Hybrid optimization-based secured routing in mobile ad-hoc network

Abstract

Mobile Ad hoc Networks (MANETs) pose significant routing challenges due to their decentralized and dynamic nature. Node mobility results in frequent changes in network topology, leading to unsFIG connectivity and link quality. Traditional RPs designed for static networks are inadequate for MANETs. To deal with these issues, a secure routing approach is proposed using the Red Panda-Lyrebrid Optimization (RePLO) algorithm, which combines the advantages of the Red Panda Optimization (RPO) and Lyrebird Optimization Algorithm (LOA) algorithms. The proposed approach consists of five steps: (i) configuring the system model, (ii) developing the energy model, (iii) creating the mobility model, (iv) selecting cluster heads using the RePLO algorithm, and (v) routing using the RePLO algorithm. The RePLO algorithm optimizes cluster head selection and routing while considering specific constraints such as delay, distance, energy, & security for Cluster Head (CH) selection, and link quality and enhanced trust for routing optimization. The effectiveness of the proposed approach is evaluated using various metrics to demonstrate its efficiency in MANET routing. By integrating multiple optimization techniques and considering critical constraints, the RePLO algorithm offers a systematic and secure solution for MANET routing. The evaluation results confirm the efficacy of the proposed approach in improving network performance, reliability, and security. Overall, the RePLO algorithm presents a promising approach to tackle the routing issues inherent in MANETs, paving the way for more robust and efficient communication in mobile ad hoc networks.

Keywords

MANET Routing protocol Cluster head selection RePLO algorithm ABP mechanism

1. Introduction

In a MANET, wireless mobile nodes form a dynamic network without infrastructure, often termed as infrastructure-less [1, 2]. These networks, known as Mobile Ad hoc Networks (MANETs), consist of wireless mobile nodes that autonomously exchange data amongst each other, operating independently of a fixed base station or wired backbone network [3]. A mobile ad hoc network facilitates communication between nodes without relying on any infrastructure support [4]. Additionally, nodes within a MANET can move freely in any direction, horizontally or vertically [5]. The increasing usage of MANETs in various applications has driven the evolution and enhancement of RPs [6]. Apart from MANETs, there exist other types of ad hoc networks like VANETs [7], SPANs, and WMNs [8], all of which play significant roles in modern technology [9].

MANETs offer several advantages, especially in scenarios with crumbling infrastructure, such as military operations where it forms a Wireless Backbone network facilitating communication between soldiers and vehicles on battlefields, provides internet access, information dissemination, and even tourist information [10, 11]. However, MANETs operate with limited resources, necessitating RPs with minimal energy and computational overheads [12, 13]. Dynamic topology variations pose challenges in designing protocols that ensure both security and energy efficiency [14, 15], crucial factors given the reliance on battery power in MANET nodes [16].

Routing protocols for MANETs must contend with dynamic topologies, real-time communication, resource constraints, bandwidth management, and packet overheads, leading to complexities [17]. While various RPs exist for MANETs, many suffer from high energy consumption, impacting node battery life [18]. Security is a paramount concern in MANETs due to the vulnerability to routing attacks [19, 20, 21], wherein nodes within signal range can intercept and manipulate packets, potentially compromising the network’s integrity [22]. Data can be routed by Mobile Ad hoc Networks (MANETs) in a number of ways, depending on the needs and circumstances of the network. Every node in the network keeps up-to-date routing data for every other node using proactive routing. Routing tables or updates are exchanged on a regular basis to accomplish this. Routes are only established via reactive routing as necessary. A node starts a route discovery process to find a way when it wishes to send data to another node.To capitalize on each strategy’s advantages, proactive and reactive routing components are combined in hybrid routing. It uses reactive techniques for less frequently accessed locations and maintains routes to frequently used nodes proactively. Geographic routing makes decisions based on the coordinates, or position, of nodes. Usually, it tries to forward packets to the location of the destination node. Energy-aware routing protocols aim to conserve node energy by considering energy levels or battery capacities of nodes when making routing decisions.

In response to these challenges, a hybrid optimization algorithm is proposed as a secure cluster-based RP for MANETs. This proposed protocol, RePLO, aims to enhance efficiency and security. This protocol aims to enhance efficiency while providing robust security measures to protect against potential attacks, ensuring the integrity and reliability of communication within the network. Further, the significant enhancements that improve the efficacy of the proposed RePLO-based securedRP are outlined as follows:

–
Proposing RePLO algorithm for optimal CH selection and routing in MANETs. It is a hybrid optimization algorithm that combines the RPO and LOA algorithms. Compared to the conventional RPO algorithm, RePLO offers several advantages by addressing its limitations through key enhancements. These enhancements include OBL initialization during the population initialization phase, the integration of Levy Flight distribution in the exploration phase, and the hybridization of RPO and LOA using an ABP mechanism in the exploitation phase.
–
Proposing an enhanced trust constraint for optimizing routing using the RePLO algorithm. This constraint is integrated with link quality considerations to enhance the reliability of routing decisions. Unlike traditional trust metrics that rely solely on direct and indirect trusts, RePLO incorporates a modified equation that takes into account direct, indirect, and communication trusts. This comprehensive approach ensures a more thorough assessment of node reliability in the network.

Hence, the overall procedure of the proposed RePLO-based securedRP for MANETs is structured as follows: a review of existing literature is conducted in Section 2, the outline of the proposed framework is elucidated in Section 3, simulation and experimental analyses are performed in Section 4, and the entire process is summarized in Section 5.
2. Literature review

Below, several recent papers about MANET routing have been examined:

In 2023, G.R. Rama Devi et al. [23] implemented a cross-layered RP, integrating PSO with an adapted contention window technique. It aimed to establish constant and energy-efficient routing paths, utilizing parameters like average energy load, traffic index, trust value, and data success rate from the network layer. After creating paths, it measured network bottlenecks at the MAC layer, optimizing bottlenecks and communication-based on energy loads and bottlenecks. Node trust was calculated from group trust and quality trust, while security was enhanced through ECC and Diffie-Hellman key exchanges.

In 2022, Abhay Bhatia et al. [24] evaluated the analysis of MANET’s role in a wireless real-time communication setup for NCS. Using AODV routing, communication among 150 nodes was maintained. Simulation in NS2 involved adjusting node clusters to estimate network metrics. MANET’s fixed topology allowed flexibility and scalability without infrastructure. AODV routing, being decentralized, scaled effectively with network size, providing adaptability to dynamic configurations.

In 2022, Subha R et al. [25] introduced an AFLIPLFFM to enhance network throughput and packet delivery ratio by accurately predicting path stability. AFLIPLFFM computed the IPR of mobile nodes and utilized it as input for a fuzzy inference engine to determine path stability. This process employed IF-THEN-based rules and triangular membership functions inherited from the Mamdani Fuzzy Inference Engine, ensuring effective path stability prediction.

In 2022, N.S. Saba Farheen et al. [26] suggested a node location prediction approach, based on temporal and spatial characteristics within its neighborhood, to estimate probable locations using a hybrid approach. The approach aimed to enhance routing performance without increasing packet overhead by employing a multi-path RP that integrated assessed probability locations and implemented path deviation at key points along the route.

In 2021, Uppalapati Srilakshmi et al. [27] demonstrated the study of the integration of Hill Climbing and GA in multiphase scenarios via a GAHC-style hybrid algorithm. Initially, density peak was utilized, predicting the selection of CHs based on direct, recent, and indirect trust metrics. Trust threshold worth nodes were computed. CHs engaged in multi-hop routing and the optimal path was determined by aggregating routes from these CHs. Selection criteria relied on the predicted hybrid protocol and aggregate features including throughput, latency, and connection quality.

In 2021, Prasant Kumar Pattnaik et al. [28] suggested an algorithm which addressed challenges in Optimal MANET Routing by incorporating mobility and obstacle awareness for multipath communication. It utilized the DeCasteljau Algorithm with Bezier curves to navigate obstacles and employed a speed-based mobility estimation concept to mitigate mobility consequences. Optimal routing paths were selected based on mobility prediction indicators, path availability, link duration, and network connectivity. Evaluation using Network Simulator-2 demonstrated the protocol’s effectiveness in minimizing delay, network overhead, and energy consumption while improving data delivery in MANET.

In 2020, Jinbin Tu et al. [29] introduced an AAS for active-RPs, demonstrating its effectiveness against various attacks. Employing BAN logic to address potential malicious nodes, AAS showcased compatibility with multiple RPs. Experimental results indicated a notable increase in packet delivery rate, enhancing overall performance by 33.9% and by 18.4% in networks with malicious nodes. AAS exhibited robustness, surpassing the average network connection rate of the Cap-OLSR protocol by 1.6 times and maintaining 79.2% of network performance during simulations with malicious node attacks.

In 2022, G. Rajeshkumar et al. [30] implemented a time synchronization algorithm for mobile contexts, employing Median synchronization message and KF to enhance accuracy. A multi-objective approach utilized the MOPSO algorithm to optimize cluster number and reduce energy loss in nodes, enhancing energy efficiency and reducing network traffic. CTAA method identified unauthorized nodes in MANET, while MOPSO optimized the route and minimized energy dissipation. The proposed CTAA-MPSO method achieved a PDR of 3.3% according to research findings.

In 2023, Orchu Aruna et al. [31] presented ML-ORAfor MANETs, seamlessly blended parameter configurations, utilized HPSO to select CHs, incorporated clustering mechanisms, and integrated k-NNs for intrusion detection. Assessments conducted in NS-3 demonstrated its prowess in adapting to dynamic network conditions, yielding notable outcomes such as a 15 ms latency, 95% packet delivery ratio, 4 Mbps throughput, and 85% energy efficiency. ML-ORA emerged as a promising remedy for addressing routing complexities in MANETs, thereby boosting both efficiency and security in transmitting data across ever-changing wireless environments.

In 2023, Alaotibi et al. [46] have suggests implementing a new geographic routing protocol in MANET, where the Rock Hyraxes Swarm Optimization (RHSO) and Whale Optimization Algorithm (WOA) are hybridized to create the Hybrid Roxes Whale Optimization (HRWO) algorithm, which performs the optimal route selection process. Additionally, a number of factors are taken into account for the best routing, including the average distance between nodes (mobility-related data based on location), delay, link lifetime, packet loss, and risk assessment.

In 2023, Ramaswamy et al. [47] develops a hybrid energy-efficient secured quality of service (QoS) based multipath routing protocol was proposed in this article. For the selection of cluster heads following initial cluster formations, a modified crow search in conjunction with the tunicate swarm butterfly optimization algorithm (TSBO) and a density-based clustering approach plan is suggested. The cluster head is chosen from among all the nodes, and a node’s authentication is provided using the collaborative trust-based approach (CTBA), which uses the trust factor for mobile ad hoc network (MANET) data transfer. Lastly, this article proposed a hybrid multipath routing protocol that combines a fruit fly algorithm with multi-objective grey wolf optimization (MO-GWO) to execute the safe routing technique.

Table 1
Methodologies, features, and limitations of existing MANET-related approaches.

Author [Citation] Methodology Feature Limitation

G.R. Rama Devi et al. [23] ESCL-PSO It achieved a higher PDR while minimizing overhead and energy consumption. ECC algorithms and parameters might not have undergone extensive scrutiny or standardization, resulting in possible trust concerns regarding their security and reliability.

Abhay Bhatia et al. [24] AODV protocol It didn’t necessitate extra overhead for data packets. The frequent route discovery and maintenance tasks of AODV could result in heightened energy usage, thereby diminishing the network’s overall lifespan.

Subha R et al. [25] AFLIPLFFM It offered precise forecasts of path stability. The integration of adaptive fuzzy logic might have introduced considerable complexity and computational overhead to the model.

N.S. Saba Farheen et al. [26] HM-MPR Achieved reduced delay and overhead while attaining a higher PDR. Further enhancements in performance could have been achieved by incorporating delay tolerance into routing.

Uppalapati Srilakshmi et al. [27] GAHC It generated a maximum throughput and achieved a maximum PDR. This study focused solely on selective packet-dropping attacks.

Prasant Kumar Pattnaik et al. [28] MOAR protocol It delivered superior improvements in terms of average delay, PDR, average energy consumption, and throughput. Its complexity stemmed from the requirement to account for dynamic network topologies, node mobility patterns, and obstacle information.

Jinbin Tu et al. [29] AAS It demonstrated effectiveness in thwarting selective false routing attacks, routing spoofing attacks, forwarding attacks, and byzantine attacks. The compatibility of the security authentication scheme for RPs was still in need of improvement.

G. Rajeshkumar et al. [30] CTAA-MPSO It could offer a higher PDR and reduce network traffic. Integrating trust considerations and multiple objectives into PSO may have elevated the computational overhead of the algorithm.

Orchu Aruna et al. [31] HPSO Findings revealed ML-ORA’s superior performance in dynamic networks, boasting a 95% PDR, 15ms delay, 4Mbps throughput, and 85% energy efficiency. This underscores its capacity to improve both efficacy and security in data transmission within MANETs. In this framework, there was a requirement for optimizing energy efficiency to extend the operational duration of battery-powered devices.

Author [Citation]	Methodology	Feature	Limitation
G.R. Rama Devi et al. [23]	ESCL-PSO	It achieved a higher PDR while minimizing overhead and energy consumption.	ECC algorithms and parameters might not have undergone extensive scrutiny or standardization, resulting in possible trust concerns regarding their security and reliability.
Abhay Bhatia et al. [24]	AODV protocol	It didn’t necessitate extra overhead for data packets.	The frequent route discovery and maintenance tasks of AODV could result in heightened energy usage, thereby diminishing the network’s overall lifespan.
Subha R et al. [25]	AFLIPLFFM	It offered precise forecasts of path stability.	The integration of adaptive fuzzy logic might have introduced considerable complexity and computational overhead to the model.
N.S. Saba Farheen et al. [26]	HM-MPR	Achieved reduced delay and overhead while attaining a higher PDR.	Further enhancements in performance could have been achieved by incorporating delay tolerance into routing.
Uppalapati Srilakshmi et al. [27]	GAHC	It generated a maximum throughput and achieved a maximum PDR.	This study focused solely on selective packet-dropping attacks.
Prasant Kumar Pattnaik et al. [28]	MOAR protocol	It delivered superior improvements in terms of average delay, PDR, average energy consumption, and throughput.	Its complexity stemmed from the requirement to account for dynamic network topologies, node mobility patterns, and obstacle information.
Jinbin Tu et al. [29]	AAS	It demonstrated effectiveness in thwarting selective false routing attacks, routing spoofing attacks, forwarding attacks, and byzantine attacks.	The compatibility of the security authentication scheme for RPs was still in need of improvement.
G. Rajeshkumar et al. [30]	CTAA-MPSO	It could offer a higher PDR and reduce network traffic.	Integrating trust considerations and multiple objectives into PSO may have elevated the computational overhead of the algorithm.
Orchu Aruna et al. [31]	HPSO	Findings revealed ML-ORA’s superior performance in dynamic networks, boasting a 95% PDR, 15ms delay, 4Mbps throughput, and 85% energy efficiency. This underscores its capacity to improve both efficacy and security in data transmission within MANETs.	In this framework, there was a requirement for optimizing energy efficiency to extend the operational duration of battery-powered devices.

Furthermore, existing approaches related to MANET are summarized in Table 1, detailing its methodologies, features, and limitations.

2.1. Problem definition

MANET functions as a decentralized infrastructure, comprising mobile hosts that establish their network or connections dynamically without central management. The network’s dynamic nature introduces complexities, with frequent changes in topology. Bandwidth constraints, limited energy, and storage capacities of mobile nodes impose significant limitations. Communication between nodes is often restricted due to small transmission ranges, necessitating multiple hops for routing paths, with neighboring nodes acting as routers. Several MANET RPs have been developed, such as CTAA-MPSO [30] and ESCL-PSO [23], aiming to reduce power consumption while maintaining high PDRs. However, these protocols had increased computational overhead and posed security and reliability concerns. AODV protocol [24], utilized by Abhay Bhatia et al., didn’t add extra overhead to data packets, but its frequent route discovery and maintenance activities could escalate energy consumption, reducing the network’s lifespan. AFLIPLFFM [25] accurately predicted path stability, but its fuzzy techniques introduced complexity and computational overhead. Although HM-MPR [26] and AAS [29] offered better performance compared to other models, they still required improvements. GAHC achieved high throughput and PDR but only addressed selective packet-dropping attacks [27]. The MOAR protocol, introduced by Prasant Kumar Pattnaik et al., [28] enhanced average delay, energy consumption, PDR, and throughput. However, considering dynamic network topologies, node mobility patterns, and obstacle information made it more complex. Addressing these challenges necessitates the development of methods with superior performance.

3. Outline of RePLO-based routing for MANETs

The RePLO-based routing for MANETs follows a systematic approach aimed at ensuring efficient and secure communication within the network.

The steps involved in the systematic approach of RePLO-based routing for MANETs are:

1.
System model configuration
2.
Development of the energy model
3.
Development of the mobility model
4.
Cluster head selection using the RePLO algorithm
5.
Routing using the RePLO algorithm

Firstly, the system model is established, adopting a multi-objective perspective to address critical factors such as delay, distance, energy consumption, link quality, security, and trust. This model encompasses a diverse array of nodes, including normal nodes, CHs, and a central BS.

Next, an energy model is determined to monitor and manage the energy consumption of nodes across various operational states. Additionally, the mobility model plays a crucial role in understanding and simulating the movement behaviors of mobile nodes over time, with a random point mobility model employed in this scenario.

Cluster head selection is a pivotal step in MANET operation, involving the meticulous application of a hybrid optimization algorithm that combines the strengths of RPO and LOA techniques. This process ensures optimal performance while taking into account critical constraints such as delay, distance, energy & security.

Subsequently, routing optimization is carried out using the RePLO algorithm, which integrates both CH selection and routing optimization functionalities. By combining RPO and LOA, the RePLO algorithm effectively addresses link quality and trust considerations for routing optimization. Unlike traditional trust metrics, RePLO incorporates a modified equation that evaluates node reliability based on direct, indirect, and communication trusts, leading to a more comprehensive assessment.
3.1. System model configuration

In the design of a MANET system model, a multi-objective approach is adopted, taking into account several critical factors including delay, distance, energy consumption, link quality, security & trust. The system architecture involves a source node transmitting data packets to a designated target node within the network. This network comprises a diverse set of nodes, including normal nodes, a group of CHs, and a central BS [32]. The MANET system design is represented in Fig. 1, and the parameters for its simulation setup are presented in Table 2.

Table 2
Simulation parameters.

Field area 100 $\times$ 100 m²

Number of mobile nodes 100

The probability of a node becoming CH 0.1

Mobility model Random manner

Mobility of a node (10–20) m/s

Packet size 4000 bits

Field area	100 $\times$ 100 m²
Number of mobile nodes	100
The probability of a node becoming CH	0.1
Mobility model	Random manner
Mobility of a node	(10–20) m/s
Packet size	4000 bits

Figure 1.

System design of MANET.

The selection of CHs is optimized using the RePLO algorithm, which integrates the strengths of both RPO and LOA. RePLO optimally chooses CHs while adhering to specific constraints such as minimizing delay, optimizing distance, conserving energy, and enhancing security. By leveraging the capabilities of both RPO and LOA, RePLO ensures efficient clustering of nodes, enhancing overall network performance.

Moreover, the routing mechanism within this MANET system model is orchestrated by the RePLO algorithm, which considers additional constraints such as link quality and trust. This RP aims to establish reliable communication paths while considering the quality of links and the trustworthiness of nodes within the network. By incorporating these factors into the routing decisions, the RePLO algorithm facilitates robust and dependable data transmission throughout the MANET system.

Overall, the MANET system model integrates advanced optimization techniques and multi-objective considerations to enhance various aspects of network performance, including efficiency, reliability, and security, thereby providing a comprehensive solution for dynamic and resource-constrained wireless communication environments.

3.2. Development of the energy model

An energy model is essential for monitoring and managing the energy consumption of nodes within a MANET [33]. This model tracks the energy usage across different operational states of the nodes, including idle, receive, transmit, and sleep modes. By capturing the energy consumption patterns in each state, the energy model provides insights into the overall energy dynamics of the network. This information is crucial for optimizing energy utilization, prolonging node lifetime, and enhancing the efficiency of communication protocols. Additionally, the energy model enables the estimation of remaining battery capacity, allowing for proactive energy management strategies such as dynamic power management and energy-aware routing. Through the integration of this energy model into the MANET system, network operators can make informed decisions to balance energy consumption and network performance, ultimately ensuring sustainable and reliable operation in resource-constrained environments.

3.3. Development of the mobility model

The mobility model in terms of the MANET framework serves as a crucial component for understanding and simulating the movement behaviors of mobile nodes over time [34]. It elucidates how the acceleration, location, and velocity of nodes evolve throughout the simulation duration. In this particular scenario, a random point mobility model is employed to simulate node movements.

Initially, at the time $t$ , the nodes $u$ and $v$ are situated at locations $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ , respectively. These nodes exhibit variable velocities as they traverse in specific directions with angles $θ_{1}$ and $θ_{2}$ relative to the positive x-axis. Over a time duration $T$ , from $T = 0$ to $t$ , node $u$ moves a distance $D_{1}$ , while node $v$ moves a distance $D_{2}$ .

Upon reaching time $t$ , the nodes $u$ and $v$ attain updated locations $(x_{6}, y_{6})$ and $(x_{3}, y_{3})$ , respectively. The calculation of the updated location of the node $u$ is governed by an equation as depicted in Eq. (1) where, $V_{u}$ indicates variable velocity of node $u$ and its value is (10–20) m/s, $R$ denotes current round, $θ = (0 - 2 π)$ and $t = \frac{R}{1000}$ .

\begin{array}{l} x_{6} = x_{1} + V_{u} * t * \cos θ \\ y_{6} = y_{1} + V_{u} * t * \sin θ \end{array}

(1)

Figure 2.

Updated location of node u after mobility.

Figure 2 illustrates the updated locations of nodes after their mobility has been simulated, providing a visual representation of their movement trajectories.

This mobility model facilitates the emulation of realistic node mobility patterns, crucial for assessing the performance of RPs in MANETs.

3.4. Cluster head selection using RePLO algorithm

Figure 3.

Illustration of CH selection process using RePLO algorithm in MANET environment.

In the designed MANET system model, the presence of 100 mobile nodes underscores the complexity and scale of the network. An integral aspect of MANET operation is the selection of CHs, pivotal nodes responsible for managing and coordinating communication within their respective clusters. An illustration of CH selection using the RePLO algorithm in a MANET environment based on constraints such as delay, distance, energy & security is shown in Fig. 3.

The process of CH selection is conducted meticulously, leveraging a hybrid optimization algorithm to ensure optimal performance while considering various critical constraints. This hybrid optimization algorithm integrates the strengths of two distinct optimization techniques: RPO and LOA. By incorporating elements from both RPO and LOA, the hybrid algorithm achieves enhanced effectiveness in CH selection.

Several constraints guide the CH selection process, including delay, distance, energy, and security considerations. These constraints are pivotal in determining the suitability of candidate nodes for assuming the role of CHs within the network. By accounting for these constraints, the algorithm ensures that CHs are strategically located to facilitate efficient data transmission, minimize latency, conserve energy resources, and uphold network security standards.

Through the collaborative efforts of the hybrid optimization algorithm and the consideration of multifaceted constraints, the MANET system model attains an optimal configuration of CHs. This optimized CH selection process has a pivotal role in enhancing the overall performance and reliability of the MANET, laying the foundation for robust and efficient communication in dynamic and resource-constrained environments.

3.4.1. Key constraints in CH selection via RePLO algorithm

The selection of CHs in MANETs has an essential part in optimizing resource utilization and network performance. The RePLO algorithm offers an effective approach for CH selection, considering various critical constraints such as delay, distance, energy& security. The detailed descriptions of these constraints are delineated below.

–
Delay: It indicates the time taken for data packets to travel from the source node to the target node in the network.
$\begin{aligned} D e = \frac{D}{S} \end{aligned}$
(2)

In Eq. (2), the term ‘ $S$ ’ denotes the speed of the data transmission and its value is 2.1 $\times$ 10⁸ m/s.
–
Distance: It represents the distance between each CH to BS within the network. This constraint is determined using Euclidean distance which is expressed in Eq. (3) which $(x_{i}, y_{i})$ denotes the coordinates of CH and $(x_{j}, y_{j})$ indicates BS coordinates.
$\begin{aligned} D_{c h - b s} & = \sqrt{(x_{i} - x_{j})^{2} + (y_{i} - y_{j})^{2}} \end{aligned}$
(3)

$\begin{aligned} Distance & = mean [D_{c h - b s}] \end{aligned}$
(4)
–
Energy: Energy constraints ensure that nodes operate within their energy budget to prolong network lifetime and avoid premature battery depletion.
$\begin{aligned} E = mean [r_{E_{c h}}] \end{aligned}$
(5)

In Eq. (5), the term ‘ $r_{E_{c h}}$ ’ indicates the remaining energy in CH.
–
Security: It represents a measure of the security difference between a CH and a particular node $a$ within the network and this measure is calculated using Eq. (6) where, $a = 1, 2, 3, \dots, N$ and $N$ is the number of mobile nodes. The probability of security risks in MANETs depends on how well security measures match network task requirements. Inadequate security protocols increase the risk probability. Risk probability is assessed using a formula Eq. (7), while security level evaluation is detailed in Eq. (8).
$\begin{aligned} S e c (a) = {C H}_{S e c} - a_{S e c} \end{aligned}$
(6)

$\begin{aligned} \begin{array}{l} i f S e c (a) ⩽ 0 \\ R i s k = 1 \\ e l s e i f 0 < S e c (a) ⩽ 1 \\ R i s k = 1 - e^{[- 3 / 2 * S e c (a)]} \\ e l s e i f 1 < S e c (a) ⩽ 2 \\ R i s k = 1 - e^{[- 1 / 2 * S e c (a)]} \\ e l s e \\ R i s k = 0 \end{array} \end{aligned}$
(7)

$\begin{aligned} S e c = 1 - Risk \end{aligned}$
(8)

By considering these constraints, the RePLO algorithm enables the selection of CHs that optimize network performance, enhance resource utilization, and ensure the robustness and security of MANETs in dynamic and challenging environments.
3.4.2. Objective function and solution encoding of RePLO algorithm for CH selection

The objective function in terms of the RePLO algorithm for CH selection aims to minimize fitness by considering various constraints. These constraints, including delay, distance, energy, and security, are normalized using Eq. (9) to account for their different ranges. Equation (9), denoted as $C^{norm}$ , normalizes the constraints based on their minimum and maximum values, ensuring fair comparison across different constraints. The values of variables $A$ and $B$ in Eq. (9) are 0.9 and 0.1, respectively and $C^{norm} = [{D e}^{norm}, D^{norm}, E^{norm}, {S e c}^{norm}]$ .

\begin{aligned} C^{norm} = \frac{C - min (C)}{max (C) - min (C)} * (A - B) + B \end{aligned}

(9)

The objective function itself is formulated as a weighted sum of the normalized constraints, here, $w_{1}, w_{2}, w_{3},$ and $w_{4}$ representing the weights assigned to each constraint. These weights reflect the relative importance of each constraint in the CH selection process. The objective function can be represented as:

\begin{aligned} F_{{O b j}_{1}} = min [(w_{1} * {D e}^{norm}) + (w_{2} * D^{norm}) + (w_{3} * (1 - E^{norm})) + (w_{4} * {S e c}^{norm})] \end{aligned}

(10)

In Eq. (10), the weights of constraints are commonly denoted as $w_{x}, {x = 1, 2, 3, 4}$ here, $w_{x} = \frac{C_{x}^{norm}}{\sum C^{norm}}; \sum w_{x} = 1$ .

Furthermore, the solution encoding for CH selection involves defining lower and upper bounds, which are $1$ and $N - 2$ respectively, where $N$ represent the number of nodes in the network. In this context, with a problem size of 10 and a population size of 10, the encoding scheme ensures that each potential CH is within the valid range of node indices.

3.5. Routing using RePLO algorithm

Figure 4.

Illustration of routing process using RePLO algorithm in MANET environment.

Routing in MANETs is complex due to their dynamic and decentralized nature. Nodes communicate directly or via intermediaries, creating a network without fixed infrastructure. Efficient RPs are crucial for node communication. In this research, a hybrid optimization algorithm termed RePLO is employed for secure routing. This algorithm, combining RPO and LOA, handles both CH selection and routing optimization. An illustration of routing using the RePLO algorithm in a MANET environment based on constraints such as link quality and enhanced trust is shown in Fig. 4.

The RePLO algorithm incorporates crucial constraints like link quality and enhanced trust for routing optimization. Unlike traditional trust metrics relying only on direct and indirect trusts, RePLO uses a modified equation considering direct, indirect, and communication trusts. This provides a more thorough assessment of node reliability.

By integrating these constraints, RePLO ensures routing decisions consider both link quality and enhanced trust. This enhances network robustness, reduces the risk of attacks, and promotes reliable data communication. Ultimately, RePLO routing in MANETs offers a sophisticated and effective strategy for improving network performance and reliability in dynamic environments.

3.5.1. Key constraints for routing via RePLO algorithm

Routing in MANETs using the RePLO algorithm considers two critical constraints such as link quality and enhanced trust. These constraints are pivotal for confirming secure and reliable data transmission within the network. The detailed descriptions of these constraints are given below.

Link quality- It refers to the quality of data packets received by the receiver in the network. In the context of secure routing, assessing link quality is essential for ensuring that data packets are transmitted over reliable paths with minimal packet loss, latency, and interference.

\begin{aligned} L q = \frac{N o . o f p a c k e t r e c e i v e d}{N o . o f p a c k e t t r a n s m i t t e d} \end{aligned}

(11)

Enhanced trust- Trust is a critical factor in ensuring the security and reliability of communication in MANETs. While traditional trust metrics typically rely on direct and indirect trusts between nodes [35], the RePLO algorithm incorporates an enhanced trust constraint that goes beyond conventional trust metrics. This enhanced trust metric considers factors such as improved direct trust, indirect trust, and communication trust, which evaluates the trustworthiness of nodes based on their communication behavior and reliability in transmitting data packets. By factoring in enhanced trust metrics, the RePLO algorithm enables more robust and secure routing decisions, enhancing the network’s resilience against malicious attacks, unauthorized access, and unreliable nodes. The equations for evaluating trust conventionally ( $C_{u, v}^{T})$ and enhanced trust ( $E_{u, v}^{T})$ proposed in this research are formulated in Eq. (12).

\begin{aligned} C_{u, v}^{T} & = [w_{1} * {D T}_{u, v}] + [w_{2} * {I D T}_{u, v}] \end{aligned}

(12)

\begin{aligned} E_{u, v}^{T} & = [w_{1} * {D T}_{u, v}] + [w_{2} * {I D T}_{u, v}] + [w_{3} * {ComT}_{u, v}] \end{aligned}

(13)

In Eqs (12) and (13), $w_{1}, w_{2},$ and $w_{3}$ indicates the weights of direct, indirect and communication trusts, respectively. The weights of constraints are commonly denoted as $w_{y}, {y = 1, 2, 3, 4}$ here, $\sum w_{y} = 1$ . The factors such as direct, indirect, and communication trust metrics are denoted as ${D T}_{u, v}, {I D T}_{u, v},$ and ${ComT}_{u, v}$ . 1.

Direct trust: It refers to the trustworthiness of neighboring nodes based on direct interactions and observations. It assesses the node’s behavior, reliability, and performance in transmitting data packets directly to other nodes within its communication range. In conventional trust evaluation, direct trust is typically assessed using Eq. (14). However, in enhanced trust evaluation, the determination of ‘direct trust’ adopts a novel approach, as depicted in Eq. (15). Using PDR [36] enhances direct trust evaluation by accurately gauging node reliability in wireless networks. Unlike rank threshold, PDR directly measures packet delivery success, providing a granular assessment of node trustworthiness. Integration of PDR in trust models leads to informed decisions, enhancing network performance and reliability.

\begin{aligned} {D T}_{u, v} & = \frac{[E + R B + U + R_{T}]}{4} \end{aligned}

(14)

\begin{aligned} {D T}_{u, v} & = \frac{[E + R B + U + P D R]}{4} \end{aligned}

(15)

where,

E

denotes energy, RB indicates routing behavior,

U

represents unselfishness,

R_{T}

indicates rank threshold, and PDR denotes packet delivery ratio. The evaluation of these terms is conducted using the following equations:

\begin{aligned} Routing~Behavior, R B & = \frac{Forwarded Data Packets}{Received Data Packets} \end{aligned}

(16)

\begin{aligned} Energy, E & = \frac{r_{E}}{i_{E}} w h e r e, r_{E} - R e m a i n i n g e n e r g y & i_{E} - Initial energy \end{aligned}

(17)

\begin{aligned} U n s e l f i s h n e s s, U & = R B - [\frac{FDPs as sender}{R D P s}] \end{aligned}

(18)

\begin{aligned} P D R & = \frac{Total no . of packets received}{Total no . of packets transmitted} \end{aligned}

(19)

Indirect trust: It evaluates the trustworthiness of nodes based on recommendations or endorsements from other nodes in the network. It considers the trust ratings assigned by neighboring nodes to their own neighbors and propagates these ratings across the network.

If node $u$ and node $v$ have a minimal number of transactions, and they share common neighboring nodes denoted by $n_{c}$ (where $n_{c} = n_{1}, n_{2}, n_{3}$ , then the direct trust of node $u$ with $n_{c}$ and the direct trust of the node $n_{c}$ with $v$ are computed. The factor ‘indirect trust’ in enhanced trust evaluation is evaluated as in Eq. (20).

\begin{aligned} {I D T}_{u, v} = \frac{\sum_{n_{c} = 1}^{n_{c} = 4} [{D T}_{u, n_{c}} * {D T}_{n_{c}, v}]}{\sum_{n_{c} = 1}^{n_{c} = 4} [{D T}_{u, n_{c}}]} \end{aligned}

(20)

Communication trust: It evaluates the trustworthiness of nodes by tracking the successful delivery of packets from a source node to the destination without any loss [37]. Thereby, the equation below represents the PDR-based communication trust where, ${p d r}_{i}$ indicates PDR of $i$ th time, $μ$ represents mean and its value is 0, and $σ$ indicates standard deviation and its value is 1.

\begin{aligned} {C o m T}_{u, v} = \frac{1}{\sqrt{2 σ^{2} π}} . e^{\frac{- ({p d r}_{i} - μ)^{2}}{2 σ^{2}}} \end{aligned}

(21)

Incorporating direct, indirect, and communication trust metrics into the evaluation of node trustworthiness enhances the proposed trust evaluation, providing a comprehensive assessment of node reliability in MANETs. This approach, coupled with considerations of link quality, aids in identifying trustworthy nodes for routing decisions. Consequently, this strategy mitigates security risks and fosters reliable and secure communication in dynamic and challenging network environments.

Thus, by considering both link quality and improved trust as constraints, the RePLO algorithm ensures that routing decisions in MANETs prioritize secure and reliable communication paths. This approach helps to mitigate security risks, enhance data confidentiality and integrity, and improve overall network performance and resilience in dynamic and challenging environments.

3.5.2. Objective function amd solution encoding of RePLO algorithm for routing

The objective function for routing using the RePLO algorithm aims to minimize fitness while considering constraints such as link quality and enhanced trust. This objective function is formulated as follows:

\begin{aligned} F_{{O b j}_{2}} = min [(w_{1} * (1 - L q)) + (w_{2} * (1 - E_{u, v}^{T}))] \end{aligned}

(22)

In this equation, $w_{1}$ and $w_{2}$ represent the weights assigned to the link quality and enhanced trust constraints, respectively.

The solution encoding for routing involves defining lower and upper bounds of 0 and 1, respectively. With a problem size of $N - 2$ , where $N$ indicates the number of nodes in the network, and a population size of 10, the solution space is restricted to the range (0,1). Additionally, the path ID is determined by identifying the indices where the solution equals 1, indicating the presence of a path.

3.6. Mathematical model of RePLO algorithm

The RePLO algorithm, introduced in this research, serves as a hybrid optimization approach proposed for both CH selection and routing in MANETs. This algorithm combines two distinct optimization algorithms: RPO [38] and LOA [39] to leverage its strengths and avoid its limitations. Within the RePLO algorithm, updates are integrated into the framework of RPO to boost its effectiveness for CH selection and routing. These updates include several pivotal modifications such as OBL initialization, Levy Flight distribution, and hybridization of RPO and LOA using ABP. In order to lessen the effects of attacks and guarantee the network’s ongoing operation, hybrid optimization can include resilience techniques like redundancy, distributed trust management, and quick topology reconfiguration. In particular, the hybrid Red Panda-Lyrebird Optimization seems to be a specialized or speculative optimization technique that is not well-known or recorded in mainstream literature, with respect to its benefits. Generally speaking, hybrid optimization strategies take advantage of the complementing advantages of many algorithms or techniques to maximize convergence speed, solution quality, or robustness against local optima. Still, it’s difficult to list all of the benefits of the Red Panda-Lyrebird Optimization without more particular information.

The RePLO algorithm, which combines characteristics of both RPO and LOA, is proposed as an advantageous alternative to conventional RPO and LOA algorithms. RPO brings its unique optimization mechanisms to the forefront, while LOA contributes its distinctive strategy for exploitation. This hybridization process aims to achieve stability between exploration and exploitation, facilitating more efficient and effective CH selection and routing decisions in MANETs.

The RePLO algorithm’s capacity to integrate innovative updates into RPO, combined with the fusion of LOA’s exploitation capabilities, positions it as a promising solution for optimizing CH selection and routing in MANETs.

3.6.1. Population initialization

In the RePLO algorithm, a population-based metaheuristic approach, red pandas are utilized as its members. Each red panda within the algorithm’s population represents a potential solution to the given problem, offering specific values for problem variables in accordance with its location within the solution space. This conceptualization transforms each red panda, or candidate solution, into a mathematical vector. As a result, the red pandas collectively form a matrix, as indicated by Eq. (23), where each row resembles a red panda representing a potential solution, and each column denotes recommended values for the corresponding problem variable.

In the RPO algorithm, random initialization is employed to initialize the locations of red pandas in the solution space. However, this approach often leads to inefficient exploration of the solution space. Random initialization tends to heighten the risk of becoming trapped in local optima, thereby restricting the algorithm’s effectiveness in identifying globally optimal solutions. The conventional way of adjusting the locations of red pandas in the solution space in the RPO algorithm is formulated in Eq. (24).

In contrast, during the initialization phase of the RePLO algorithm, the population of red pandas undergoes OBL initialization [40], marking the first update in the algorithm. To initiate the RePLO process, the locations of red pandas within the solution space are initialized using OBL initialization, as illustrated in Eq. (25). This proactive initialization strategy enhances the algorithm’s capability to explore the solution space effectively and mitigates the risk of premature convergence to suboptimal solutions.

\begin{aligned} P & = {[\begin{array}{l} P_{1} \\ ⋮ \\ P_{i} \\ ⋮ \\ P_{n} \end{array}]}_{n \times m} = {[\begin{matrix} p_{1, 1} & \dots & p_{1, j} & \dots & p_{1, m} \\ ⋮ & ⋱ & ⋮ & . . . & ⋮ \\ p_{i, 1} & \dots & p_{i, j} & \dots & p_{i, m} \\ ⋮ & . . . & ⋮ & ⋱ & ⋮ \\ p_{n, 1} & \dots & p_{n, j} & \dots & p_{n, m} \end{matrix}]}_{n \times m} \end{aligned}

(23)

\begin{aligned} p_{i, j} & = B_{j}^{L} + {a r b}_{i, j} . (B_{j}^{U} - B_{j}^{L}); i = 1, 2, 3, \dots, n & j = 1, 2, 3, \dots, m . \end{aligned}

(24)

\begin{aligned} p_{i, j}^{^{'}} & = B_{j}^{L} + B_{j}^{U} - P_{b e s t} + {a r b}_{i, j} * (P_{b e s t} - p_{i, j}); i = 1, 2, 3, \dots, n & j = 1, 2, 3, \dots, m . \end{aligned}

(25)

In the RePLO algorithm, $P$ represents the population matrix of red pandas’ locations, where $P_{i}$ denotes the $i$ th red panda, denoted as a potential solution. Each $p_{i, j}$ in $P_{i}$ represents its $i$ th dimension, corresponding to a problem variable. With $m$ indicating the number of problem variables and $n$ signifying the number of red pandas, ${a r b}_{i, j}$ represents arbitrary numbers within the interval [0,1], while $B_{j}^{U}$ and $B_{j}^{L}$ represent the upper and lower bounds of the $i$ th problem variable, respectively.

Given that each red panda’s location serves as a candidate solution for the problem, we can evaluate the objective function equivalent to each of these solutions. For instance, in problems such as optimal CH selection and routing in MANETs, the objective function can be assessed. The assessed values for the objective functions of CH selection and routing are represented in Eqs (10) and (22), respectively.

The efficiency of potential solutions in an optimization algorithm hinges on the assessment of the objective function. The optimal outcome of the objective function signifies the most promising potential solution, whereas the worst outcome indicates the least desirable potential solution. With iterative updates to potential solutions, both the best and worst solutions are adjusted in each iteration. Upon completion of the algorithm, the most successful potential solution attained during the iterations is identified as the problem solution. The method of updating candidate solutions in the proposed algorithm comprises two distinct stages: exploration and exploitation.

3.6.2. Proposed exploration phase: Foraging behavior of red pandas

During the exploration stage of RePLO, the localization of red pandas imitates their innate foraging instincts. With remarkable sensory capabilities in scent, sound, and sight, red pandas adeptly navigate their environment to locate sustenance in the wilderness. In the RePLO design, each red panda evaluates the locations of its counterparts, identifying those associated with improved objective function values as potential food sources. These candidate food resource locations are determined through a comparison of objective function values, as defined in Eq. (26). Subsequently, each red panda randomly selects one of these proposed locations as its designated food source.

\begin{aligned} {F S}_{i} = {P_{l} | l \in {1, 2, 3, \dots, n} a n d F_{O b j}^{l} < F_{O b j}^{i}} \cup {P_{b e s t}} \end{aligned}

(26)

Equation (26), ${F S}_{i}$ represents the set of proposed food sources for the $i$ th red panda and $P_{b e s t}$ denotes the location of the red panda with the best value for the objective function. Moving towards the food source results in significant changes in the locations of red pandas. This behavior enhances the RePLO algorithm’s capability for exploration and global search within the problem-solving space.

In the conventional RPO algorithm, red pandas simulate their foraging behavior by adjusting their locations towards the best candidate solution, or food source which is shown in Eq. (27). This conventional approach of random movements in the RPO algorithm often results in the algorithm becoming trapped in local optima, thereby hindering its ability to discover globally optimal solutions due to limited exploration capability. To mitigate this issue, the RePLO algorithm incorporates Levy Flight distribution [41] during the Exploration Phase. Levy Flight distribution permits occasional large steps in the solution space, aiding the algorithm to break free from local optima and explore distant regions more effectively. Consequently, this integration enables the algorithm to overcome the disadvantage of being confined to local optima and enhances its capacity to search for and converge towards globally optimal solutions. The equation representing the foraging behavior of red pandas, adjusted towards the best candidate solution or food source, incorporates Levy Flight distribution within the RePLO algorithm, as depicted in Eq. (28). Additionally, Eq. (29) illustrates the equation of Levy Flight distribution.

\begin{aligned} P_{i}^{L 1} : p_{i, j}^{L 1} & = p_{i, j} + {a r b}_{i, j} . ({S F S}_{i, j} - β . p_{i, j}) \end{aligned}

(27)

\begin{aligned} P_{i}^{L 1} & = p_{i, j} + | l e v y (δ) | . ({S F S}_{i, j} - β . p_{i, j}) \end{aligned}

(28)

\begin{aligned} l e v y (δ) & = \frac{V}{| U |^{1 / ϕ}} \end{aligned}

(29)

where

U

specifies an arbitrarily selected number drawn from the Gaussian distribution

λ (0, 1)

ϕ

indicates power-law index and its value is 0.5,

V

denotes an arbitrarily selected number drawn from the Gaussian distribution

λ (0, σ^{2})

and

σ

represents the standard deviation and its formulation is shown in Eq. (30) where

Γ

indicates the gamma function.

\begin{aligned} σ = {[\frac{Γ (1 + ϕ) * \sin (\frac{π + ϕ}{2})}{Γ (\frac{1 + ϕ}{2}) * ϕ * 2^{(\frac{ϕ - 1}{2})}}]}^{1 / ϕ} \end{aligned}

(30)

If the objective function shows improvement in the updated location, the red panda’s location is updated using Eq. (31).

\begin{aligned} P_{i} = {\begin{cases} P_{i}^{L 1}; F_{O b j}^{i, L 1} < F_{O b j}^{i} \\ P_{i}; e l s e \end{cases} \end{aligned}

(31)

In Eq. (27), Eqs (28) and (31), $P_{i}^{L 1}$ represent the updated location of the $i$ th red panda on the basis of the exploration phase of the RePLO algorithm, $F_{O b j}^{i, L 1}$ indicates the objective function value associated with this updated location, ${a r b}_{i, j}$ is an arbitrarily generated number within the range [0,1], $p_{i, j}^{L 1}$ denotes the $j$ th dimension of this updated location, ${S F S}_{i}$ represents the selected food source for the $i$ th red panda, with ${S F S}_{i, j}$ representing its $i$ th dimension, and $β$ is a random selection from the set {1,2}.

3.6.3. Proposed exploitation phase: Tree climbing and resting behavior of red pandas

The second phase of the RePLO algorithm intricately ties the localization of red pandas to their skill in climbing trees and finding resting spots within them. Red pandas naturally prefer spending a significant portion of their time resting atop trees, seamlessly transitioning to adjacent trees after ground foraging activities. This behavior, marked by movements towards trees and subsequent climbing, triggers subtle modifications in the locations of red pandas, enhancing the RePLO algorithm’s ability for exploitation and local search within promising regions.

However, the conventional RPO algorithm often gets stuck in local optima, hindering effective exploration of globally optimal solutions. To overcome this drawback, the RePLO algorithm introduces an ABP mechanism [42], emulating the innate tree-climbing behavior of red pandas. Integrated into the exploitation phase, the ABP governs the calculation of updatedlocations for each red panda which is determined in Eq. (33). This method of computing updatedlocations for each red panda allows the RePLO algorithm to achieve accelerated exploration during the early optimization stages and thorough exploration of promising solutions. The ABP equation is delineated in Eq. (32) where the current iteration and the maximum number of iterations are indicated as It and $M_{I t}$ .

\begin{aligned} A B P = 1 - (1.01 * \frac{{I t}^{3}}{M^{{I t}^{3}}}) \end{aligned}

(32)

\begin{aligned} \begin{array}{l} i f A B P > r a n d \\ C a l c u l a t a n u p d a t e d p o s i t i o n o f i t h R e P L O m e m b e r u s i n g \\ p_{i, j}^{L 2} = p_{i, j} + \frac{B_{j}^{L} + a r b_{i . j} . (B_{j}^{U} - B_{j}^{L})}{I t}, I t = 1, 2, 3, \dots, M_{I t} . \\ e l s e \\ C a l c u l a t a n u p d a t e d p o s i t i o n o f i t h R e P L O m e m b e r u s i n g \\ p_{i, j}^{L 2} = p_{i, j} + (1 - 2 {a r b}_{i . j}) . (\frac{B_{j}^{U} - B_{j}^{L}}{I t}) . \\ e n d \end{array}} \end{aligned}

(33)

In Eq. (33), $P_{i}^{L 2}$ represents the updated location of the $i$ th red panda on the basis of the exploitation phase of the RePLO algorithm, $F_{O b j}^{i, L 2}$ indicates the objective function value associated with this updated location, ${a r b}_{i, j}$ is a arbitrarily generated number within the range [0,1], and $p_{i, j}^{L 2}$ denotes the $j$ th dimension of this updated location.

When recalculating the locations of red pandas, if an enhancement in the objective function’s value is detected, the updated location replaces the previous one using Eq. (34). This iterative refinement process enables the algorithm to converge towards optimal solutions more effectively.

\begin{aligned} P_{i} = {\begin{cases} P_{i}^{L 2}; F_{O b j}^{i, L 2} < F_{O b j}^{i} \\ P_{i}; e l s e \end{cases} \end{aligned}

(34)

By leveraging the power of the hybrid optimization technique, RePLO seeks to enhance network performance, reliability, and security in dynamic and challenging MANET environments by optimizing CH selection and routing.

4. Results and discussion

4.1. Simulation procedure

The proposed optimization-based MANET routing model was implemented through simulation using Python. Specifically, the Python version employed was “Python 3.7”. Additionally, the simulation utilized a processor with an “11th Gen Intel(R) Core(TM) i5-1135G7 running at 2.40 GHz (with a maximum speed of 2.42 GHz),” while the system had an installed RAM size of “16.0 GB”.

4.2. Performance analysis

Figure 5.

Network setup a) 100 nodes and b) 200 nodes.

A comprehensive analysis was conducted to compare the performance of the RePLO mode with conventional approaches. This in-depth evaluation encompassed a wide array of essential metrics, including Delay, Residual Energy, Security, Distance, Link Quality, and Trust. Moreover, both Convergence Analysis and Statistical Analysis were performed. Furthermore, the effectiveness of the RePLO scheme was not only compared against traditional methods such as LOA [39], RPO [38], GWO [43], BSA [44], and RHO [45] but also against state-of-the-art techniques like GAHC [27] and HPSO [31]. Additionally, the network setup for nodes 100 and 200 is illustrated in Fig. 5.

4.3. Delay analysis

Figure 6.

Delay analysis on RePLO and conventional methods a) 100 nodes and b) 200 nodes.

In the realm of MANETs, efficient RPs are crucial for seamless communication among nodes. In this context, the evaluation of delay performance is paramount for optimizing routing strategies. In the quest for enhanced performance, the RePLO approach is compared with various optimization techniques, including the LOA, RPO, GWO, BSA, RHO, GAHC [27] and HPSO [31]. Figure 6(a) and 6(b) depicts a comparative analysis of these techniques under node configurations of 100 and 200, shedding light on their efficacy in minimizing delay. Particularly, attention is drawn towards the pivotal role of optimal cluster head selection in achieving minimized delay ratings, highlighting the significance of this aspect in MANET routing optimization. In the comparative analysis conducted for round 2000, the delay performance of the RePLO optimization-based MANET routing strategy is examined alongside existing algorithms. Figure 6(a) depicts the exposure of delay analysis under the scenario with 100 nodes. For the RePLO algorithm, the obtained minimized delay value is 1.839 $\times$ e^{- 7}. Meanwhile, LOA demonstrates delay performance at 3.816 $\times$ e^{- 7}, RPO at 3.675 $\times$ e^{- 7}, GWO at 4.293 $\times$ e^{- 7}, BSA at 4.089 $\times$ e^{- 7}, RHO at 3.518 $\times$ e^{- 7}, GAHC [27] at 3.271 $\times$ e^{- 7}, and HPSO [31]at 4.136 $\times$ e^{- 7}, respectively. This comprehensive comparison aims to assess the effectiveness of each algorithm in minimizing delays, with a particular focus on optimal cluster head selection within MANET routing. The results highlight the potential advantages of the RePLO approach over conventional methods in achieving lower delay ratings.

4.4. Distance analysis

Figure 7.

Distance analysis on RePLO and conventional methods a) 100 nodes and b) 200 nodes.

The evaluation of optimization-based MANET routing strategies involves a critical examination of distance assessments between RePLO and conventional approaches across varying node densities. As depicted in Fig. 7(a) and 7(b), the distance analysis spans scenarios with 100 and 200 nodes, illustrating the comparative performance of different routing strategies. Effective cluster head selection relies heavily on minimizing distance ratings to ensure efficient network operation and resource utilization. In the evaluation of distance ratings for MANET routing strategies across 200 nodes at 2000 rounds, a notable discrepancy emerges between RePLO and conventional methodologies. Notably, the RePLO approach showcases the most promising performance, yielding an average distance rating of 42.895 m. This signifies its efficiency in establishing shorter routing paths within the network. In contrast, conventional routing approaches like LOA, RPO, GWO, BSA, RHO, GAHC [27], and HPSO [31] exhibit notably higher average distance ratings: around 67.951 m, 65.686 m, 85.902 m, 86.571 m, 68.731 m, 62.079 m and 64.851 m, respectively. This stark contrast underscores the superiority of optimization-based routing strategies in enhancing the efficiency and reliability of MANET communication. Thus, in the pursuit of optimal MANET performance, the adoption of the RePLO strategy holds considerable promise for improving overall network efficiency and effectiveness.

4.5. Residual energy analysis

Figure 8.

Residual Energy analysis on RePLO and conventional methods a) 100 nodes and b) 200 nodes.

In the domain of optimization-based MANET routing, the analysis of residual energy holds significant importance as it directly impacts the longevity and efficiency of the network. Figure 8(a) and 8(b) provide a detailed exploration of the residual energy dynamics, comparing the performance of a RePLO scheme against conventional strategies. Initially, both the RePLO and conventional strategies exhibit higher residual energy levels. However, as rounds progress, a noticeable decrease in residual energy is observed across all strategies. Remarkably, the RePLO approach consistently maintains maximal residual energy ratings throughout the entire duration, showcasing its potential for sustaining network longevity and robustness. Notably, the RePLO scheme showcases superior residual energy levels, approximately 0.287J for 100 nodes and 0.271J for 200 nodes, indicating more efficient energy utilization compared to conventional models such as LOA, RPO, GWO, BSA, RHO, GAHC [27], and HPSO [31]. In contrast, the conventional strategies exhibit lower residual energy levels ranging between 0.213J to 0.268J for both node configurations. This discrepancy highlights the efficacy of the RePLO scheme in preserving energy resources throughout various rounds of network operation. Overall, the findings emphasize the significance of the RePLO approach in enhancing the efficiency and reliability of MANETs by prioritizing energy conservation and sustainability.

4.6. Link quality analysis

Figure 9.

Link Quality analysis on RePLO and conventional methods a) 100 nodes and b) 200 nodes.

In exploring the efficacy of optimization-based MANET routing strategies, a crucial aspect lies in the analysis of link quality, often quantified through PDR. Figure 9(a) and 9(b) present a comprehensive comparison between the PDR of a RePLO approach and conventional methodologies, including LOA, RPO, GWO, BSA, RHO, GAHC [27], and HPSO [31], across networks of 100 and 200 nodes. The fundamental objective of this analysis is to maximize link quality, as reflected by PDR, to ensure the effective performance of the routing model. In examining the link quality for MANET routing strategies at around 1500 across 200 nodes, the RePLO model stands out with an impressive link quality of 0.685. This exceeds the performance of conventional strategies, which exhibit link quality values as follows: LOA with 0.526, RPO with 0.439, GWO with 0.441, BSA with 0.589, RHO 0.468, GAHC [27] 0.468 and HPSO [31] 0.475, respectively. Such discrepancies underline the superiority of the RePLO approach in maximizing link quality, essential for ensuring reliable and efficient communication within MANETs. By consistently achieving higher PDR levels, the RePLO model demonstrates its capacity to facilitate seamless data transmission even in dynamic and resource-constrained environments.

4.7. Security analysis

Figure 10.

Security analysis on RePLO and conventional methods a) 100 nodes and b) 200 nodes.

The assessment of security is paramount in optimizing MANET routing strategies. Figure 10(a) and 10(b) depicts a comprehensive analysis comparing the security of both RePLO and conventional methods in MANET routing optimization. This evaluation aims to ascertain the robustness of each approach in safeguarding data transmission and network integrity. The security ratings must be higher for effective MANET routing, ensuring resilience against potential security threats and unauthorized access. In the comparative analysis conducted for round 500 with 100 nodes, the security performance of the RePLO optimization-based MANET routing method is contrasted with conventional approaches, including LOA, RPO, GWO, BSA, RHO, GAHC [27], and HPSO [31]. Figure 10(a) illustrates the security analysis, showcasing the security ratings obtained by each method. Notably, the RePLO method emerged with the highest security value of 0.889, signifying its robustness against potential security threats and vulnerabilities. Conversely, the conventional methods demonstrated minimized security ratings, indicating potential weaknesses in their security measures and protocols. LOA achieved a security rating of 0.795, RPO scored 0.783, GWO obtained 0.788, BSA yielded 0.792, and RHO achieved 0.681, while both GAHC [27] and HPSO [31] scored 0.715 and 0.694.

4.8. Trust analysis

Figure 11.

Trust analysis on RePLO and conventional methods a) 100 nodes and b) 200 nodes.

The assessment of trustworthiness plays a crucial role in optimizing MANET routing strategies. Figure 11(a) and 11(b) provide a detailed comparison of trust evaluation between the RePLO scheme and traditional strategies in MANET routing optimization. The primary objective is to maximize trust ratings, ensuring reliable and secure communication among network nodes. Evaluating trust is essential for mitigating security risks and fostering collaboration within the network. In the assessment of trust ratings for optimization-based MANET routing strategies at around 1000 in node 200. Particularly, the RePLO scheme demonstrates a superior trust rating of 0.897, emphasizing its effectiveness in fostering trust within the network. In contrast, traditional strategies exhibit comparatively lower trust ratings, ranging between 0.789 to 0.596. This discrepancy highlights the efficacy of the RePLO scheme in instilling higher levels of trust among network nodes, essential for ensuring dependable and secure communication within MANETs.

4.9. Convergence analysis

Figure 12.

Convergence analysis on RePLO and conventional methods a) 100 nodes and b) 200 nodes.

The convergence analysis of optimization-based MANET routing methods is crucial for understanding their efficiency and effectiveness over successive iterations. Figire 12(a) and 12(b) provide a comprehensive comparison of convergence across nodes 100 and 200, highlighting the performance of the RePLO approach and conventional methods, including LOA, RPO, GWO, BSA, RHO, GAHC [27], and HPSO [31]. As illustrated in the figures, both the RePLO and conventional strategies initially displayed higher cost ratings in the initial iterations. However, as the iterations progressed, there was a noticeable decrease in the cost rates across all methods. Remarkably, the RePLO scheme consistently exhibited the lowest cost ratings compared to conventional methods, indicating its superior convergence and efficiency in achieving optimal routing solutions. In a focused examination of iteration 25, the comparative analysis highlights a significant disparity in cost ratings between the RePLO approach and traditional methods in optimization-based MANET routing. Impressively, the RePLO scheme achieved the lowest cost rate of 0.297, underscoring its efficiency in resource utilization and convergence. Conversely, traditional methods including LOA, RPO, GWO, BSA, RHO, GAHC [27], and HPSO [31] recorded maximized cost ratings, indicative of higher resource expenditure and potentially slower convergence.

4.10. Statistical analysis of fitness

Table 3
Statistical analysis of fitness for node 100.

Methods Median Minimum Mean Standard deviation Maximum

LOA 0.305 0.301 0.307 0.006 0.318

RPO 0.305 0.303 0.310 0.008 0.321

GWO 0.300 0.300 0.307 0.008 0.318

BSA 0.304 0.302 0.309 0.007 0.318

RHO 0.302 0.302 0.306 0.008 0.323

GAHC [27] 0.300 0.300 0.307 0.010 0.323

HPSO [31] 0.301 0.301 0.305 0.007 0.318

RePLO 0.297 0.297 0.304 0.010 0.322

Methods	Median	Minimum	Mean	Standard deviation	Maximum
LOA	0.305	0.301	0.307	0.006	0.318
RPO	0.305	0.303	0.310	0.008	0.321
GWO	0.300	0.300	0.307	0.008	0.318
BSA	0.304	0.302	0.309	0.007	0.318
RHO	0.302	0.302	0.306	0.008	0.323
GAHC [27]	0.300	0.300	0.307	0.010	0.323
HPSO [31]	0.301	0.301	0.305	0.007	0.318
RePLO	0.297	0.297	0.304	0.010	0.322

Table 4

Statistical analysis on fitness for node 200.

Methods	Median	Minimum	Mean	Standard deviation	Maximum
LOA	0.300	0.300	0.307	0.009	0.318
RPO	0.301	0.301	0.308	0.008	0.318
GWO	0.308	0.304	0.311	0.006	0.321
BSA	0.302	0.301	0.307	0.010	0.326
RHO	0.304	0.303	0.308	0.007	0.318
GAHC [27]	0.305	0.301	0.308	0.008	0.326
HPSO [31]	0.301	0.301	0.305	0.007	0.319
RePLO	0.299	0.299	0.304	0.010	0.325

In the evaluation of optimization-based MANET routing strategies, statistical analysis serves as a crucial tool for comparing the efficacy of different methods. Tables 3 and 4 provide a comprehensive examination of fitness function performance across nodes 100 and 200, contrasting a RePLO scheme with conventional methods including LOA, RPO, GWO, BSA, RHO, GAHC [27], and HPSO [31]. In terms of the minimum statistical metric for fitness at node 100, the LOA, RPO, and HPSO [31] share the highest fitness value of 0.301, followed closely by RHO and GAHC [27] with a fitness of 0.302. Meanwhile, GWO demonstrates the lowest fitness among the conventional methods at 0.300, followed by BSA at 0.302. In contrast, the RePLO method achieved a notably lower fitness value of 0.297. This discrepancy suggests that the RePLO approach may offer a potential advantage in optimizing MANET routing efficiency by achieving lower fitness metrics compared to conventional methods. For node 200, the mean statistical metric provides valuable insights into the average fitness performance of each optimization-based MANET routing method. Among the conventional models, GWO demonstrates the highest fitness value of 0.311, indicating relatively better overall fitness performance compared to other traditional methods. On the other hand, the RePLO method exhibits a mean value of 0.304, showcasing competitive performance but slightly lower than GWO.

5. Conclusion

This research introduced a secure routing method for MANETs utilizing the RePLO hybrid optimization algorithm, amalgamating RPO and LOA techniques. The structured framework encompassed five key stages: system model configuration, energy model development, mobility model establishment, cluster head selection via the RePLO algorithm, and routing implementation using RePLO. RePLO played a pivotal role in optimizing CH selection and routing while considering specific constraints such as delay, distance, energy, and security for CH selection, and link quality and enhanced trust for routing. The evaluation involved assessing various metrics, showcasing the efficacy of this approach in MANET routing. This research culminated in the development and validation of a comprehensive and systematic approach for secure and efficient MANET routing, promising enhanced network performance and reliability in dynamic and decentralized environments. For the RePLO algorithm, the obtained minimized delay value is 1.839 $\times$ e^{- 7}. Meanwhile, LOA demonstrates delay performance at 3.816 $\times$ e^{- 7}, RPO at 3.675 $\times$ e^{- 7}, GWO at 4.293 $\times$ e^{- 7}, BSA at 4.089 $\times$ e^{- 7}, RHO at 3.518 $\times$ e^{- 7}, GAHC [27] at 3.271 $\times$ e^{- 7}, and HPSO [31] at 4.136 $\times$ e^{- 7}, respectively. MANETs are widely employed in military operations when communication and quick deployment in dangerous and changing areas are essential. Ad hoc networks can be formed by nodes, such as drones, cars, and soldiers, to exchange real-time data, plan maneuvers, and stay aware of their surroundings. Wireless sensor networks (WSNs) use MANETs to provide ad hoc communication between sensor nodes for the purpose of gathering and transmitting environmental data. Monitoring of the environment, habitats, agriculture, and industry are some examples of applications.

Footnotes

Nomenclature

References

Sarhan

. Elephant herding optimization Ad Hoc on-demand multipath distance vector routing protocol for MANET. IEEE Access. 2021; 9: 39489-99.

Saxena

Dinesh

David

Tiwari

Monisha

Chauhan

. Addressing the distinct security vulnerabilities typically emerge on the mobile ad-hoc network layer. NeuroQuantology. 2023; 21(3): 169.

Poria

Sangwan

Duhan

Dalal

. Analyzing the effects of shadowing and fading on the performance of Ad Hoc routing protocols in Manet.

Dahiya

Sangwan

Duhan

Dalal

. OLSR v2 Implementation and Performance Evaluation over OLSRv1 in MANET using QualNet 61. Int J Sci Eng Res. 2013; 4: 2458-63.

Lakshmi

Vaishnavi

. A trusted security approach to detect and isolate routing attacks in mobile ad hoc networks. Journal of Engineering Research. 2023.

Hrabcak

Dobos

Papaj

Ovsenik

. Multilayered network model for mobile network infrastructure disruption. Sensors. 2020; 20(19): 5491.

Manivannan

Moni

Zeadally

. Secure authentication and privacy-preserving techniques in Vehicular Ad-hoc NETworks (VANETs). Vehicular Communications. 2020; 25: 100247.

Liu

Cheng

Jia

Liu

. Deep reinforcement learning for communication flow control in wireless mesh networks. IEEE Network. 2021; 35(2): 112-9.

Niu

Shan

Yang

. Identification of critical nodes for enhanced network defense in MANET-IoT networks. IEEE Access. 2020; 8: 183571-82.

10.

Yang

Sun

Chen

Meng

Ying

. Dispersed computing for tactical edge in future wars: vision, architecture, and challenges. Wireless Communications and Mobile Computing. 2021; 2021(1): 8899186.

11.

Priyambodo

Wijayanto

Gitakarma

. Performance optimization of MANET networks through routing protocol analysis. Computers. 2020; 10(1): 2.

12.

Nirmaladevi

Prabha

. A selfish node trust aware with Optimized Clustering for reliable routing protocol in Manet. Measurement: Sensors. 2023; 26: 100680.

13.

Hasan

Mishra

Ray

. Fuzzy logic based cross-layer design to improve Quality of Service in Mobile ad-hoc networks for Next-gen Cyber Physical System. Engineering Science and Technology, an International Journal. 2022; 35: 101099.

14.

Veeraiah

Khalaf

Prasad

Alotaibi

Alsufyani

Alghamdi

Alsufyani

. Trust aware secure energy efficient hybrid protocol for manet. IEEe Access. 2021; 9: 120996-1005.

15.

Prasad

. Enhanced energy efficient secure routing protocol for mobile ad-hoc network. Global Transitions Proceedings. 2022; 3(2): 412-23.

16.

Jayalakshmi

Hemanand

Kumar

Rani

. An efficient route failure detection mechanism with energy efficient routing (Eer) protocol in manet. International Journal of Computer Network and Information Security. 2021; 13(2).

17.

Chen

Zhou

Cheng

. An adaptive on-demand multipath routing protocol with QoS support for high-speed MANET. IEEE Access. 2020; 8: 44760-73.

18.

Gopalan

Vignesh

Rajkumar

Velmurugan

Deepa

Dhanapal

. Fuzzified swarm intelligence framework using FPSOR algorithm for high-speed MANET-Internet of Things (IoT). Measurement: Sensors. 2024; 31: 101000.

19.

Tahboush

Agoyi

. A hybrid wormhole attack detection in mobile ad-hoc network (MANET). IEEE Access. 2021; 9: 11872-83.

20.

Reddy

Dhananjaya

. The AODV routing protocol with built-in security to counter blackhole attack in MANET. Materials Today: Proceedings. 2022; 50: 1152-8.

21.

Al-Shareeda

Manickam

. Man-in-the-middle attacks in mobile ad hoc networks (MANETs): Analysis and evaluation. Symmetry. 2022; 14(8): 1543.

22.

Narayana

Gopi

Anveshini

Lakshmi

. Enhanced path finding process and reduction of packet droppings in mobile ad-hoc networks. International Journal of Wireless and Mobile Computing. 2020; 18(4): 391-7.

23.

Devi

Das

Murthy

. Secure cross-layer routing protocol with authentication key management scheme for manets. Measurement: Sensors. 2023; 29: 100869.

24.

Bhatia

Kumar

Jain

Kumar

Verma

Illes

Aschilean

Raboaca

. Networked control system with MANET communication and AODV routing. Heliyon. 2022; 8(11).

25.

Subha

Anandakumar

. Adaptive fuzzy logic inspired path longevity factor-based forecasting model reliable routing in MANETs. Sensors International. 2022; 3: 100201.

26.

Farheen

Jain

. Improved routing in MANET with optimized multi path routing fine tuned with hybrid modeling. Journal of King Saud University-Computer and Information Sciences. 2022; 34(6): 2443-50.

27.

Srilakshmi

Veeraiah

Alotaibi

Alghamdi

Khalaf

Subbayamma

. An improved hybrid secure multipath routing protocol for MANET. IEEE Access. 2021; 9: 163043-53.

28.

Pattnaik

Panda

Sain

. Design of novel mobility and obstacle-aware algorithm for optimal MANET routing. IEEE Access. 2021; 9: 110648-57.

29.

Tian

Wang

. An active-routing authentication scheme in MANET. IEEE Access. 2021; 9: 34276-86.

30.

Rajeshkumar

Kumar

Bhatia

Mashat

Dadheech

. An Improved Multi-Objective Particle Swarm Optimization Routing on MANET. Computer Systems Science and Engineering. 2023; 44(2).

31.

Orchu

Sameerunnisa

Ramachandran

, Routing in mobile ad Hoc networks using machine learning techniques. 2024.

32.

Devika

Sudha

. Power optimization in MANET using topology management. Engineering Science and Technology, an International Journal. 2020; 23(3): 565-75.

33.

Upadhyay

Kumar

. Effect of Mobility on Energy Consumption in MANET Routing Protocols: A Review Study. IRACST-International Journal of Computer Networks and Wireless Communications (IJCNWC), ISSN.:2250-3501.

34.

Yadav

Tripathi

. QMRPRNS: Design of QoS multicast routing protocol using reliable node selection scheme for MANETs. Peer-to-Peer Networking and Applications. 2017; 10: 897-909.

35.

Tandon

Srivastava

. Trust-based enhanced secure routing against rank and sybil attacks in IoT. In 2019 twelfth international conference on contemporary computing (IC3). 2019; 1-7. IEEE.

36.

Sirajuddin

Rupa

Iwendi

Biamba

. TBSMR: A Trust-Based Secure Multipath Routing Protocol for Enhancing the QoS of the Mobile Ad Hoc Network. Security and Communication Networks. 2021; 2021(1): 5521713.

37.

Loret

Kumar

. An Improved Trust Based Energy Efficient Routing Protocol for Wireless Sensor Networks. Journal of Internet Technology. 2021; 22(7): 1509-16.

38.

Givi

, Dehghani

, Hubálovský

. Red panda optimization algorithm: An effective bio-inspired metaheuristic algorithm for solving engineering optimization problems. IEEE Access. 2023; 11: 57203-27.

39.

Dehghani

Bektemyssova

Montazeri

Shaikemelev

Malik

Dhiman

. Lyrebird optimization algorithm: a new bio-inspired metaheuristic algorithm for solving optimization problems. Biomimetics. 2023; 8(6): 507.

40.

Abd Elaziz

Ewees

Ibrahim

. Opposition-based moth-flame optimization improved by differential evolution for feature selection. Mathematics and Computers in Simulation. 2020; 168: 48-75.

41.

Iacca

dos Santos Junior

de Melo

. An improved Jaya optimization algorithm with Lévy flight. Expert Systems with Applications. 2021; 165: 113902.

42.

Cai

Chen

Huang

. Improving monarch butterfly optimization algorithm with self-adaptive population. Algorithms. 2018; 11(5): 71.

43.

Mirjalili

Lewis

. Grey wolf optimizer. Advances in Engineering Software. 2014; 69: 46-61.

44.

Meng

Gao

Liu

Zhang

. A new bio-inspired optimisation algorithm: Bird Swarm Algorithm. Journal of Experimental and Theoretical Artificial Intelligence. 2016; 28(4): 673-87.

45.

Wang

Gao

Zenger

Coelho

. A novel metaheuristic algorithm inspired by rhino herd behavior. InEUROSIM Congress on Modelling and Simulation and SIMS Conference on Simulation and Modelling. 2018; 1026-1033. Linköping University Electronic Press.

46.

Alotaibi

. Geographic routing in mobile ad hoc networks (MANET) using hybrid optimization model: a multi-objective perspective. Applied Intelligence. 2023; 53(9): 11214-28.

47.

Ramasamy

Ramalingam

Chitraivel

. Energy efficient secured-quality of service routing protocol for mobile ad hoc network using multi-objective optimization. Indonesian Journal of Electrical Engineering and Computer Science. 2023; 31(3): 1486-95.

Hybrid optimization-based secured routing in mobile ad-hoc network

Abstract

Keywords

1. Introduction

3. Outline of RePLO-based routing for MANETs

Table 2 Simulation parameters. Field area 100 × 100 m2 Number of mobile nodes 100 The probability of a node becoming CH 0.1 Mobility model Random manner Mobility of a node (10–20) m/s Packet size 4000 bits

3.3. Development of the mobility model

3.6.1. Population initialization

4.1. Simulation procedure

4.2. Performance analysis

Footnotes

Nomenclature

References

Table 2
Simulation parameters.

Field area 100 $\times$ 100 m²

Number of mobile nodes 100

The probability of a node becoming CH 0.1

Mobility model Random manner

Mobility of a node (10–20) m/s

Packet size 4000 bits