Skip to main content. Advertisement Hide. Introduction to Genetic Algorithms for Engineering Optimization. This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access. Davidor, Y. Analogous crossover. Google Scholar. Dawkins, R. The Blind Watchmaker.

New York: Penguin Books. The Selfish Gene. New York: Oxford University Press. Deb, K, Reddy, A.

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Optimal scheduling of casting sequence using genetic algorithms. Deb, K. Multi-objective optimization using evolutionary algorithms. Chichester, UK: Wiley. An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering, 2—4 , — An introduction to genetic algorithms. Sadhana , 24 4 , — Car suspension design for comfort using geneticalgorithms.

In Thomas Back Ed. Optimization for engineering design : Algorithms and examples. Delhi: Prentice-Hall. Genetic algorithms in optimal optical filter design. Balagurusamy and B. Sushila Eds. Complex Systems , 9 — An investigation of niche and species formation in genetic function optimization, Proceedings of the Third International Conference on Genetic Algorithms , pp. Demie, M. Optimization of characteristics of the elasto-damping elements of a passenger car by means of a modified Nelder-Mead method.

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Simulation 62 4 , — CrossRef Google Scholar. Holland, J. There are 4 main processes that are being utilised extensively in the 5 main stages in the proposed algorithm see Fig. These are now explained in the following subsections. In Stage 1, each node is given a unique label.

The SDI score for each couple of nodes are calculated. In Stage 3, the size of communities is further increased by using CLP 2.

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On the other hand, the number of detected communities are reduced by using GM 1 and GM 2 processes. The dash symbol indicates combination of the processes. The number of communities are further reduced in Stage 4. The processes in this stage are executed recursively until it reaches a stability where the number of communities cannot be reduced anymore. There are two ways of proceeding Stage 5. The first way is to execute all the parts in this stage.

It is common to find that after a few iterations of the LPA, some of the detected communities are far stronger than most of the others.

## Constraint Networks. Targeting Simplicity for Techniques and Algorithms

These communities will grow exponentially in the later stages of the LPA. Eventually, this phenomenon may lead to trivial detection, where the LPA only detects a single community that consists of all the nodes in a network. In order to prevent this kind of detection, communities that exceed a strength threshold are exempted from the propagation and merging processes. By doing so, the other communities have the chance to grow without competing with those communities.

Given that and as the set of communities and their corresponding member nodes in the communities, the term is defined as the intra-community degree. For instance, shows that is connected to 5 other member nodes in community. Then, the strength value of the member nodes in the communities is defined as:. As consequence, the strength value of the communities can be obtained:. Finally, is defined as a set of communities with.

Nodes are updated synchronously in CLP unless stated otherwise. Let node be the targeted node. A community c i is eligible to claim if it fulfils the following conditions:. Let be the total number of edges between and. If Q0 is the minimum and Q1 is the first quartile of , then must be larger or equal to Q0 or Q1. This condition is defined differently at various stages of the algorithm. However, this condition does not always increase or retain the strength of the communities after the solo nodes enter the communities. Therefore, CLP Condition 3 is implemented for this purpose.

Finally, CLP Condition 2 ensures that the target solo nodes do not enter the exempted communities. If there is a tie between multiple communities, the mean of the SDI of the competing communities is compared. For example, let there be a tie between communities c 1 and c 2. The targeted node v S 1 is connected to c 1 and c 2 via , and , , respectively.

If the of v S 1 with , is higher than that for v S 1 with , , it will enter c 1 provided that the CLP Condition 3 is satisfied. The labels of the nodes remain the same if there is a tie in the. As a consequence, V GR are updated asynchronously. Start with the largest community in descending order, a couple of communities, c i and c j , can be merged if the following conditions are met:.

Then, this condition is defined as. Let be the total number of intra-community edges in the communities. Two ratios are obtained, where RatioA is the average number of edges in c j and RatioB is the average number of edges between c i and c j. Then this condition is defined as:. Nonetheless, this merging strategy can still maintain the strength of the merged communities to some extent. The details of the stages and their corresponding processes are explained in the following subsections.

It must be noted that does not include node y and vice verse. The term represents the number of mutual neighbouring nodes of x and y. This stage aims to detect as many communities as possible in a network.

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Nodes with one degree are grouped with their sole neighbouring nodes to form communities. Let be a set of neighbouring nodes of node x , and the highest SDI score of node x is defined as. In this CLP, a community c i must have at least one member node which has the highest SDI score with the target solo node ,. CLP Condition 2 is not required here. CLP Condition 3 is defined as. The labels of the nodes remain the same if there is a tie between multiple communities.

CLP Condition 3 is defined as here. The labels of the nodes again remain the same if there is a tie between multiple communities. In this stage, both the CLP 2 and GNR 2 processes are executed iteratively in order to further increase the sizes of the communities. In order to reduce the large number of communities that are detected in Stage 2, GM1 and GM2 are introduced in this stage. GM 1: Execute the GM process on communities with more than 3 member nodes,. This step prevents the communities with lesser than 4 member nodes from disrupting the merging process, which have the potential of forming monster size communities.

GM 2: Unlike GM 1, all the detected communities, regardless of their sizes, can be merged. However, a new condition where the modularity score does not decrease after the merging is added in GM 2. This additional condition controls the merging of the communities with lesser than 4 member nodes. In Stage 4, GM 1 and GM 2 are executed iteratively to further reduce the number of communities, until the networks reach a stability where the number of communities cannot be further reduced. In the last stage, STL-CLP is used to boost the size of the communities that do not grow in size during the previous stages.

Furthermore, the remaining communities will be merged for the last time by using GM 3. In networks with a weak community structure, some of the processes are omitted in order to avoid trivial detection. This procedure is explained in the legend of Fig. This is a CLP which prioritises the growth of the small communities. In addition, must be 2 times higher than the second highest number of connection from the solo node to the other communities.

Aside from that, CLP Condition 3 is defined differently depending on whether the c i is an exempted community or not. GM 3: Generally, this process is very similar to GM 2, except that it can handle ties between multiple communities.

The pair of communities with the is merged, provided that the modularity does not decrease after the merging. Furthermore, it is a free-for-all GM where all the communities, including the exempted communities, have the chance to merge. Hence, GM Condition 1 is omitted in this process. The time complexity of the initial labelling is represented by. As the solo and grouped nodes are updated separately in the CLP and GNR processes, the time complexity of the propagation process is also split.

Stage 4 of the proposed algorithm is iterative. Let t S 4 be the number of iterations before Stage 4 reaches a convergence in the labels. The time complexity of Stage 4 is. By referring to the algorithm flowchart see Fig. How to cite this article : Chin, J. A semi-synchronous label propagation algorithm with constraints for community detection in complex networks. Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Uncovering disease mechanisms through network biology in the era of next generation sequencing. Ding, R. Weng, L. Virality prediction and community structure in social networks. Fatt, C. The structure of collaboration in the journal of finance.

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Friendship and mobility: User movement in location-based social networks. In Proc. Download references. The authors would like to acknowledge Professor Michael Brunger of Flinder University for his careful reading of the paper and for some useful suggestions. The funding bodies had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Both authors wrote the main manuscript text. Both authors conceived and designed the algorithm.

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Both authors reviewed the manuscript. Correspondence to Kuru Ratnavelu. This work is licensed under a Creative Commons Attribution 4. International Journal of Modern Physics C Physica A: Statistical Mechanics and its Applications Journal of Physics: Conference Series