network decomposition using kernighan–lin strategy aided harmony search algorithm
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in [14,15] a hybrid swarm intelligence based harmony search is
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Swarm and Evolutio
Swarm and Evolutionary Computation 7 (2012) 16been applied to combined heat and power economic dispatchE-mail address: email@example.com (K.S. Swarup).network partitioning as an optimization problem and tries to used to solve economic dispatch. HS algorithm has been used fortransmission network planning . The exploratory power ofthe HS algorithm is analyzed in  and the work in  givesparameter setting free harmony search algorithm. In  HS has
2210-6502/$ - see front matter & 2012 Elsevier B.V. All rights reserved.
n Corresponding author. Tel.: 91 44 2257 4440; fax: 91 44 2257 4401.annealing was done by Irving and Sterling in . Later Chang et al.proposed the application of tabu search for network partitioningin . A new ant colony optimization has also been used for
solving structural optimization problems in . In [12,13] animproved harmony search is applied to optimal economic powerdispatch, dynamic economic dispatch with wind energy is solvedtional methods generate connected clusters with less number ofinterconnections but fails to balance the size of the clusters .Ding et al. proposed clustering of power networks using geneticalgorithm in . Optimal tearing of network using simulated
called harmony search algorithm (HSA) is used to solvepartitioning problem of large-scale power networks. The harmsearch algorithm has been applied to many optimizationblems in engineering and design. To mention a few it is usean essential part of distributed computing of power systemproblems.
In the literature several approaches have been proposed fornetwork decomposition like matrix decomposition, successiveapproximation and heuristic clustering techniques. The conven-
posed so far in the literature are computation intensive andinvolves procedures based on natural selection crossover andmutation. It also requires a large population size and occupiesmore memory.
In this paper one of the recently evolving heuristic algorithm1. Introduction
Power system is a complicatedgeographically distributed multi arand monitoring of the system is comincreases rapidly. On the othercomputing technology had givencomputing and parallel processingimplementation of distributed combroken down into subproblems andtorn into subnetworks. Hence netwterconnected betweenhe centralized controls the size of the systemthe advancements insight into distributedwer systems. For thethe problem has to beysical network must beecomposition becomes
minimize a common objective function . The objective functionis formed in such a way that it represents the computational loadand the communication between the clusters. The networkpartitions are done for a wide range of applications in powersystems control and monitoring. In , multi-partitioning ofpower network is done using simulated annealing for stateestimation. Zhongxu et al. proposed network partitioning fordistributed reactive power optimization in . A new methodfor partitioning is proposed in  for voltage collapse margincalculations. Ref.  gives a metaheuristic technique for cluster-ing web documents. However, the evolutionary methods pro-Regular Paper
Network decomposition using Kernighasearch algorithm
G.A. Ezhilarasi, K.S. Swarup n
Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai
a r t i c l e i n f o
Received 1 October 2011
Received in revised form
6 July 2012
Accepted 9 July 2012Available online 28 September 2012
Harmony search algorithm
a b s t r a c t
Power system is a large-s
centralized control becom
For implementation of thi
the network decompositio
(HS) algorithm. To improv
method called Kernighan
the partitioning of digital a
of the partitioned clusters
out on IEEE Standard sy
journal homepage: wwwLin strategy aided harmony
network with a number of components and interconnections for which
umbersome. For multi-area computations, decentralization is necessary.
proach network decomposition becomes an essential task. In this paper
roblem is solved as an optimization problem using the harmony search
e performance of the HS algorithm, a widely used graph bi-partitioning
(KL) strategy is used in the improvisation process. KL strategy is used in
VLSI circuits and is suitable for bi-partitioning networks. The connectivity
checked by means of graph traversal techniques. Simulation are carried
s and found to be very effective in decomposition of the system
& 2012 Elsevier B.V. All rights reserved.
is also handled by balancing the number of nodes in each of the
the conventional graph theory methods and many evolutionarymethods like genetic algorithm, simulated annealing and tabusearch. In this work we propose to solve the network decomposi-tion using a recently evolved metaheuristic algorithm calledharmony search (HS) algorithm. HS evolved from the process ofmusic composition based on the improvisation of harmony. Theharmony in the music composition is analogous to the solutionvector of the optimization problem and the improvisations madeby the musicians represents the search towards the optimum.This algorithm is independent of the initial values and theprevious iteration values. The search is based on the harmonymemory considering rate and pitch adjustment rate. The optimi-zation procedure of the HS algorithm involves two main stepsnamely initialization of the harmony and HS parameters andimprovisation of the existing harmony. This is done iteratively fora xed number of improvisations. Improvisation is done based onthe HS parameter harmony memory considering rate (HMCR). Inthis work the pitch adjustment is done based on KernighanLinstrategy in order to improve the search strategy. This method istermed as the KernighanLin strategy aided harmony searchalgorithm (KL-HS).
Generate Random HM
Check connectivity of clustersusing BFS
Calculate Fitness Value
Input system data and initializethe HS parameters
G.A. Ezhilarasi, K.S. Swarup / Swarm and Evolutionary Computation 7 (2012) 162decomposed networks. The number of edges in each subnetworkwill also increase the computations involved in each subnetwork.
2.1. Problem formulation
Network decomposition can be viewed as a combinatorialoptimization problem with main objective being to minimizethe number of tie lines between the subnetworks. It also needs tobalance the number of nodes and lines within the subnetworksfor load balancing during computation. Hence the problem can bemathematically formulated as follows:
Min CM,N,L aM3bN2gL 1where M is the maximum number of tie lines between theclusters, N is the maximum number of nodes in a cluster, L isthe maximum number of lines in a cluster, a,b,g are weightingfactors for each term.
This optimization is subject to the constraint that the nodes ineach cluster must form a connected graph. This constraint checksthe observability of the network at the instant of decompositionof the network.
2.2. Solution methodology
Network decomposition has been in the literature in variousproblem and in  it is used for optimal scheduling of dieselgenerators. In , multi-objective HS algorithm is used to solvethe optimal power ow problem and in  environmentaleconomic dispatch is solved using the same. In software engi-neering the HS algorithm has been used for the task assignmentproblem  and a novel global harmony search algorithm isdescribed in . Self-adaptive harmony search is proposed in for expert system applications. A novel derivative of har-mony search for discrete optimization problems has been pro-posed in . In  a hybrid method has been proposedcombining the harmony search method with the sequentialquadratic programming method and a global harmony searchalgorithm is proposed for unconstrained optimization problemsas well. Hence the literature shows the applicability of the HSalgorithm to a wide range of optimization problems in powersystems and other engineering applications.
This paper proposes the application of harmony search algo-rithm aided by KernighanLin strategy to solve the networkdecomposition problem and it is organized as follows. Section 2deals with the problem formulation of network partitioning.Section 3 describes the KernighanLin strategy aided harmonysearch algorithm (KL-HS) and the implementation methodologyin detail to the network partitioning problem. Section 4 presentsthe simulation results done on IEEE standard test cases to assessthe effectiveness of the proposed method.
2. Network decomposition
Power system is a interconnected network that can be repre-sented by a graph GV ,E, with V vertices and E edges. Theobjective of network decomposition is to group the closelycoupled parts of the network and localize it, in order to make itidentical to a network of computers connected through commu-nication. This will facilitate the distributed computing of powersystem applications over a computing network. The major phy-sical coupling factor of a interconnected network is th