scholarly journals Efficient and Easy-to-Implement Mixed-Integer Linear Programs for the Traveling Salesperson Problem with Time Windows

2018 ◽  
Vol 30 ◽  
pp. 157-166 ◽  
Author(s):  
Philipp Hungerländer ◽  
Christian Truden
Keyword(s):  
Time Windows ◽  
Mixed Integer ◽  
Linear Programs ◽  
Traveling Salesperson Problem ◽  
Integer Linear Programs

scholarly journals Distributionally robust mixed integer linear programs: Persistency models with applications

2014 ◽  
Vol 233 (3) ◽  
pp. 459-473 ◽  
Author(s):  
Xiaobo Li ◽  
Karthik Natarajan ◽  
Chung-Piaw Teo ◽  
Zhichao Zheng
Keyword(s):  
Mixed Integer ◽  
Linear Programs ◽  
Integer Linear Programs ◽  
Distributionally Robust

An optimality cut for mixed integer linear programs

1999 ◽  
Vol 119 (3) ◽  
pp. 671-677
Author(s):  
Gilbert Laporte ◽  
Frédéric Semet
Keyword(s):  
Mixed Integer ◽  
Linear Programs ◽  
Integer Linear Programs

scholarly journals Analyzing Infeasible Mixed-Integer and Integer Linear Programs

1999 ◽  
Vol 11 (1) ◽  
pp. 63-77 ◽  
Author(s):  
Olivier Guieu ◽  
John W. Chinneck
Keyword(s):  
Mixed Integer ◽  
Linear Programs ◽  
Integer Linear Programs

Variable Fixing for Two-Arc Sequences in Branch-Price-and-Cut Algorithms on Path-Based Models

2020 ◽  
Vol 54 (5) ◽  
pp. 1170-1188 ◽  
Author(s):  
Guy Desaulniers ◽  
Timo Gschwind ◽  
Stefan Irnich
Keyword(s):  
Vehicle Routing ◽  
Time Windows ◽  
Solution Process ◽  
Mixed Integer ◽  
Linear Programs ◽  
Vehicle Routing Problems ◽  
Routing Problems ◽  
Routing Problem ◽  
Benchmark Instances ◽  
Variable Fixing

Variable fixing by reduced costs is a popular technique for accelerating the solution process of mixed-integer linear programs. For vehicle-routing problems solved by branch-price-and-cut algorithms, it is possible to fix to zero the variables associated with all routes containing at least one arc from a subset of arcs determined according to the dual solution of a linear relaxation. This is equivalent to removing these arcs from the network used to generate the routes. In this paper, we extend this technique to routes containing sequences of two arcs. Such sequences or their arcs cannot be removed directly from the network because routes traversing only one arc of a sequence might still be allowed. For some of the most common vehicle-routing problems, we show how this issue can be overcome by modifying the route-generation labeling algorithm in order to remove indirectly these sequences from the network. The proposed acceleration strategy is tested on benchmark instances of the vehicle-routing problem with time windows (VRPTW) and four variants of the electric VRPTW. The computational results show that it yields a significant speedup, especially for the most difficult instances.

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