# network decomposition using kernighan–lin strategy aided harmony search algorithm

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network decomposition in [5]. These methods formulate the

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in [14,15] a hybrid swarm intelligence based harmony search is

Contents lists available at SciVerse ScienceDirect

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Swarm and Evolutio

Swarm and Evolutionary Computation 7 (2012) 16been applied to combined heat and power economic dispatchE-mail address: swarup@ee.iitm.ac.in (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 [16]. The exploratory power ofthe HS algorithm is analyzed in [17] and the work in [18] givesparameter setting free harmony search algorithm. In [19] HS has

2210-6502/$ - see front matter & 2012 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.swevo.2012.07.002

n Corresponding author. Tel.: 91 44 2257 4440; fax: 91 44 2257 4401.annealing was done by Irving and Sterling in [3]. Later Chang et al.proposed the application of tabu search for network partitioningin [4]. A new ant colony optimization has also been used for

solving structural optimization problems in [11]. 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 [1].Ding et al. proposed clustering of power networks using geneticalgorithm in [2]. 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 [6]. 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 [7], multi-partitioning ofpower network is done using simulated annealing for stateestimation. Zhongxu et al. proposed network partitioning fordistributed reactive power optimization in [8]. A new methodfor partitioning is proposed in [9] for voltage collapse margincalculations. Ref. [10] 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

Article history:

Received 1 October 2011

Received in revised form

6 July 2012

Accepted 9 July 2012Available online 28 September 2012

Keywords:

Network decomposition

Distributed computing

Harmony search algorithm

KernighanLin 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

hierarchically.

journal homepage: wwwLin strategy aided harmony

36, India

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.

evier.com/locate/swevo

nary Computation

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

Start

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 [20] it is used for optimal scheduling of dieselgenerators. In [21], multi-objective HS algorithm is used to solvethe optimal power ow problem and in [22] environmentaleconomic dispatch is solved using the same. In software engi-neering the HS algorithm has been used for the task assignmentproblem [23] and a novel global harmony search algorithm isdescribed in [24]. Self-adaptive harmony search is proposed in[25] for expert system applications. A novel derivative of har-mony search for discrete optimization problems has been pro-posed in [26]. In [27] 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

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