Table of Contents
ISRN Communications and Networking
Volume 2012, Article ID 340720, 7 pages
Research Article

Application of Particle Swarm Optimizer on Load Distribution for Hybrid Network Selection Scheme in Heterogeneous Wireless Networks

1Faculty of Engineering & Technology, Multimedia University, Jalan Ayer Keroh Lama, 75450 Melaka, Malaysia
2Faculty of Engineering, Multimedia University, 63000 Cyberjaya, Malaysia
3MIMOS Berhad, Technology Park Malaysia, 71700 Kuala Lumpur, Malaysia

Received 23 March 2012; Accepted 19 June 2012

Academic Editors: W.-H. Fang, A. K. Somani, and C.-W. Yi

Copyright © 2012 Yoke Chek Yee et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Mobile terminal with multiradios is getting common nowadays with the presence of heterogeneous wireless networks such as 3G, WiMAX, and WiFi. That Network selection mechanism plays an important role in ensuring mobile terminals are always connected to the most suitable network. In this paper, we introduce and evaluate the performance of load distribution model to facilitate better network selection. We focus on the optimization of network resource utilization using the particle swarm optimizer (PSO) with the objective to distribute the system load according to the various conditions of the heterogeneous networks in order to achieve minimum system cost. Simulation results showed that the proposed approach outperformed the conventional iterative algorithm by a cost improvement of 7.24% for network size of 1000 mobile terminals using 10 particles.

1. Introduction

There has been a drastic and huge development in both mobile technologies such as global system for mobile communications (GSM), general packet radio service (GPRS), and universal mobile telecommunications system (UMTS) which promise high mobility, wide coverage, but low bandwidth rate, as well as on other wireless technologies such as wireless fidelity (WiFi) and worldwide interoperability for microwave access (WiMAX) which offer faster rates at lower cost but suffered from limited mobility and coverage. The different characteristics of these mobile/wireless technologies help compensating for coverage, mobility, bandwidth, and speed, and this helps meeting the requirements due to the increase of user demands in a complementary manner [1]. It is therefore believed that the future network infrastructure will consist of coverage overlapping of heterogeneous networks [2], where multiradios mobile devices could seamlessly and conveniently access to any network in a ubiquitous manner according to the concept of always best connected (ABC) [3].

The challenge to ubiquitous access to any network lies on an efficient and effective mobility management framework which initially focused on enabling seamless vertical handover across heterogeneous networks due to user mobility. Recently, vertical handover is also considered as proactive means to system performance improvement [4, 5]. Realizing a seamless and ubiquitous network access heavily depends on the second phase in vertical handover process called handover decision, which determines and selects one of the most optimal alternative networks to connect to. The selection of network is usually based on parameters such as signal strength, network conditions, battery power, application types, mobile node condition, operator policies, and user preferences [6]. Such selection could be executed by the mobile terminal (MT) in a distributed manner or performed by the network in a centralized manner.

The basic idea of distributed network selection is to enable each MT with capability to receive other network metrics beyond signal information in order to draw conclusion on the best network for subsequent connection. However, such distributed approach failed to consider the load unbalance problem in the entire heterogeneous network [8]. A typical implementation of distributed approach can be found in [9], which is based on session initiation protocol (SIP) following the IEEE media independent handover (MIH) framework, whereby the triggering of handover was mainly based on the signal strength information. Unlike existing distributed approaches which mainly concentrated on network layer performance such as blocking probability and utilization, authors in [10] formulated the heterogeneous networks as a restless bandit system with multimedia application layer performance consideration. Nevertheless, no discussion was made on the overall load balancing across heterogeneous networks.

Load balancing has been considered as one of the key technologies in converged heterogeneous networks [11] as it helps improving resource utilization and scales system capacity and as a result providing better connectivity to users. In [12], load balancing issue for both streaming and elastic applications is studied across both cellular and WiFi networks, whereby streaming application is distributed to cellular network because of its larger coverage and consistent QoS guarantees, while the elastic application is assigned to the WiFi network. In [13], the authors extended a similar study across both WiMAX and WiFi networks, whereby the system is modelled as a G/G/K loss-queue system. However, such study assumed that the capacity of WiFi networks is fixed and had no performance impact on the number of associated MTs. The concept of soft load balancing was also introduced in [13] whereby IP traffic was divided into subflows to be distributed into various different access network based on parameters such as channel conditions, topological environment, multipath, and path loss information overall system performance. There are pros and cons in both distributed and centralized network selection approaches and as such motivated the study of hybrid network selection approaches in recent years [1416], which in general combine the best schemes/elements from both distributed and centralized approaches into a more effective and efficient network selection framework.

As an effort to support the hybrid network selection approach, we propose a centralized load balancing model to facilitate better network selection. The basis of our model is a system-level cost function which takes into consideration both the network bandwidth and errors to determine the optimal load distribution among heterogeneous networks with minimal system cost. Figure 1 shows an overlay of heterogeneous wireless networks with different cell sizes (e.g., macrocell, microcell, and picocell), similar to the next generation wireless network setup that could be owned by one or multicooperative operators as described in [15] through a central management server. Mobile terminal (MT) is equipped with multiple radios or network interfaces that are capable of attaching to any of these networks. The result of optimal load distribution could then be translated into an adjustment value that will be utilized by the MT to perform network selection as described in the hybrid approach in [7]. Our contribution here is to improve the iterative scheme as proposed in [7] with the evolutionary approach called particle swarm optimizer (PSO) in order to achieve local and possibly global optimal solutions. The choice of particle size also provides extra implementation flexibility on minimal cost versus runtime length.

Figure 1: Overlay of heterogeneous wireless networks.

This remainder of the paper is organized as follows. Section 2 describes the derivation of the system cost function. Section 3 presents both the iterative algorithm and the proposed PSO algorithm. The description of the simulation model is provided in Section 4. Section 5 discusses the results, and Section 6 summarizes the paper.

2. Cost Function

Since the proposed PSO approach is a centralized network selection scheme, it is therefore assumed that the cost function at the central load management system for determining optimal load distribution refers to the total cost of all networks (i.e., from satellite, macrocell, microcell to picocell network) on supporting all users’ communications [7] as in (1) as follows: 𝑁Cost1,𝑁2,,𝑁𝑀=𝐶1𝑁1+𝐶2𝑁2++𝐶𝑀𝑁𝑀=𝑀𝑖=1𝐶𝑖𝑁𝑖,(1) where 𝐶𝑖 is the cost of 𝑖th network, 𝑁𝑖 has to pay for supporting MTs which connect to it, and M is the maximum number of networks in the entire system. This means that to support all the users in the network, the 𝑖th network has to spend a certain amount of resources such as available bandwidth, processing capability, and computational resource. All these costs are denoted by cost 𝐶𝑖(𝑁𝑖). In short, 𝐶𝑖 is a cost function that relies on the total number of users in network i, represented by (𝑁𝑖). The larger the network (𝑁𝑖) is, the larger the cost (𝐶𝑖) will be. This is because more resources of the network 𝑁𝑖 have to be utilized.

The cost function in (1) depends on the total bandwidth offered to all users (B) and the service quality. These two parameters are proportional to the user size in the network. If 𝑁𝑖 increases, it implies that the requested bandwidth by the users increases. Since the total bandwidth is limited, the quality of service (QoS) may be degraded if 𝑁𝑖 increases. Hence, to maintain the service quality, the metric of service quality 𝐸𝑖(err) is included in the cost function as well. We define 𝐸𝑖(err) to be the total of all different errors caused by the increase of active user size, network traffic congestion, packet lost, and so forth. Setting all these constraints helps defining a near-realistic heterogeneous network environment whereby heavy traffic shall incur congestion which leads to transmission errors, long service request delays, and maybe link disconnections. However, our model does not include error which is caused by poor channel link or other factors that are not related to the increase of 𝑁𝑖. Hence, 𝐶𝑖 in (1) can be written as 𝐶𝑖𝑁𝑖=𝑐𝑖(𝑏)𝐵𝑖+𝑐𝑖(𝑒)𝐸𝑖(err),(2) where 𝑐𝑖(𝑏) and 𝑐𝑖(𝑒) are the cost of offering one unit of bandwidth and the cost of correcting each error, respectively. Note that both 𝑐𝑖(𝑏) and 𝑐𝑖(𝑒) are constants that can be selected to make the sum of the values in different units meaningful. We further assume that 𝐵𝑖= Avg (𝐵𝑖)𝑁𝑖, where Avg (𝐵𝑖) is the average bandwidth requested by each user in network i.

Since 𝐸𝑖(err) is the average number of errors that may occur within a time period, it can be written as 𝐸𝑖(err)=𝑘=1𝑘𝑝𝑖(𝑘),(3) where 𝑝𝑖(𝑘) is the probability of having k errors in network i. If 𝑞𝑖 is the probability of having only one error during the communication period, then  𝑝𝑖(𝑘)=𝑞𝑘𝑖, and (3) becomes 𝐸𝑖(err)=𝑘=1𝑘𝑞𝑘𝑖=𝑞𝑖+2𝑞2𝑖++𝑘𝑞𝑘𝑖=𝑞+𝑖1𝑞𝑖2.(4) Given the probability that a single communication (i.e., of one user) has errors within a time period due to network congestion is 𝑎𝑖, then a single communication with no error within the time period is 1𝑎𝑖. The probability that 𝑁𝑖 communications have no error within one unit time is equal to  (1𝑎𝑖)𝑁𝑖. Therefore, the probability that 𝑁𝑖 users’ communications have errors in a time period can be expresses as 𝑞𝑖=11𝑎𝑖𝑁𝑖.(5) Thus, (2) can be rewritten as 𝐶𝑖𝑁𝑖=𝛼𝑐𝑖𝐵(𝑏)Avg𝑖𝑁𝑖+𝛽𝑐𝑖𝑞(𝑒)𝑖1𝑞𝑖2=𝛼𝑐𝑖(𝑏)𝑁𝑖+𝛽𝑐𝑖𝑞(𝑒)𝑖1𝑞𝑖2.(6)

Note that the Avg (𝐵𝑖) can be absorbed into the cost constant 𝑐𝑖(𝑏), and both α and β are the respective weight of the bandwidth and error parameters in the cost function. Both (1) and (6) are the cost functions which will be minimized by the proposed PSO algorithm.

3. Optimization Schemes

As described, it is assumed that the maximum number of MTs in the entire system is fixed for a certain time period, and the number of networks in the system is M. Given 𝑁1+𝑁2++𝑁𝑀=𝑁, it means that our defined cost function falls under the nonlinear integer problem since 𝑁𝑖 is an integer. Therefore, it is very hard to find the optimal solution for such cost function. We also assume that the cost constants 𝑐𝑖(𝑏) and  𝑐𝑖(𝑒) can be obtained from the central module of the network system, whereby 𝑐𝑖(𝑏) contains the value of Avg (𝐵𝑖) that can be obtained from the system according to [17] (e.g., through traffic monitoring/logging over certain period of time). Given the average error probability per unit time of each network 𝑎𝑖, the weight of bandwidth α, the error parameter β, and both cost constants 𝑐𝑖(𝑏) and  𝑐𝑖(𝑒), the proposed network-based selection cost function can be summarized as Given𝛼,𝛽,𝑐𝑖(𝑏),𝑐𝑖(𝑒),𝑎𝑖𝑁Find1,𝑁2,,𝑁𝑀𝑁,𝑀integervariables.MinimizeCost1,𝑁2,,𝑁𝑀=Min𝑀𝑖=1𝐶𝑖𝑁𝑖Subjectto𝑀𝑖=1𝑁𝑖=𝑁.(7)

We have evaluated and compared the proposed approach against the iterative algorithm in [7]. Both algorithms are explained in the following subsections.

3.1. Iterative Algorithm

This algorithm works on a simple principle. The network with the highest cost (𝐶max) that is caused by large number of active users should be reduced, whereas the network with the least number of users (𝐶min) should be increased. These two extreme networks will have their δ number of users exchanged at each iterative step. In each iteration, the costs of all networks 𝐶𝑖 are recalculated and reordered by cost value. During the next iteration, the next (maybe the same or different) networks with the highest and lowest cost will exchange their δ users. This iteration ends only when the new total cost value is larger than the old one, which was precalculated at the very beginning before the algorithm starts running. See Algorithm 1 for the summary of iterative algorithm.

Algorithm 1

The results of executing the algorithm will be the optimized users distribution (𝑁1,𝑁2,,𝑁𝑀) with minimal overall system cost. However, such optimized solution may not guarantee a global optimal solution, and very likely it is just a local minimal solution because it generates only one possible result. To address the limitation of the simple iterative algorithm, we adopt one of the evolutionary algorithms (i.e., PSO) in order to accomplish more optimized results and increase the chances of achieving global optimal solution at the cost of higher complexity as explained in the next few sections. PSO was chosen because it could lead to computational faster convergence than genetic algorithm [1821].

3.2. PSO Algorithm

PSO is a well-known evolutionary computation technique developed by Kennedy and Eberhart [22]. PSO is developed according to the social behaviour metaphor. The algorithm is initialized with a population of random candidate solutions conceptually known as particles. Each particle is assigned an arbitrary velocity and will iteratively traverse into the problem space. It is then attracted towards the location of the best fitness achieved so far by the particle itself as well as by location of the best fitness achieved so far by other particles across the entire population. A complete theoretical analysis of the algorithm is presented in [23].

This subsection explains the PSO motion equations. Let 𝑌𝑚(𝑡) be the position of the mth particle at time t, a vector whose 𝑖th component is 𝑦𝑚,𝑖(𝑡). Subsequently, 𝑉𝑚(𝑡) is the current velocity of the mth particle at time t, a vector in whose 𝑖th component is 𝑣𝑚,𝑖(𝑡). Similarly, the best position found by particle m at time t or earlier is represented by  𝐿𝑚(𝑡), which also consists of component 𝑙𝑚,𝑖(𝑡). Eventually, G(t) is the best position of all particles at time t or earlier, with component 𝑔𝑖(𝑡). Each particle moves around in space based on the following equations: 𝑣𝑚,𝑖(𝑡+1)=𝑤𝑣𝑚,𝑖(𝑡)+𝑐1×𝑙×rand()𝑚,𝑖(𝑡)𝑦𝑚,𝑖(𝑡)+𝑐2×𝑔×rand()𝑖(𝑡)𝑦𝑚,𝑖𝑦(𝑡)(8)𝑚,𝑖(𝑡+1)=𝑦𝑚,𝑖(𝑡)+𝑣𝑚,𝑖(𝑡+1),(9) where (8) describes the velocity update for each dimension i of the particle m. The continuous-valued particle swarm algorithm limits 𝑣𝑚,𝑖 by a value 𝑣max, which is a parameter of the system. Subsequently, 𝑐1 and 𝑐2 are two positive constants called acceleration coefficients that affect the maximum size step that each particle can take in a single iteration; rand()  is a uniformly distributed random number in the interval [0, 1]. Equation (9) describes the updating of position at 𝑖th dimension in particle m. In this study, we use 𝑐1=𝑐2=2.0 as suggested in [24]. The use of the inertia weight w is to speed up the convergence rate in finding the optimal solution. As initially developed, w is often reduced linearly from about 1.2 to 0.4 during a run as in [24]. The correct choice of the inertia weight provides a balance between both global and local exploitation and thus reduces the number of iterations on average in order to find a sufficiently optimal solution. To adapt PSO into the calls distribution optimisation problem, the real value 𝑦𝑚,𝑖 is rounded up to an integer value, and this integer value is assigned to 𝑁𝑚.

Following is the high-level sequence of the proposed Algorithm 2 which utilizes and calculates the equations described earlier.

Algorithm 2

4. Simulation Model

We have conducted a simulation study based on 4 heterogeneous access networks, that is, M = 4 as shown in Figure 1. The total number of MTs, N = 200, 400, 600, 800, and 1000, are covered by these four networks. It is further assumed that the total number of MTs is fixed during a period of time, with only unforced handover being considered. Both α and β are set to 10000 each, implying that the offering bandwidth and correcting errors are of equal importance to each network. Both cost constants 𝑐𝑖(𝑏) and  𝑐𝑖(𝑒) are obtained from [7] as shown in Table 1.

Table 1: System parameters.

In this study, we have investigated 3 performance metrics. First is on the effect of applying the PSO algorithm onto achieving minimal system cost as compared to the iterative algorithm in [7], in networks with different number of MTs. We also set a baseline PSO with only two particles as the basic reference, which simulates the general nature of an iterative algorithm, against the proposed flexibility of PSO configurations with more than two particles. Second is on seeking for further understanding on the effect of particle size onto achieving minimal system cost. Last is on investigating the use of PSO with different particle size for network with large number of users.

5. Results and Discussion

Table 2 shows the optimal calls distribution for N from 200 to 1000, with their respective minimum costs, and the actual calls distribution size across the 4 networks using 10 particles. In general, the minimal cost increases as the network size grows as shown in Figure 2. The calls distribution is not evenly spread across all 4 networks with the highest loads always on network 4. This is because it has the smallest 𝑎𝑖, that is the network with the lowest probability of having errors due to network congestion. The same explanation goes to network 3 for having the lowest or zero loads. Both 𝑐𝑖(𝑏) and 𝑐𝑖(𝑒) did not bring any significant effect to the overall distribution because their values are not much different across the 4 networks. Hence, it is concluded that 𝑎𝑖 carries the highest weight in determining the optimal calls distribution.

Table 2: Minimum cost and calls distribution for different network sizes.
Figure 2: Minimum cost versus network size.

Detailed calls distribution for each of the 10 particles is shown in Table 3 sorted in ascending order based on the minimal cost achieved.

Table 3: Minimum cost and calls distribution for 10 particles.

As compared to the results from [7], which achieved the minimal cost of 14.08 with the distributions of 240, 319, 121, and 320 as indicated in the last row of Table 2, it clearly shows that the PSO algorithm with a minimal cost of 13.06 has outperformed the iterative algorithm. The limitation of the iterative algorithm lies very much on the initial calls distribution across the networks (which determines the initial cost), and also on a single walkthrough in the problem space guided by the initial cost calculated. Such approach would most likely achieve only local optimal solution. Unlike the iterative algorithm, PSO employs a variable number of particles to seek for optimal solution, which helps increasing the chance of achieving global optimal solution, that is, a cost improvement of 7.24% for network size of 1000 MTs.

Table 4 shows the optimal calls distribution of utilizing different number of particles, from 2, 5, 10, 15, 20 to 40, with their respective minimum costs, and the actual calls distribution size across the 4 networks for 1000 MTs. In general, the minimal cost decreases as the particle size grows, but with some interesting exceptions as shown in Figure 3. For example, utilizing 10 particles seems to incur slightly higher cost (close to 1%) than 5 particles, that is, failed to reduce the overall system cost further. The same observation goes to the case with 20 and 15 particles. However, based on the results in Table 2, PSO algorithm should still be a favourable approach here for achieving better optimization with very minor glitches on particle size configurations.

Table 4: Minimum cost and calls distribution for different particle sizes.
Figure 3: Minimum cost over the number of particles.

6. Summary and Future Works

This paper has formulated the cost function for calls distribution in heterogeneous networks based on two parameters, namely, the offering bandwidth and service quality (i.e., probability of having communication errors) and presented an approach using PSO to seek for minimal system cost. The proposed approach outperformed the iterative algorithm in the literature by a cost improvement of 7.24% for network size of 1000 MTs using 10 particles. Our proposed approach has higher chance of achieving global optimal solution as compared to the iterative algorithm given the option to utilize a variable number of particles in the problem space.

One possible future work is to consider more parameters besides bandwidth and service quality, and this includes application types, battery power, operator policies, and perhaps user preferences. It is also interesting to study the load balancing issues with different theories and models such as evolutionary games for performance comparison.


  1. J. S. Kim, E. Serpedin, D. R. Shin, and K. Qaraqe, “Handoff triggering and network selection algorithms for load-balancing handoff in CDMA-WLAN integrated networks,” Eurasip Journal on Wireless Communications and Networking, vol. 2008, Article ID 136939, 2008. View at Publisher · View at Google Scholar · View at Scopus
  2. M. M. Alkhawlani and K. A. Alsalem, “Radio network selection for tight-coupled wireless networks,” in Proceedings of the 7th International Conference on Informatics and Systems (INFOS '10), Cairo, Egypt, March 2010. View at Scopus
  3. N. Passas, S. Paskalis, A. Kaloxylos et al., “Enabling technologies for the always best connected concept,” Wireless Communications and Mobile Computing, vol. 6, no. 4, pp. 523–540, 2006. View at Publisher · View at Google Scholar · View at Scopus
  4. X. Liu, V. O. K. Li, and P. Zhang, “Joint radio resource management through vertical handoffs in 4G networks,” in Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '06), December 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. A. E. M. Taha, H. S. Hassanein, and H. T. Mouftah, “Vertical handoffs as a radio resource management tool,” Computer Communications, vol. 31, no. 5, pp. 950–961, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. Y. C. Yee, K. N. Choong, A. L. Y. Low, and S. W. Tan, “SIP-based proactive and adaptive mobility management framework for heterogeneous networks,” Journal of Network and Computer Applications, vol. 31, no. 4, pp. 771–792, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. X. Jiang, Mobility management in next generation all-IP based wireless systems [Ph.D. thesis], Georgia Institute of Technology, Atlanta, Ga, USA, 2004.
  8. H. Jia, Z. Zhang, P. Cheng, H. H. Chen, and S. Li, “Study on network selection for next-generation heterogeneous wireless networks,” in Proceedings of IEEE 17th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC '06), September 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. K. N. Choong, V. S. Kesavan, S. L. Ng, F. de Carvalho, A. L. Y. Low, and C. Maciocco, “SIP-based IEEE802.21 media independent handover—A BT Intel collaboration,” BT Technology Journal, vol. 25, no. 2, pp. 219–230, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. P. Si, F. R. Yu, H. Ji, and V. C. M. Leung, “Optimal network selection in heterogeneous wireless multimedia networks,” in Proceedings of IEEE International Conference on Communications (ICC '09), Dresden, Germany, June 2009. View at Publisher · View at Google Scholar · View at Scopus
  11. B. Li, W. Shi, and Y. Zhao, “A load balancing algorithm based on dividing IP flow for high-speed traffic over heterogeneous wireless networks,” in Proceedings of the 3rd International Congress on Image and Signal Processing (CISP '10), pp. 4294–4298, Yantai, China, October 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. W. Song and W. Zhuang, “Multi-service load sharing for resource management in the cellular/WLAN integrated network,” IEEE Transactions on Wireless Communications, vol. 8, no. 2, pp. 725–735, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. J. Xu, Y. Jiang, A. Perkis, and E. Khloussy, “Multi-service load balancing in a heterogeneous network with vertical handover,” in Proceedings of the 1st European Teletraffic Seminar, Poznan, Poland, 2011.
  14. W. Song, W. Zhuang, and Y. Cheng, “Load balancing for cellular/WLAN integrated networks,” IEEE Network, vol. 21, no. 1, pp. 27–33, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. M. M. Alkhawlani and A. A. Hussein, “Intelligent radio network selection for next generation networks,” in Proceedings of the 7th International Conference on Informatics and Systems (INFOS '10), Cairo, Egypt, March 2010. View at Scopus
  16. D. Niyato and E. Hossain, “Dynamics of network selection in heterogeneous wireless networks: an evolutionary game approach,” IEEE Transactions on Vehicular Technology, vol. 58, no. 4, pp. 2008–2017, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. H. J. Wang, R. H. Katz, and J. Giese, “Policy-enabled handoffs across heterogeneous wireless networks,” in Proceedings of the 2nd IEEE Workshop on Mobile Computing Systems and Applications (WMCSA '99), pp. 51–61, February 1999. View at Publisher · View at Google Scholar · View at Scopus
  18. X. Wu, S. Lei, J. Yang, H. Xu, J. Cho, and S. Lee, “Swarm based sensor deployment optimization in Ad Hoc sensor networks,” in Proceedings of the 2nd International Conference on Embedded Software and Systems, pp. 533–541, Xi'an, China, 2005.
  19. S. Pandey, L. Wu, S. M. Guru, and R. Buyya, “A particle swarm optimization-based heuristic for scheduling workflow applications in cloud computing environments,” in Proceedings of the 24th IEEE International Conference on Advanced Information Networking and Applications (AINA '10), pp. 400–407, April 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. M. Khodier and M. Al-Aqeel, “Linear and circular array optimization: a study using particle swarm intelligence,” Progress In Electromagnetics Research B, no. 15, pp. 347–373, 2009. View at Google Scholar · View at Scopus
  21. S. Deb, C. J. Singh, N. B. Singh, A. K De, and S. K. Sarkar, “Parameter optimization of quantum well nanostructure: a PSO and GA based comparitive study,” International Journal of Latest Trends in Computing, vol. 35, no. 1, pp. 35–40, 2010. View at Google Scholar
  22. J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks, vol. 1, pp. 1942–1948, December 1995. View at Scopus
  23. M. Clerc and J. Kennedy, “The particle swarm-explosion, stability, and convergence in a multidimensional complex space,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 1, pp. 58–73, 2002. View at Publisher · View at Google Scholar · View at Scopus
  24. C. F. Teo, Y. C. Foo, S. F. Chien, A. L. Y. Low, A. H. You, and G. Castañón, “Wavelength converters placement in all optical networks using particle swarm optimization,” Photonic Network Communications, vol. 10, no. 1, pp. 23–37, 2005. View at Publisher · View at Google Scholar · View at Scopus