A Comparison of Heuristics for the Discrete Cost Multicommodity Network Optimization Problem

Gabrel, Virginie; Knippel, Arnaud; Minoux, Michel

doi:10.1023/b:heur.0000004812.23590.a2

Cited by 31 publications

(26 citation statements)

References 14 publications

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“…The quantities to be transported can either be of a material nature such as power or goods, or of a non-material nature such as information packets, which are transported on the Internet, or influence, which is transported on social networks [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. Optimization of network transport is thus an important problem for a variety of fields in science and technology.…”

Section: Introductionmentioning

confidence: 99%

Transport optimization on complex networks

Danila

Marsh

et al. 2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

100

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We present a comparative study of the application of a recently introduced heuristic algorithm to the optimization of transport on three major types of complex networks. The algorithm balances network traffic iteratively by minimizing the maximum node betweenness with as little path lengthening as possible. We show that by using this optimal routing, a network can sustain significantly higher traffic without jamming than in the case of shortest path routing. A formula is proved that allows quick computation of the average number of hops along the path and of the average travel times once the betweennesses of the nodes are computed. Using this formula, we show that routing optimization preserves the small-world character exhibited by networks under shortest path routing, and that it significantly reduces the average travel time on congested networks with only a negligible increase in the average travel time at low loads. Finally, we study the correlation between the weights of the links in the case of optimal routing and the betweennesses of the nodes connected by them.Keywords: complex networks, scaling laws, transport * dbogdan@mail.uh.edu † marshj@ainfosec.com ‡ bassler@uh.edu 1 One of the most important problems in the study of complex networks is how to best route transport on the networks. This problem is important because transport is the main function of many natural and human-made networks. Often, the transport routes used on networks are the so-called shortest-path routes, which are the routes with the minimum number of hops between any two nodes. However, this approach, which is currently used to route transport of information packets on the Internet, typically leads to congestion and eventually jamming of highly connected nodes of the networks called hubs. For this reason and in light of recent research, interest has developed in finding the routing rules that allow a given network to bear the maximum possible traffic. Specifically, the problem can be stated as follows. Given a complex network and a set of processing power and traffic demand constraints for its nodes, find the set of routing rules which allow the network to bear the highest possible amount of traffic without jamming. This problem is known to be NP -hard, meaning that the time required for the computation of an exact solution increases with the number of nodes faster than any polynomial. In this paper we argue that a heuristic transport routing optimization algorithm recently published by us achieves near-optimal transport routing in polynomial time and show this to be true for three important types of complex networks. Of course, any optimized routing when compared to shortest-path routing occurs at the expense of increasing the average number of hops between the nodes. We show that with our algorithm the average number of hops after optimization increases with the number of nodes no faster than logarithmically and that optimization significantly decreases the average travel time on congested networks.

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Section: Introductionmentioning

confidence: 99%

Transport optimization on complex networks

Danila

Marsh

et al. 2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

100

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“…In the case of the Internet, link weights are typically assigned manually by operators according to simple rules based on experience [1]. Recently, a series of heuristic algorithms have also been proposed for network traffic optimization [1,2,3,4,5]. These rules and algorithms are aimed at avoiding or reducing link overload by a judicious link weight assignment.…”

mentioning

confidence: 99%

Optimal transport on complex networks

Danila

Marsh³

et al. 2006

Phys. Rev. E

218

187

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We present a novel heuristic algorithm for routing optimization on complex networks. Previously proposed routing optimization algorithms aim at avoiding or reducing link overload. Our algorithm balances traffic on a network by minimizing the maximum node betweenness with as little path lengthening as possible, thus being useful in cases when networks are jamming due to queuing overload. By using the resulting routing table, a network can sustain significantly higher traffic without jamming than in the case of traditional shortest path routing.

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“…A survey of the developments in this field is given in [4] and, more recently, in [21,23,30]. In particular, IPRR belongs to the wide class of Discrete Cost Multicommodity Flow problem with Survivability constraints (DCSMCF), as the cost for reserving capacity on links is a step cost function.…”

Section: Related Workmentioning

confidence: 99%

“…As described in [23], the first Local Search based algorithms in the field of Network Design use link adding, dropping and branching (swapping) moves. More recently, many different kinds of perturbation to a given solution have been proposed to produce clever neighborhoods able to direct the search toward interesting regions and/or to generate in a faster way probably improving solutions (see, e.g., [11,21,30,31]). All of these moves (which are different from the simple link adding, dropping or swapping) are based on the possibility of arbitrarily moving commodities or fractions of them toward different routings.…”

Section: Neighborhoodsmentioning

confidence: 99%

Tailoring neighborhood search for the internet protocol network design problem with reliability and routing constraints

Giovanni

Tadei

2006

Networks

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The Internet Protocol Network Design Problem with Reliability and Routing Constraints (IPRR) can be shortly stated as follows. A telecommunication network is given in terms of a set of nodes and a set of traffic demands; we want to define the minimum cost capacity reservation such that all the traffic is routed even under fault scenarios. Capacity is provided by reserving some already installed devices of a given capacity between pairs of nodes and traffic must be loaded on the network according to the OSPF-ECM (Open Shortest Path FirstEqual Commodity Multipath) protocol, with additional constraints on the maximum number of hops. The problem is ᏺᏼ-Hard and literature proposes neighborhood search heuristics that do not take the reliability and max-hop requirements into account, or assume a simplified OSPF routing. The design and the implementation of the components of any neighborhood search algorithms are strongly conditioned by the reliability and routing constraints, which imply a huge amount of hopconstrained shortest paths to be taken into account. This work shows how the components of these heuristics can be implemented, with particular emphasis to the setting up of an efficient neighborhood evaluation procedure, the discussion of its incremental version, and the introduction of effective reduced-size neighborhoods. Computational experiments on instances derived from real networks are also presented, and they show the proposed components make the neighborhood search a viable approach for IPRR.

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A Comparison of Heuristics for the Discrete Cost Multicommodity Network Optimization Problem

Cited by 31 publications

References 14 publications

Transport optimization on complex networks

Transport optimization on complex networks

Optimal transport on complex networks

Tailoring neighborhood search for the internet protocol network design problem with reliability and routing constraints

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