A global optimization method for continuous network design problems

Li, Changmin; Yang, Hai; Zhu, Daqi; Meng, Qiang

doi:10.1016/j.trb.2012.05.003

Cited by 73 publications

(40 citation statements)

References 33 publications

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“…For further work, these different problems and solution techniques should be considered. Hub location problems can be applied to other network design problems, multimodal systems, or multiple airport systems [67][68][69][70], and this can also be studied for future work. In this paper, we used CPLEX directly; future work could implement more sophisticated methods, such as Benders decomposition.…”

Section: Discussionmentioning

confidence: 99%

Finding p-Hub Median Locations: An Empirical Study on Problems and Solution Techniques

Sun

Dai

Zhang

et al. 2017

Journal of Advanced Transportation

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Hub location problems have been studied by many researchers for almost 30 years, and, accordingly, various solution methods have been proposed. In this paper, we implement and evaluate several widely used methods for solving five standard hub location problems. To assess the scalability and solution qualities of these methods, three well-known datasets are used as case studies: Turkish Postal System, Australia Post, and Civil Aeronautics Board. Classical problems in small networks can be solved efficiently using CPLEX because of their low complexity. Genetic algorithms perform well for solving three types of single allocation problems, since the problem formulations can be neatly encoded with chromosomes of reasonable size. Lagrangian relaxation is the only technique that solves reliable multiple allocation problems in large networks. We believe that our work helps other researchers to get an overview on the best solution techniques for the problems investigated in our study and also stipulates further interest on cross-comparing solution techniques for more expressive problem formulations.

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Section: Discussionmentioning

confidence: 99%

Finding p-Hub Median Locations: An Empirical Study on Problems and Solution Techniques

Sun

Dai

Zhang

et al. 2017

Journal of Advanced Transportation

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“…Early approaches include the use of simulated annealing [10] and genetic algorithms [38]. Li et al [18] reduce the problem to a sequence of mathematical programs with concave objectives and convex constraints, and show that the accumulation point of the sequence of solutions is a global optimum. If the sequence is terminated early, they show weak bounds on the quality of the solution that are consequential only under strong assumptions on the delay function and agents' demands.…”

Section: Related Workmentioning

confidence: 99%

“…Many of these algorithms are surveyed in [34]. More recent papers give algorithms that obtain global optima [18,19,32], but make no guarantees on the quality of solutions that can be obtained in polynomial time.…”

Section: Introductionmentioning

confidence: 99%

Network improvement for equilibrium routing

Bhaskar

Ligett

2015

SIGecom Exch.

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In routing games, agents pick their routes through a network to minimize their own delay. A primary concern for the network designer in routing games is the average agent delay at equilibrium. A number of methods to control this average delay have received substantial attention, including network tolls, Stackelberg routing, and edge removal.A related approach with arguably greater practical relevance is that of making investments in improvements to the edges of the network, so that, for a given investment budget, the average delay at equilibrium in the improved network is minimized. This problem has received considerable attention in the literature on transportation research and a number of different algorithms have been studied. To our knowledge, none of this work gives guarantees on the output quality of any polynomial-time algorithm. We study a model for this problem introduced in transportation research literature, and present both hardness results and algorithms that obtain nearly optimal performance guarantees.• We first show that a simple algorithm obtains good approximation guarantees for the problem.Despite its simplicity, we show that for affine delays the approximation ratio of 4/3 obtained by the algorithm cannot be improved.• To obtain better results, we then consider restricted topologies. For graphs consisting of parallel paths with affine delay functions we give an optimal algorithm. However, for graphs that consist of a series of parallel links, we show the problem is weakly NP-hard.• Finally, we consider the problem in series-parallel graphs, and give an FPTAS for this case.Our work thus formalizes the intuition held by transportation researchers that the network improvement problem is hard, and presents topology-dependent algorithms that have provably tight approximation guarantees.

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“…""" =yxSwQB |Ov@u=tR w ?=NDv= |= Q@ pL VwQ wO [3] "CU= xOW xO=iDU= 'CU= xm@W QO R}v |WwQ [4] "CU= xOW x=Q= |}xrLQtOvJ |=yxm@W |L=Q] |xDUw}B |xrUt Qw]u=ty [5] …”

mentioning

confidence: 99%