Fuzzy Zoning: A Lagrangean relaxation approach

2016 ◽  
Author(s):  
Siamak Naderi ◽  
Kemal Kilic
Keyword(s):  
Lagrangean Relaxation

Solving Vehicle Routing Problems Using Constraint Programming and Lagrangean Relaxation in a Metaheuristics Framework

2011 ◽  
Vol 4 (2) ◽  
pp. 61-81 ◽  
Author(s):  
D. Guimarans ◽  
R. Herrero ◽  
J. J. Ramos ◽  
S. Padrón
Keyword(s):  
Vehicle Routing ◽  
Constraint Programming ◽  
Complete Solution ◽  
Lagrangean Relaxation ◽  
Variable Neighbourhood Search ◽  
Relaxation Methods ◽  
Routing Problem ◽  
Neighbourhood Search ◽  
Test Instance ◽  
Initial Feasible Solution

This paper presents a methodology based on the Variable Neighbourhood Search metaheuristic, applied to the Capacitated Vehicle Routing Problem. The presented approach uses Constraint Programming and Lagrangean Relaxation methods in order to improve algorithm’s efficiency. The complete problem is decomposed into two separated subproblems, to which the mentioned techniques are applied to obtain a complete solution. With this decomposition, the methodology provides a quick initial feasible solution which is rapidly improved by metaheuristics’ iterative process. Constraint Programming and Lagrangean Relaxation are also embedded within this structure to ensure constraints satisfaction and to reduce the calculation burden. By means of the proposed methodology, promising results have been obtained. Remarkable results presented in this paper include a new best-known solution for a rarely solved 200-customers test instance, as well as a better alternative solution for another benchmark problem.

Approximate k -MSTs and k -Steiner trees via the primal-dual method and Lagrangean relaxation

2004 ◽  
Vol 100 (2) ◽  
pp. 411-421 ◽  
Author(s):  
Fabi�n A. Chudak ◽  
Tim Roughgarden ◽  
David P. Williamson
Keyword(s):  
Lagrangean Relaxation ◽  
Steiner Trees ◽  
Dual Method ◽  
Primal Dual

scholarly journals An ADD/DROP procedure for the capacitated plant location problem

2004 ◽  
Vol 24 (1) ◽  
pp. 151-162 ◽  
Author(s):  
Claudio Thomas Bornstein ◽  
Manoel Campêlo
Keyword(s):  
Heuristic Algorithm ◽  
Location Problem ◽  
Lagrangean Relaxation ◽  
Upper Bounds ◽  
Transportation Costs ◽  
Plant Location ◽  
Computational Results ◽  
Lower And Upper Bounds

The capacitated plant location problem with linear transportation costs is considered. Exact rules and heuristics are presented for opening or closing of facilities. A heuristic algorithm based on ADD/DROP strategies is proposed. Procedures are implemented with the help of lower and upper bounds using Lagrangean relaxation. Computational results are presented and comparisons with other algorithms are made.

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