An Improved Petal Heuristic for the Vehicle Routeing Problem

1996 ◽  
Vol 47 (2) ◽  
pp. 329 ◽  
Author(s):  
Jacques Renaud ◽  
Fayez F. Boctor ◽  
Gilbert Laporte
Keyword(s):  
Vehicle Routeing ◽  
Vehicle Routeing Problem

A guided tabu search for the heterogeneous vehicle routeing problem

2008 ◽  
Vol 59 (12) ◽  
pp. 1659-1673 ◽  
Author(s):  
C D Tarantilis ◽  
E E Zachariadis ◽  
C T Kiranoudis
Keyword(s):  
Tabu Search ◽  
Vehicle Routeing ◽  
Vehicle Routeing Problem

The Vehicle Routeing Problem

1994 ◽  
Vol 7 (1) ◽  
pp. 11-13 ◽  
Author(s):  
Alberto G. Canen ◽  
Nelio D. Pizzolato
Keyword(s):  
Vehicle Routeing ◽  
Vehicle Routeing Problem

scholarly journals Erratum: A guided tabu search for the heterogeneous vehicle routeing problem

2008 ◽  
Vol 59 (12) ◽  
pp. 1698-1699 ◽  
Author(s):  
C D Tarantilis ◽  
E E Zachariadis ◽  
C T Kiranoudis
Keyword(s):  
Tabu Search ◽  
Vehicle Routeing ◽  
Vehicle Routeing Problem

scholarly journals Probabilistic Analysis of Unit-Demand Vehicle Routeing Problems

2007 ◽  
Vol 44 (1) ◽  
pp. 259-278 ◽  
Author(s):  
Agustín Bompadre ◽  
Moshe Dror ◽  
James B. Orlin
Keyword(s):  
Approximation Algorithm ◽  
Lower Bounds ◽  
Probabilistic Analysis ◽  
Open Problem ◽  
Optimal Cost ◽  
Vehicle Routeing ◽  
Unit Demand ◽  
Number Of Customers ◽  
Independent Identically Distributed ◽  
Vehicle Routeing Problem

We analyze the unit-demand Euclidean vehicle routeing problem, where n customers are modeled as independent, identically distributed uniform points and have unit demand. We show new lower bounds on the optimal cost for the metric vehicle routeing problem and analyze them in this setting. We prove that there exists a constant ĉ > 0 such that the iterated tour partitioning heuristic given by Haimovich and Rinnooy Kan (1985) is a (2 - ĉ)-approximation algorithm with probability arbitrarily close to 1 as the number of customers goes to ∞. It has been a longstanding open problem as to whether one can improve upon the factor of 2 given by Haimovich and Rinnooy Kan. We also generalize this, and previous results, to the multidepot case.

scholarly journals Probabilistic Analysis of Unit-Demand Vehicle Routeing Problems

2007 ◽  
Vol 44 (01) ◽  
pp. 259-278 ◽  
Author(s):  
Agustín Bompadre ◽  
Moshe Dror ◽  
James B. Orlin
Keyword(s):  
Approximation Algorithm ◽  
Lower Bounds ◽  
Probabilistic Analysis ◽  
Open Problem ◽  
Optimal Cost ◽  
Vehicle Routeing ◽  
Unit Demand ◽  
Number Of Customers ◽  
Independent Identically Distributed ◽  
Vehicle Routeing Problem

We analyze the unit-demand Euclidean vehicle routeing problem, where n customers are modeled as independent, identically distributed uniform points and have unit demand. We show new lower bounds on the optimal cost for the metric vehicle routeing problem and analyze them in this setting. We prove that there exists a constant ĉ > 0 such that the iterated tour partitioning heuristic given by Haimovich and Rinnooy Kan (1985) is a (2 - ĉ)-approximation algorithm with probability arbitrarily close to 1 as the number of customers goes to ∞. It has been a longstanding open problem as to whether one can improve upon the factor of 2 given by Haimovich and Rinnooy Kan. We also generalize this, and previous results, to the multidepot case.

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