Sage Journals: Discover world-class research

Abstract

Vehicular ad hoc networks consist of access points for communication, transmission, and collecting information of nodes and environment for managing traffic loads. Clustering can be performed in the vehicular ad hoc networks for achieving the desired goals. Due to the random range of vehicular ad hoc networks, stability is the major issue on which major research is still in progress. In this article, a moth flame optimization–driven clustering algorithm is presented for vehicular ad hoc networks, replicating the social behavior of moth flames in creating efficient clusters. The proposed framework is extracted from the living routine of moth flames. The proposed framework allows efficient communication by creating the augmented number of clusters due to which it is termed as intelligent algorithm. Besides this, the use of unsupervised clustering technique emphasizes to call it as an intelligent clustering algorithm. The recommended intelligent clustering using moth flame optimization framework is executed for resolving and optimizing the clustering problem in vehicular ad hoc networks, the primary focus of the proposed scheme is to improve the stability in vehicular ad hoc networks. This proposed method can also be used for the transmission of data in vehicular networks. Intelligent clustering using moth flame optimization is then proved by relative study with two variants of particle swarm optimization: multiple-objective particle swarm optimization and comprehensive learning particle swarm optimization and a variant of ant colony optimization: ant colony optimization–based clustering algorithm for vehicular ad hoc network. The simulation demonstrates that the intelligent clustering using moth flame optimization is provisioning optimal outcomes in contrast to widely known metaheuristics. Furthermore, it provides a robust routing mechanism based on the clustering. It is suitable for large highways for the productivity of quality communication, reliable delivery for each vehicle and can be widely applicant.

Keywords

Vehicular ad hoc networks clustering ad-hoc network moth flame optimizer intelligent transportation system

Introduction

The simplest definition of network is a collection of devices for the communication. Basically, different devices are connected to each other so that these devices can easily communicate or transmit data to each other. Networks are usually deployed in the different domains for the specific reasons. In some scenarios, the network is created on temporary basis. This types of network is called adhHon network. These networks can be infrastructure less and with the infrastructure as well. In adhHoc networks, there are many sub-divisions such as vehicular ad hoc networks (VANETs), mobile ad hoc networks (MANETs), and flying ad hoc networks (FANETs). The primary focus of this research is in VANETs. The concepts of ad hoc is being implemented in different scenarios, now spreading and being used almost everywhere. Therefore, the usage of this method has increased the number of using devices. The continuous increase in the usage and demand make the researchers to think about the new ideas for the better productivity. Currently, a lot of research is carried in the domain of VANETs, specially about the VANETs protocols communication models and architecture.¹ VANETs distribute wireless communication facilities for road side units and vehicles running on the road.^2,3 The primary focus is to provide the services to the users available on the road.⁴ The VANET is now considered the rising field in the implementation and research perspective as well. Because many projects are still going on globally for the intelligent transportation systems (ITS). In VANETs, there are further streams such as, vehicle-to-vehicle (V2V), vehicle-to-infrastructure (I2V or V2I), and the last approach is hybrid which is the combination of both mentioned algorithms (V2X). Their applications lead to the facilitation in the handling of traffic jam and many other aspects.^5,6 The potential core of ITS is to provide the efficient communication mechanism during the transportation. However, road safety is also a primary factor of ITS.⁷

VANETs come under the scope of ITS. The research domain of scalability is significant for network designers. In the last several years, we have witnessed improved research output on inter-vehicle communications. New justifications and procedures must be developed for automobile’s targeted movement patterns. The new research topic in the VANETs is how to cluster or group the vehicles. In VANETs, vehicles communicate with each other. Automobiles gather the information of traffic on the road, environmental factors, and other parameters.⁸ The gathered information is then transmitted to the anticipated vehicles. The transmission of information is a real challenging issue due to the frequent change in structure of the network. To address this issue, clustering is the eventual solution. The aim is to efficiently operate routing, healthcare applications,⁹ mobility management,^10,11 military applications,¹² safety alarms,¹³ data dissemination,¹⁴ and Internet connectivity.¹⁵ This topic will continue to remain generally there for another few years. We believe to have greater exploration in near future in the core topic of clustering algorithms, analysis, comparison as well as evaluation of clustering algorithms, preparation of simulation statistics and so on. Real-life experiments outdoor are among the major challenges leftover in this domain.² Clustering is one of the solutions to solve the issue of scalability. It is imperative for effective utilization of resources and load balancing on scheduling data access with cooperative load balancing VANETs. In clustering, we group together the nodes that lie in the same geographical neighborhood which helps to make the network more scaleable.^2,3 We will use evolutionary algorithms (EA) in our research. EAs are motivated from the natural model of evolution. They are centered on a basic model of biological evolution. We generate an environment in which probable solutions can evolve to resolve a specific problem. The surroundings are molded by the factors of the problem and inspire the evolution to get the best possible solutions.

Evolutionary computation includes numerous sorts of EA. Some of them are genetic programming (GP), genetic algorithms, evolutionary programming, evolution strategies, and learning classifier systems. EA offers decent estimated explanations to problems that cannot be resolved simply by other methods. Numerous optimization problems lie in this group. They may be very computationally exhaustive to find a precise answer but occasionally a near-optimal explanation is adequate. In circumstances like these, evolutionary techniques are successful. Since the vehicular node clustering is a continuous problem, and the EAs are very effective for this type of problems,⁴ a system is proposed for solving/optimizing the vehicular node clustering problem in VANETs. Figure 1 shows the general structure of VANETs. Our main contribution is to propose a routing protocol for the VANETs so that robustness in communication can be achieved. We have applied the nature-based technique to solve the scalability issue of VANETs. By using it, the load balancing is also achieved, and it reduces the computational complexity as well. Furthermore, the simulation results are compared with the well-known existing algorithms to show the comprehensive analysis.

Figure 1.

A schematic of ITS services in VANETs.

Related work

The EA helps us to solve the NP-hard problems.¹⁶ The clustering problem also lies in the mentioned category. For solving the clustering problem in VANETs, proposed framework is based on the metaheuristics. Some of the already techniques for the VANETs are as follows.

Despite VANET is regarded as a subordinate class of MANET, it has many features differing from MANET such as very high movement of vehicles, which generates the consistent variations of network topology.¹⁷ These can be changing node density, fluctuation of road, and positions of vehicles present in the road. Therefore, the clustering procedures for MANET are incompatible for VANET. Many researches dealing with clustering of VANETs are motivated on diminishing network overhead price and the total number of clusters produced. These algorithms usually do not measure the vehicles interests such as any linked information used to distinguish vehicle from another. That information can be finding free parking space, traffic congestion, and so on. As a result, in this research, the authors proposed an innovative clustering algorithm which is built on agent technology. It solves the issues cited above and thus improves overall routing performance in VANET.

The primary goal is to define agent properties. The idea is to improve the conventional systems so that overall performance is upgraded. Different from preceding works, the clustering algorithm described makes group of vehicles that have the same context information throughout the cluster formation technique. Oranj et al.¹⁸ proposed that there are numerous routing protocols for VANETs. Maximum methods ignore factors that influence performance of actual VANET applications such as environmental variations. Environmental changes can affect both performance and throughput in VANET. The authors, in this research, have suggested a routing technique which is centered on vigorous MANET on-demand protocol and ant colony optimization (ACO).

These protocols consider environmental changes. For finding routes through graphs, ACO algorithm is a method and is accepted broadly. In the proposed scheme, two factors were measured to estimate revealed routes: path reliability and delay time. The results showed that the projected ACO procedure achieved enhanced performance as equated to other approaches. Chen et al.¹³ proposed the clustering for VANETs offers many benefits. Since VANET is an extremely vibrant scenario, the firmness of existing clustering algorithms displays meager robustness. In this work, an innovative multi-hop clustering system for VANETs is proposed. This algorithm creates cluster heads (CHs) through vicinity tracking relationship among vehicles. The arrangement is founded on a rational supposition that an automobile cannot surely recognize which automobile in its neighbors are the best appropriate to be its CH. On the other hand, which automobile in its one-hop expanse is the steadiest and comparable with it can simply be recognized. Therefore, they must surely fit in the identical cluster. Subsequently, an automobile can indicate its CH by succeeding the steadiest automobile. The comparative movement among two automobiles joining the advantages founded on the trailed figure and the past subsequent evidence allows a vehicle to identify which target to track. This approach upgrades the steadiness of clusters throughout network development.¹⁹ Aadil et al.^20,21 proposed the ACO-based clustering algorithm for the VANETs.

Wahab et al.²² proposed the clustering scheme based on the quality of service (QoS) by using the optimized link-state routing (OLSR) and termed as QoS-OLSR. It is designed to achieve the cluster stability and QoS for the high mobile nodes. The authors have shown the results to improve the end-to-end delay and increase the packet delivery ratio in VANETs. Hassanabadi et al.²³ proposed a mobility-based clustering scheme, which is based on affinity propagation algorithm in a distributed way. This scheme used the metric of high mobility to improve the cluster stability. The authors have shown the performance in average CH and cluster member life time. Wahab et al.²⁴ have discussed the two types of vulnerabilities in network. First is due to the high mobility, which increases the complexity of buffering and monitoring of high moving vehicles. Second, scarcity of resources in terms of storage. The support vector machine is used to analyze the training set of vehicles to identify the malicious nodes in the network. The concept of QoS-OLSR is used as a clustering protocol. The results are shown in terms of accuracy and decrease the false positive rate to support the proposed model (Tables 1 –3).

Table 1.

Physics-based algorithms.

Algorithm	Description
Central force optimization in 2007⁵	Method develop from the theory of gravitational kinematics
Gravitational local search (GLSA) in 2013⁶	The main features of this heuristics derived from “Newton’s law of gravitation,” namely a gravitational search algorithm
Black hole algorithm in 2015²⁷	The theme of black hole is used to develop the bio-inspired algorithm
Charged system search in 2010²⁸	An approach taken from the behavior of charges and it is based on the Coulomb law and motion laws
Ray optimization algorithm in 2014²⁹	The law for light “Snell’s light refraction law” is mapped into algorithm for solving different problems
Artificial chemical reaction optimization algorithm published in 2011	The behavior is taken from the nature and occurrences of chemical reactions
Small world optimization algorithm (SWOA) in 2006³⁰	Concept is taken from the phenomena of small world and different searching operator’s: small-range, large-range, and random-range operators are used in it
Big bang big crunch (BB-BC)³¹ in 2014	Theme from the universe evolution is extracted to explore the non-deterministic polynomial-time hardness problems
Curved space (CSO) optimization³² in 2012	The general relativity theory is used for the curvature of space and for aptitude simple random search
Galaxy based search algorithm (GbSA)³³ in 2011	Theme of galaxies are embedded in hill climbing algorithm

Table 2.

Evolutionary algorithm.

Algorithm	Description
Evolutionary programing (EP)³⁴ in 2012	It is developed for the different evolutionary parameters, finite-state machine
Evolution strategy (ES)³⁵ in 2013	Evolution and adaption features are used in it
Differential evolution (DE)³⁶ in 2006	The crossover and mutation are used to for the generations
GP³⁷ in 2016	Genes are modified as per the problem
Biogeography-based optimizer (BBO)³⁸ in 2008	The candidate solutions are optimized recursively to measure the quality

Table 3.

Swarm intelligence algorithm.

Algorithms	Description
Fruit fly optimization algorithm (FFOA)³⁹ in 2012	The algorithm is developed by using the behavior of foraging of fruit fly
Cuckoo search (CS)⁴⁰in 2009	Logic taken from the cuckoo bird searching method
Artificial fish-swarm algorithm (AFSA)⁴¹ in 2014	Motivation extracted from the majestic behavior of fish
Termite algorithm⁴² in 2005	Biologically inspired algorithm, resembling the behavior of termites
Monkey search⁴³ in 2008	Concept taken from the living of monkey. It contains watch-jump process, climb process, and somersault process
Wasp swarm algorithm⁴⁴ in 2007	Algorithm inspired from the colonial method of living and searching food of wasp
Bee collecting pollen algorithm (BCPA)⁴⁵ in 2008	Developed by the method of collecting pollen by honey bees
Marriage in honey bees optimization algorithm (MBO)⁴⁶ in 2001	Algorithm developed for optimization from the concept of mating of honey bees
Firefly algorithm (FA)⁴⁶ in 2010	The irregular behavior of firefly to indicate the others
Dolphin partner optimization (DPO)⁴⁷ in 2009.	A viewpoint of dolphin partner optimization (DPO) was articulated, and nucleus was hosted to calculate the best location permitting to the fitness and position of team members
Krill herd (KH)⁴⁸ in 2012	Herding of krill is used to develop the algorithm
Bird mating optimizer (BMO)⁴⁹ in 2012	A novel version of EA, BMO, it is used for the continuous-optimization problems which is extracted by the breeding approaches of bird species during breeding season

Research methodology

Moth flames almost belongs to the family of butterflies and have large number of various species. Their life cycle contains two main steps: larvae and adult. They follow the moon light to travel in straight line by using the mechanism of transverse orientation. This method helps the moth flames to fly the whole journey in the same angle.^25,26 These phenomena are shown in Figure 2. The yellow line shows the flying direction of moth toward the moon while red is used to show the straight surface from which moth will fly. The green circle is used to show the angle of elevation which is made by moth taken from surface and flying direction of moth (Figure 2).

Figure 2.

Transverse orientation of moth flame.

The transverse orientation ensures the movement of moth flames to maintain the same angle during the journey. Despite the fact, it is observed that the flying pattern of the moth flames varied during the journey toward the artificial lights. Consequently, the moth flames process accurate for the far distances but fails the method of transverse orientation for too near. Since such a light is too closed as compared to the moon, the spiral fly occurred due to the keeping the same angular motion.

Mathematical modeling

The moths are considered as candidate solution in the algorithm. These candidate solutions can be in N dimensions. The moths can be represented mathematically as

$M = [\begin{matrix} m_{1, 1} & m_{1, 2} & m_{1, 3} & L & L & m_{1, d} \\ m_{2, 1} & m_{2, 2} & m_{2, 3} & L & L & m_{2, d} \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ m_{n, 1} & m_{n, 2} & m_{n, 3} & L & L & m_{n, d} \end{matrix}]$ (1)

where n shows the number of moths and d shows the dimension.

There will be a fitness values for each moth

$OM = [\begin{matrix} O M_{1} \\ O M_{2} \\ ⋮ \\ O M_{n} \end{matrix}]$ (2)

where OM is the fitness value and n is the moth number.

It can be observed that for each moth, the fitness function returns the fitness value. The first row in the matrix M (position vector) of each moth is delivered to the fitness (objective) function. Consequently, the fitness function’s output is allotted to the relevant moth as its objective function. Flames are another vital factor in the moth flame optimization (MFO) algorithm. A matrix analogous to the matrix of moths is shown as follows

$F = [\begin{matrix} F_{1, 1} & F_{1, 2} & L & F_{1, d} \\ F_{2, 1} & F_{2, 2} & L & F_{2, d} \\ ⋮ & ⋮ & ⋮ & ⋮ \\ F_{n, 1} & F_{n, 2} & L & F_{n, d} \end{matrix}]$ (3)

Here, the number of moths are indicated by n, whereas the number of dimensions (variables) are represented by d. The same is represented in equation (3), the dimensions of arrays M and F are identical. The subsequent fitness values for all the flames are stored in an array, as follows

$OF = [\begin{matrix} O F_{1} \\ O F_{2} \\ ⋮ \\ O F_{n} \end{matrix}]$ (4)

The number of moths is shown by n. The flames are considered as a solution set as shown in equations (1) and (3). There is only operational difference between them. The moths are considered as the search agent in the search space while the flames are used to point out the fittest solution obtained so far. This operation can also be defined from another angle that is; the flames are just pointing or putting the flags. These points are the fittest spots obtained by moths until now. Therefore, the remaining moths will also start searching near the fittest spotted region in the search space. In this way, the moths will achieve the best solution and converge earlier.

The MFO algorithm estimates the global optima of the optimization problem and is a three-tuple explained as follows

$MFO = (I, P, T)$ (5)

$\begin{matrix} I : ϕ \to {M, OM} \\ P : M \to M \\ T : M \to {true, false} \end{matrix}}$ (6)

$M_{i} = S (M_{i}, F_{j})$ (7)

The main function is the P function, in which the moths travel in the search space. It considers the matrix M as an input and its updated copy is returned as an output.

The T function represents termination criterion. If the termination criterion is achieved, it will return true and will return false if the termination criterion is not fulfilled.

Here, S indicates ith moth while M shows the complete search space or matrix of moths, ad F indicates the jth flame, and is the spiral function. Equation (8) shows the fitness function, where w₁, w₂,…, w_n are the weights assigned to fitness parameters. While f₁, f₂,…, f_n are the fitness parameters based on the problem. Iteration is represented by d

$w_{1} (f_{1} (d)) + w_{2} (f_{2} (d)) + \dots + w_{n} (f_{n} (d))$ (8)

Figure 3 is used to show the data flow of proposed method.

Figure 3.

Flow chart of ICMFO.

Experimentation

The experiments are described in this section. The proposed framework is implemented in the matrix laboratory R-2015a. After implementation of the novel technique, comparative analysis of intelligent clustering using moth flame optimization (ICMFO) is done with the well-known metaheuristics algorithms, that is, comprehensive learning particle swarm optimization (CLPSO), multiple-objective particle swarm optimization (MOPSO), and ant colony optimization–based clustering algorithm for vehicular ad hoc network (CACONET). The results are professionally shown in three-dimensional (3D) format for the better understanding of the outcomes. The complete working and flow of the proposed method is shown in Figure 3. The given result shows that the proposed method is producing lesser number of required clusters than others. This reduction in the required number of clusters will lead us to reduce the required resources for managing the network. This will reduce the cost of routing, the number of hop of the network. Due to less number of clusters, the packet delays will be minimized as well.

The results are shown in the Figures 4 –7, transmission range in the x-axis, number of nodes in y-axis, and number of clusters in the z-axis. The transmission range is from 100 to 600 m, the number of nodes is 30–60, while different grid size from 1000 to 4000 m is used to show the required number of cluster accordingly. The ICMFO shows the optimized number of clusters as shown in the figures represented with green-colored circles. The number of required clusters are inversely proportional to the transmission range. When the value of transmission range is increased, the required number of clusters will be decreased. We can see that ICMFO is showing the optimized results as compared to CLPSO, MOPSO, and CACONET in all the given scenarios. The size of the grid is also changed to make the results more strong and perfect. Graphs illustrate the results favorable to the ICMFO. In addition, the number of nodes/vehicles are changed so that the accuracy of the proposed method can be measured. At some point in the network, MOPSO, CLPSO, and CACONET overlaps with the proposed method. But this is due to the randomness nature of the algorithm.

Figure 4.

Number of clusters versus number of nodes versus transmission range in ICMFO, MOPSO, CLPSO, and CACONET by fixing nodes from 30 to 60, for grid size = 1000 m.

Figure 5.

Number of clusters versus number of nodes versus transmission range in ICMFO, MOPSO, CLPSO, and CACONET by fixing nodes from 30 to 60, for grid size = 2000 m.

Figure 6.

Number of clusters versus number of nodes versus transmission range in ICMFO, MOPSO, CLPSO, and CACONET by fixing nodes from 30 to 60, for grid size = 3000 m.

Figure 7.

Number of clusters versus number of nodes versus transmission range in ICMFO, MOPSO, CLPSO, and CACONET by fixing nodes from 30 to 60, for grid size = 4000 m.

The results are taken after the 10 iterations for each scenario and then the average value is taken to plot the results. Even though MOPSO provides the multiple solutions for the problem but still ICMFO is providing the optimized results for the given situation.

Load balance factor

Load balance factor (LBF) is used to evaluate the load on each CH as shown in Figures 8 –12. It is very difficult for each cluster to allocate the equal number of CNs. LBF is used for the balanced allocation of load in the cluster.

Figure 8.

Load balance factor in case of CLPSO, MOPSO, CACONET, and ICMFO when grid size is 1000 m×1000 m and transmission range varying from 100 to 600 and number of nodes = 30.

Figure 9.

Load balance factor in case of CLPSO, MOPSO, CACONET, and ICMFO when grid size is 1000 m×1000 m and transmission range varying from 100 to 600 and number of nodes = 40.

Figure 10.

Load balance factor in case of CLPSO, MOPSO, CACONET, and ICMFO when grid size is 1000 m×1000 m and transmission range varying from 100 to 600 and number of nodes = 50.

Figure 11.

Load balance factor in case of CLPSO, MOPSO, CACONET, and ICMFO when grid size is 1000 m×1000 m and transmission range varying from 100 to 600 and number of nodes = 60.

Figure 12.

Load balance factor in case of CLPSO, MOPSO, CACONET, and ICMFO when grid size is 2000 m×2000 m and transmission range varying from 100 to 600 and number of nodes = 40.

The primary cause is due to the rapid movement of neighbors from the CHs. The cardinality of the cluster size represents the load of a CH. The LBF is defined by Choubey³⁹ as

$LBF = \frac{1}{(n_{c} \times \sum_{i} {(x_{i} - μ)}^{2})}$ (9)

where n_c is the number of CHs, x_i is the cardinality of cluster i, and µ = N−n_c/n_c is the average number of neighbors of a CH (being the total number of nodes in the system) as shown in equation (9).

Conclusion and future work

In this article, the detailed exploration of evolutionary, MFO-based clustering Algorithm (ICMFO) is implemented in the vehicular adhHon networks. The graphs illustrate that proposed solution/framework (ICMFO) is more optimized. It minimizes the routing cost for the communication of the entire network by efficiently reducing the required number of clusters. Less number of clusters also leads to reduce the resources’ requirement in the network. By all this, ICMFO is considered as the well-united algorithm in the VANETs. The comparison is also done with the well-known algorithms (CLPSO, MOPSO, and CACONET) of VANETs. This analysis has also shown that the results of ICMFO are better. For the future use, we can enhance the objective function according to different problems and requirements. The proposed work can also be used for the multi-objective functions. For instance, in the proposed approach, the main objective is the stability of network using the intelligent clustering by focusing the characteristic of number of clusters. The other objectives can be taken such as social awareness, fairness index and higher access rate for the multi-objective functions. Other different algorithms, ant lion optimizer, dragon-fly algorithm, and whale optimization algorithm can also be implemented for the optimization in the VANETs.

Footnotes

Handling Editor: Razi Iqbal

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) received no financial support for the research,authorship,and/or publication of this article.

ORCID iD

Farhan Aadil

References

Lyu

Zhu

Zhou

et al . MoMAC: mobility-aware and collision-avoidance MAC for safety applications in VANETs. IEEE T Veh Technol 2018; 67: 10590–10602.

Daeinabi

Rahbar

AGP

Khademzadeh

VWCA: an efficient clustering algorithm in vehicular ad hoc networks. J Netw Comput Appl 2011; 34: 207–222.

Kumar

Chilamkurti

Park

JH.

ALCA: agent learning—based clustering algorithm in vehicular ad hoc networks. Pers Ubiquit Comput 2013; 17: 1683–1692.

Maslekar

Boussedjra

Mouzna

et al . A stable clustering algorithm for efficiency applications in VANETs. In: Proceedings of 2011 7th international wireless communications and mobile computing conference (IWCMC), Istanbul, 4–8 July 2011, pp.1188–1193. New York: IEEE.

Formato

RA.

Central force optimization. Prog Electromagn Res 2007; 77: 425–491.

Balachandar

Kannan

Newton’s law of gravity-based search algorithms. Indian J Sci Tech 2013; 6: 4141–4150.

Haouari

Moussaoui

Senouci

S-M

. Application reliability analysis of density—aware congestion control in VANETs. In: Proceedings of 2018 IEEE international conference on communications (ICC), Kansas City, MO, 20–24 May 2018, pp.1–6. New York: IEEE.

Cavalcanti

De Souza

JAR

Spohn

et al . VANETs’ research over the past decade: overview, credibility, and trends. ACM SIGCOMM Comp Com Rev 2018; 48: 31–39.

Barua

Liang

et al . RCare: extending secure health care to rural area using VANETs. Mobile Netw Appl 2014; 19: 318–330.

10.

Bechler

Wolf

. Mobility management for vehicular ad hoc networks. In: Proceedings of 2005 IEEE 61st vehicular technology conference (VTC 2005-spring), Stockholm, 30 May–1 June 2005, pp.2294–2298. New York: IEEE.

11.

Yang

Huang

Mobility management in VANET. In: Proceedings of 2013 22nd wireless and optical communication conference (WOCC), Chongqing, China, 16–18 May 2013, pp.298–303. New York: IEEE.

12.

Boukerche

Oliveira

Nakamura

et al . Vehicular ad hoc networks: a new challenge for localization-based systems. Comput Commun 2008; 31: 2838–2849.

13.

Jiang

Guo

Chen

Reliable and efficient alarm message routing in VANET. In: Proceedings of 2008 the 28th international conference on distributed computing systems workshops (ICDCS’08), Beijing, China, 17–20 June 2008, pp.186–191. New York: IEEE.

14.

Shen

Cheng

Yang

et al . Data dissemination in VANETs: a scheduling approach. IEEE T Intell Transp 2014; 15: 2213–2223.

15.

Iqbal

Challenges in designing ethical rules for infrastructures in internet of vehicles. Int J Adv Comput Sci Appl 2018; 9: 11–15.

16.

Aloise

Deshpande

Hansen

et al . NP-hardness of Euclidean sum-of-squares clustering. Mach Learn 2009; 75: 245–248.

17.

Harrabi

Jaafar

Ghedira

A novel clustering algorithm based on agent technology for VANET. Netw Protoc Algorithms 2016; 8: 1–19.

18.

Oranj

Alguliev

Yusifov

et al . Routing algorithm for vehicular ad hoc network based on dynamic ant colony optimization. Int J Electron Elect Eng 2016; 4: 79–83.

19.

Al-Mayouf

YRB

Abdullah

Ismail

et al . Evaluation of efficient vehicular ad hoc networks based on a maximum distance routing algorithm. EURASIP J Wirel Comm Netw 2016; 2016: 265.

20.

Aadil

Khan

Bajwa

et al . Intelligent clustering in vehicular ad hoc networks. KSII T Internet Inf 2016; 10: 3512–3528.

21.

Aadil

Bajwa

Khan

et al . CACONET: ant colony optimization (ACO) based clustering algorithm for VANET. PLoS ONE 2016; 11: e0154080.

22.

Wahab

Otrok

Mourad

VANET QoS-OLSR: QoS-based clustering protocol for vehicular ad hoc networks. Comput Commun 2013; 36: 1422–1435.

23.

Hassanabadi

Shea

Zhang

et al . Clustering in vehicular ad hoc networks using affinity propagation. Ad Hoc Netw 2014; 13: 535–548.

24.

Wahab

Mourad

Otrok

et al . CEAP: SVM-based intelligent detection model for clustered vehicular ad hoc networks. Expert Syst Appl 2016; 50: 40–54.

25.

Gaston

Bennie

Davies

et al . The ecological impacts of nighttime light pollution: a mechanistic appraisal. Biol Rev 2013; 88: 912–927.

26.

Frank

Rich

Longcore

Effects of artificial night lighting on moths. In: Rich

Longcore

(eds) Ecological consequences of artificial night lighting. Washington, DC: Island Press, 2006, pp.305–344.

27.

Kumar

Datta

Singh

SK.

Black hole algorithm and its applications. In: Azar

Vaidyanathan

(eds) Computational intelligence applications in modeling and control, studies in computational intelligence, vol. 575. Cham: Springer, 2015, pp.147–170.

28.

Kaveh

Talatahari

A novel heuristic optimization method: charged system search. Acta Mech 2010; 213: 267–289.

29.

Kaveh

Advances in metaheuristic algorithms for optimal design of structures. Cham: Springer, 2014.

30.

Zhuang

. Small-world optimization algorithm for function optimization. In: Proceedings of the second international conference on advances in natural computation (ICNC’06), Xi’an, China, 24–28 September 2006, pp.264–273. New York: ACM.

31.

Jordehi

AR.

A chaotic-based big bang—big crunch algorithm for solving global optimisation problems. Neural Comput Appl 2014; 25: 1329–1335.

32.

Moghaddam

Cheriet

. Curved space optimization: a random search based on general relativity theory (arXiv preprint arXiv:1208. 2214), https://arxiv.org/abs/1208.2214 (accessed 10 august 2012).

33.

Shah-Hosseini

Principal components analysis by the galaxy-based search algorithm: a novel metaheuristic for continuous optimization. Int J Comput Sci Eng 2011; 6: 132–140.

34.

Yao

Liu

Fast evolutionary programming. Evol Program 1996; 3: 451–460.

35.

Beyer

H-G

Schwefel

H-P.

Evolution strategies—a comprehensive introduction. Nat Comput 2002; 1: 3–52.

36.

Price

Storn

Lampinen

JA.

Differential evolution: a practical approach to global optimization. Berlin; Heidelberg: Springer Science and Business Media, 2006.

37.

Sarubbi

Martins

Silva

. A genetic algorithm for deploying roadside units in VANETs. In: Proceedings of 2016 IEEE congress on evolutionary computation (CEC), Vancouver, BC, Canada, 24–29 July 2016, pp.2090–2097. New York: IEEE.

38.

Simon

Biogeography-based optimization. IEEE T Evolut Comput 2008; 12: 702–713.

39.

Choubey

NS.

Fruit fly optimization algorithm for travelling salesperson problem. Int J Comput Appl (0975–8887) 2014; 107: 22–27.

40.

Cuevas

Reyna-Orta

A cuckoo search algorithm for multimodal optimization. Sci World J 2014; 2014: 497514.

41.

Neshat

Sepidnam

Sargolzaei

et al . Artificial fish swarm algorithm: a survey of the state-of-the-art, hybridization, combinatorial and indicative applications. Artif Intell Rev 2014; 42: 965–997.

42.

Roth

Termite: a swarm intelligent routing algorithm for mobile wireless ad-hoc networks. PhD Thesis, Cornell University, Ithaca, NY, 2005.

43.

Zhao

R-Q

Tang

W-S

. Monkey algorithm for global numerical optimization. J Uncertain Sys 2008; 2: 165–176.

44.

Pinto

Runkler

Sousa

. Wasp swarm optimization of logistic systems. In: Ribeiro

Albrecht

Dobnikar

et al . (eds) Adaptive and natural computing algorithms. Vienna: Springer, 2005, pp.264–267.

45.

Zhou

A novel global convergence algorithm: bee collecting pollen algorithm. In: ICIC’08 Proceedings of the 4th international conference on intelligent computing: advanced intelligent computing theories and applications—with aspects of artificial intelligence, Shanghai, China, 15–18 September 2008, pp.518–525. Berlin; Heidelberg: Springer.

46.

Abbass

HA.

MBO: marriage in honey bees optimization—a haplometrosis polygynous swarming approach. In: Proceedings of the 2001 congress on evolutionary computation (CEC 2001), Seoul, South Korea, 27–30 May 2001, pp.207–214. New York: IEEE.

47.

Shiqin

Jianjun

Guangxing

A dolphin partner optimization. In: Proceedings of 2009 WRI global congress on intelligent systems, Xiamen, China, 19–21 May 2009, pp.124–128. New York: IEEE.

48.

Gandomi

Alavi

AH.

Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci 2012; 17: 4831–4845.

49.

Askarzadeh

Bird mating optimizer: an optimization algorithm inspired by bird mating strategies. Commun Nonlinear Sci 2014; 19: 1213–1228.