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Strategic oscillation for the capacitated hub location problem with modular links

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Ángel Corberán at University of Valencia
Ángel Corberán
Juanjo Peiró
Juanjo Peiró
Juanjo Peiró
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Vicente Campos
Vicente Campos
Vicente Campos
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Fred Glover at University of Colorado Boulder
Fred Glover
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Abstract and Figures

The capacitated single assignment hub location problem with modular link capacities is a variant of the classical hub location problem in which the cost of using edges is not linear but stepwise, and the hubs are restricted in terms of transit capacity rather than in the incoming traffic. We propose a metaheuristic algorithm based on strategic oscillation, a methodology originally introduced in the context of tabu search. Our method incorporates several designs for constructive and destructive algorithms, together with associated local search procedures, to balance diversification and intensification for an efficient search. Computational results on a large set of instances show that, in contrast to exact methods that can only solve small instances optimally, our metaheuristic is able to find high-quality solutions on larger instances in short computing times. In addition, the new method, which joins tabu search strategies with strategic oscillation, outperforms the previous tabu search implementation.
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J Heuristics (2016) 22:221–244
DOI 10.1007/s10732-016-9308-7
Strategic oscillation for the capacitated hub location
problem with modular links
Ángel Corberán1·Juanjo Peiró1·
Vicente Campos1·Fred Glover2·Rafael Martí1
Received: 21 March 2014 / Revised: 7 October 2015 / Accepted: 18 January 2016 /
Published online: 28 January 2016
© Springer Science+Business Media New York 2016
Abstract The capacitated single assignment hub location problem with modular link
capacities is a variant of the classical hub location problem in which the cost of
using edges is not linear but stepwise, and the hubs are restricted in terms of transit
capacity rather than in the incoming traffic. We propose a metaheuristic algorithm
based on strategic oscillation, a methodology originally introduced in the context of
tabu search. Our method incorporates several designs for constructive and destructive
algorithms, together with associated local search procedures, to balance diversification
and intensification for an efficient search. Computational results on a large set of
instances show that, in contrast to exact methods that can only solve small instances
optimally, our metaheuristic is able to find high-quality solutions on larger instances in
short computing times. In addition, the new method, which joins tabu search strategies
with strategic oscillation, outperforms the previous tabu search implementation.
Keywords Hub location problem ·Modular link costs ·Tabu search ·Strategic
oscillation ·Iterated greedy
1 Introduction
Discrete facility location problems related to the design of transportation networks
are one of the most extensively studied problems in combinatorial optimization due
to their variety and importance. There are several variants of discrete facility location
problems, such as the p-median problem, the p-center problem, the maximal covering
BRafael Martí
rafael.marti@uv.es
1Departament d’Estadística i Investigació Operativa, Universitat de València, Valencia, Spain
2OptTek Systems, Boulder, CO, USA
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... The algorithm adopts the strategic oscillation search framework with an original responsive mechanism to guide the search to oscillate around the boundary of feasible and infeasible regions. Previous investigations have disclosed the general idea of strategic oscillation (SOS, [12]) to be quite effective for a number of constrained optimization problems, such as the quadratic multiple knapsack problem [11], the capacitated hub location problem [9], the maximally diverse grouping problem [10], the quadratic minimum spanning tree problem [31], the α-neighbor p-center problem [40], and the bipartite boolean quadratic programming problem [45,49]. In this work, we show the benefits of strategic oscillation for solving the DCKP. ...
... S ← S /* S replaces S when the threshold T is satisfied */ 11: break; 12: As shown in Algorithm 2, the FLS procedure first performs some initialization tasks (lines [3][4][5]. Then the search enters the 'while' loop (lines [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] to improve the input solution S iteratively by sequentially exploring three neighborhoods N F 1 to N F 3 (see [46] for more details). Each iteration of the 'while' loop performs three operations. ...
... As shown in Algorithm 3, after some initialization tasks (lines 3-7), the SOS procedure performs the 'while' loop to examine candidate solutions (lines [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Each iteration of the loop calculates, according to Equation (8), the critical value CV (S ) of each non-prohibited neighboring solution S within the neighborhood N + (line 10), where N + is the union of three relaxed neighborhoods (see Section 2.5.2 for these relaxed neighborhoods.) ...
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... S ← S /* S replaces S when the threshold T is satisfied */ 11: break; 12: As shown in Algorithm 2, the FLS procedure first performs some initialization tasks (lines [3][4][5]. Then the search enters the 'while' loop (lines [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] to improve the input solution S iteratively by sequentially exploring three neighborhoods N F 1 to N F 3 (see [46] for more details). Each iteration of the 'while' loop performs three operations. ...
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