Optimization with Extremal Dynamics

Boettcher, Stefan; Percus, Allon G.

doi:10.1103/physrevlett.86.5211

Cited by 313 publications

(253 citation statements)

References 25 publications

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“…Note that the algorithm picks the "least fit" element of a set and changes its parameters. Therefore, it is a from extremal optimization [18]. However, this algorithm assigns parameters in a deterministic way, unlike many of the other existing extremal optimization algorithms.…”

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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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confidence: 99%

Optimal transport on complex networks

Danila

Marsh³

et al. 2006

Phys. Rev. E

218

187

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“…Indeed, it is possible to relate the current optimization problem for Q with classical problems in statistical physics, e.g. the spin glass problem of finding the ground state energy [15], where algorithms inspired in natural optimization processes as simulated annealing [16] and genetic algorithms [17] have been successfully used.In this Letter, we propose a new divisive algorithm that optimizes the modularity Q using an heuristic search based on the Extremal Optimization (EO) algorithm proposed by Boettcher and Percus [18,19]. This algorithm is inspired in turn in the evolution model of , and basically operates optimizing a global variable by improving extremal local variables that involve coevolutionary avalanches.…”

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confidence: 99%

Community detection in complex networks using extremal optimization

2005

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We propose a novel method to find the community structure in complex networks based on an extremal optimization of the value of modularity. The method outperforms the optimal modularity found by the existing algorithms in the literature. We present the results of the algorithm for computer simulated and real networks and compare them with other approaches. The efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks. PACS numbers:The description of the structure of complex networks has been one of the focus of attention of the physicist's community in the recent years. The levels of description range from the microscopic (degree, clustering coefficient, centrality measures, etc., of individual nodes) to the macroscopic description in terms of statistical properties of the whole network (degree distribution, total clustering coefficient, degree-degree correlations, etc.) [1,2,3,4]. Between these two extremes there is a "mesoscopic" description of networks that tries to explain its community structure. The general notion of community structure in complex networks was first pointed out in the physics literature by Girvan and Newman [5], and refers to the fact that nodes in many real networks appear to group in subgraphs in which the density of internal connections is larger than the connections with the rest of nodes in the network.The community structure has been empirically found in many real technological, biological and social networks [6,7,8,9, 10] and its emergence seems to be at the heart of the network formation process [11].The existing methods intended to devise the community structure in complex networks have been recently reviewed in [10]. All these methods require a definition of community that imposes the limit up to which a group should be considered a community. However, the concept of community itself is qualitative: nodes must be more connected within its community than with the rest of the network, and its quantification is still a subject of debate. Some quantitative definitions that came from sociology have been used in recent studies [12], but in general, the physics community has widely accepted a recent measure for the community structure based on the concept of modularity Q introduced by Newman and Girvan [13]:where e rr are the fraction of links that connect two nodes inside the community r, a r the fraction of links that have one or both vertices inside of the community r, and the sum extends to all communities r in a given network. Note that this measure provides a way to determine if a certain mesoscopic description of the graph in terms of communities is more or less accurate. The larger the values of Q the most accurate a partition into communities is.The search for the optimal (largest) modularity value is a NP-hard problem due to the fact that the space of possible partitions grows faster than any power of the system size. For this reason, a heuristic search strategy is mandatory to restrict th...

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“…At the same time new firm (with the same index) is established at a new random position with some initially random size. This death-birth process is analogous to the so called extremal dynamics principle [1] applied to e.g. models of the wealth distribution [12] and stock markets [7].…”

Section: Firm Growthmentioning

confidence: 99%

Statistical properties of agent-based market area model

Kuscsik

Horváth

2012

Unifying Themes in Complex Systems VII

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One dimensional stylized model taking into account spatial activity of firms with uniformly distributed customers is proposed. The spatial selling area of each firm is defined by a short interval cut out from selling space (large interval). In this representation, the firm size is directly associated with the size of its selling interval.The recursive synchronous dynamics of economic evolution is discussed where the growth rate is proportional to the firm size incremented by the term including the overlap of the selling area with areas of competing firms. Other words, the overlap of selling areas inherently generate a negative feedback originated from the pattern of demand. Numerical simulations focused on the obtaining of the firm size distributions uncovered that the range of free parameters where the Pareto's law holds corresponds to the range for which the pair correlation between the nearest neighbor firms attains its minimum.

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Optimization with Extremal Dynamics

Cited by 313 publications

References 25 publications

Optimal transport on complex networks

Optimal transport on complex networks

Community detection in complex networks using extremal optimization

Statistical properties of agent-based market area model

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