  
Ching‐Lan Hsu
Keyword(s):  
Column Generation ◽  
Scheduling Problem ◽  
Generation Algorithm ◽  
Driver Scheduling ◽  
Bus Driver

A new column generation algorithm for Logical Analysis of Data

2011 ◽  
Vol 188 (1) ◽  
pp. 215-249 ◽  
Author(s):  
Pierre Hansen ◽  
Christophe Meyer
Keyword(s):  
Column Generation ◽  
Logical Analysis ◽  
Logical Analysis Of Data ◽  
Generation Algorithm
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