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168-179 

168 

 

 

 

Article 

Trust and adaptiveness enhancements to PRFDRA 

for secure metaheuristic path selection in MANETs 
Augustina Dede Agor1*, Lawrence Kwami Aziale1, Frank Kataka Banaseka1,  

Kwabena Owusu-Agyemang2, Selasie Aformaley Brown1, Benjamin Tei Partey2 

1Department of Information Technology Studies, University of Professional Studies, P. O. Box LG 149, Accra, Ghana 
2Department of Computer Science, Kwame Nkrumah University of Science and Technology, Private Mail Bag, University 

Post Office, Kumasi, Ghana 

A R T I C L E   I N F O 
 

Article history: 
Received 10 August 2025  
Received in revised form 
15 October 2025 
Accepted 18 November 2025 
 
Keywords:  
Security, Trust, Adaptive, SFD-MFD Switching, 
PRFDRA, MANETs 
 
*Corresponding author 
Email address: 
augustinadede.agor@upsamail.edu.gh 
 
DOI: 10.55670/fpll.futech.5.1.15 

A B S T R A C T 
 

In Mobile Ad Hoc Networks (MANETs), the Power-Aware River Formation 
Dynamics Routing Algorithm (PRFDRA) enhanced energy efficiency by forming 
power-aware paths and facilitating multi-flow diffusion. It remained vulnerable 
to internal misbehavior. RFDTrust added trust metrics to mitigate malicious 
activity, but applied them only in neighbor selection along downhill gradients. 
This limited path diversity and adaptiveness. This paper proposes TA-PRFDRA 
(Trust-Adaptive-Power-Aware River Formation Dynamics Routing Algorithm), 
a trust- and adaptiveness-enhanced version of PRFDRA. TA-PRFDRA integrates 
trust evaluation into all routing stages. It applies dynamic switching between 
Single Flow Direction (SFD) and Multi-Flow Direction (MFD) based on trust-
weighted gradient variance. The algorithm utilizes a composite trust model that 
takes into account node energy reliability, packet forwarding behavior, route 
participation, and delay consistency. Trust is applied in gradient, erosion, 
altitude, sediment transport, and path cost computations. Simulation results 
show that, compared with PRFDRA, RFDTrust, RFDManet, and TORA, TA-
PRFDRA achieved up to 1.33% higher packet delivery ratio (PDR). Average end-
to-end delay (AE2ED) decreased by 0.14 s. Detection rate (DR) increased by up 
to 30.38%. Energy consumption (EC) was reduced by up to 15.94 J. Statistical 
analysis confirmed that improvements over RFDTrust were significant. These 
results demonstrate that integrating trust into all routing processes with 
adaptive flow control enhances reliability, latency performance, security, and 
energy efficiency in MANETs. 

1. Introduction 

Mobile Ad Hoc Networks (MANETs) are decentralized, 
self-organizing networks in which mobile nodes 
communicate over wireless links without relying on fixed 
infrastructure [1]. Their dynamic topologies, limited energy 
resources, and vulnerability to internal attacks make secure 
and efficient routing a significant challenge [2]. MANETs are 
increasingly deployed in mission-critical applications such as 
disaster recovery, military coordination, and vehicular 
networks. These scenarios require routing protocols that 
maintain reliability and efficiency in high-mobility 
environments, as well as in the presence of potential insider 
threats. Nature-inspired metaheuristic algorithms have been 
explored for routing in decentralized networks. Models such 
as Ant Colony Optimization (ACO) [3], Intelligent Water Drops 
(IWD) [4], and River Formation Dynamics (RFD) [5] simulate 
natural processes to guide path selection. While these 
metaheuristics are adaptive in principle, most MANET 

implementations remain static or only partially adaptive. RFD 
models the flow of rivers, where paths evolve through erosion 
and sedimentation. Its distributed design provides a 
foundation for energy-efficient routing strategies. Agor et al. 
[1] introduced the Power-Aware River Formation Dynamics 
Routing Algorithm (PRFDRA) for MANETs. PRFDRA extends 
RFD by incorporating energy-aware and performance-based 
parameters across its routing mechanisms. Node-selection 
probabilities are computed for all neighbors, including those 
with positive, negative, and flat gradients, to enable 
probabilistic multi-flow diffusion. This design increases path 
diversity compared with single-flow RFDTrust. However, it 
does not incorporate trust or behavioral integrity metrics, 
which leaves it vulnerable to malicious nodes. RFDTrust [6] 
uses trust to guide neighbor selection via decreasing-gradient 
metrics. While this improves security, trust is not embedded 
in all RFD mechanisms. Packets follow a primarily downhill 
path, ensuring loop-free routing but limiting path diversity. 

 

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February 2026| Volume 05 | Issue 01 | Pages 168-179 

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AD. Agor et al. /Future Technology                                                                                   February 2026| Volume 05 | Issue 01 | Pages 168-179 

169 

 

This restricts adaptiveness in flat or deceptive topologies and 
reduces resilience under collusive attacks. To address these 
limitations, this study proposes the Trust-Adaptive-Power-
Aware River Formation Dynamics Routing Algorithm (TA-
PRFDRA). TA-PRFDRA integrates trust evaluation into all 
PRFDRA stages, including gradient computation, erosion 
assignment, altitude adjustment, sediment dynamics, and 
path cost calculation. A composite trust score is computed 
using packet forwarding ratio, energy reputation, route 
participation frequency, and routing metric consistency. 
High-trust nodes are favored, while untrusted nodes are 
penalized throughout the routing process. 

TA-PRFDRA also introduces adaptive switching between 
Single Flow Direction (SFD) and Multiple Flow Direction 
(MFD) modes. Switching is based on trust-weighted gradient 
variance. This allows the protocol to respond dynamically to 
local network conditions, distribute load across multiple 
paths, and improve resilience against congestion and route 
manipulation. Embedding trust in all routing stages while 
enabling adaptive flow control enhances security, reliability, 
and energy efficiency in MANETs. Accordingly, this study is 
guided by the following objectives: 
• Integrate trust metrics into all PRFDRA routing processes, 

including gradient, erosion, altitude, sediment transport, 
and path cost, to favor reliable nodes and penalize 
untrusted nodes. 

• Enhance path selection adaptiveness through dynamic SFD 
and MFD switching based on trust-weighted gradient 
variance to ensure responsiveness under varying network 
conditions. 

The remainder of the manuscript is structured as follows: 
Section 1.1 gives the problem statement. Section 1.2 discusses 
the security of MANETs, while Section 2 provides a literature 
review. Section 3 describes the methodology, while Section 4 
gives the results. Finally, Section 5 concludes the study. 

1.1 Problem statement 
Routing in MANETs is challenged by frequent topology 

changes, limited node energy, and internal misbehaviour [7]. 
PRFDRA improves energy-aware routing but assumes all 
nodes behave cooperatively, exposing routes to malicious 
disruptions. RFDTrust introduces trust evaluation to address 
this issue, but restricts forwarding choices, reducing path 
diversity and adaptability under flat or colluding topologies. 
Other existing RFD-based approaches do not combine trust 
evaluation with all routing processes. They also lack adaptive 
flow control using SFD and MFD switching [6]. These gaps 
result in an insecure and inefficient path, underscoring the 
need for a unified, trust-adaptive, and energy-efficient routing 
framework in MANETs. 

1.2 MANETs security 
Security attacks in MANETs are classified into two types: 

external and internal, as shown in Figure 1. External attacks 
are further classified into two types: attacks based on the 
attackers' actions and attacks based on operational 
ideologies. The one based on attackers' actions is also 
classified into three main groups: passive, active, and 
collaborative attacks. Active attacks can take various forms, 
including modification, dropping, timing, and fabrication. 
Attacks can also be classified based on the layered protocol 
stack. Figure 2 lists the major kinds of attacks that affect the 
various layers. Not all enumerated MANET security attacks 
have been included in the classification diagrams, as only 
representative, structurally distinct attack vectors were 
illustrated to optimize taxonomic clarity. 

 
Figure 1. External and internal attacks 

 

 
Figure 2. Attacks at the various layers 

1.3 Security schemes 
As shown in Figure 3, several approaches can be used to 

detect or prevent security attacks in MANETs. These include 
game theory, cryptographic systems, reputation mechanisms, 
credit-based schemes, secure multicasting, secure routing, 
privacy-aware and position-based routing, key management, 
intrusion detection systems, artificial intelligence, 
metaheuristic optimization, trust models, blockchain, formal 
protocol verification, incentive-based frameworks, and 
physical security. These schemes may operate individually, 
synergistically, or in combined configurations. 
Artificial intelligence: Artificial intelligence introduces 
techniques that enable networks to make intelligent 
decisions, defend nodes, and address protocol-related 
challenges. It aims to transform nodes into autonomous 



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decision-makers. The main branches used in MANET security 
include machine learning, neural networks, deep learning, 
and fuzzy logic [8]. 
Blockchain approach: This approach uses decentralized 
consensus mechanisms, cryptographic techniques, and 
immutable data storage. It helps maintain the integrity of 
network operations, prevents data tampering or 
unauthorized access, and supports transparent and auditable 
interactions among network participants. 
Credit approach: Credit-based schemes, such as the packet 
purse and packet trade models, distribute credit inside 
packets as they move through intermediate nodes. In the 
packet-purse model, credit decreases at each hop until the 
packet reaches its destination. In the packet trade model, 
intermediate nodes “trade” packets by buying and selling 
them, which incentivizes cooperation. 
Cryptography approach: Cryptographic systems encode 
information into unintelligible forms to prevent unauthorized 
access. Decryption requires a valid key. Encryption may be 
symmetric, using one shared key, or asymmetric, using 
different keys for the sender and the receiver [9]. 
Formal methods for protocol verification: This approach 
applies formal methods and model-checking techniques to 
verify security properties and correctness in MANET 
protocols. It ensures protocol robustness, resistance to 
attacks, and adherence to security specifications. 
Game theory approach: Game theory contributes 
significantly to MANET security by offering computational 
efficiency and probabilistic analysis of strategic interactions. 
It includes cooperative models, where players follow binding 
agreements, and non-cooperative models, where participants 
may alter strategies independently [9]. 
Incentive approach: Incentive-based strategies encourage 
cooperative node behaviour and discourage selfish or 
malicious actions. 
Intrusion Detection System (IDS) approach: An IDS 
monitors system activities, detects intrusions, and responds 
to breaches. IDS designs include anomaly-based, misuse-
based, and signature-based detection systems, each with its 
unique strengths and limitations [10]. 
Key management approach: Key management solutions, 
such as Certified Authority (CA) mechanisms, address node 
mobility challenges. They reduce control overhead and 
improve reliability in secure communication [11,12]. 
Metaheuristic optimization approach: Metaheuristic 
techniques improve MANET resilience by enhancing resource 
allocation, optimizing routing behaviour, and reducing 
vulnerabilities. This lowers the attack surface and increases 
robustness. 
Physical security: Physical security measures, such as 
tamper-resistant hardware, secure deployment, and node 
authentication, protect nodes from physical attacks. 
Privacy and position-based routing approach: This method 
secures communication by combining position broadcasting 
with privacy techniques. Approaches like PPBR use dynamic 
pseudo-identifiers to minimize route overhead and ensure 
end-to-end anonymity among nodes  [11]. 
Reputation approach: Reputation systems compute node 
reputation based on direct and indirect interactions. They 
help detect suspicious behaviour and guide routing decisions. 
Watchdog detects misbehaviour, while  Pathrater mitigates 
routing misbehaviour in MANETs [9]. 
Secure multicasting approach: Secure multicasting 
protects multicast traffic from DoS attacks using architectures 
such as DIPLOMA. It works with multicast routing protocols, 
allocates network resources fairly during attacks, and ensures 

both sender and receiver access to the multicast group while 
controlling bandwidth use. 
Secure routing approach: Secure routing mechanisms 
address authentication, prevent route fabrication, and 
improve protocol responsiveness. They aim to maintain 
network resilience against various routing attacks. 
Trust approach: Trust models address security challenges 
by assessing the trustworthiness of nodes. They help detect 
and mitigate malicious behaviour by evaluating factors such 
as reputation, behaviour history, and local or network-wide 
observations [13]. 

 

 
Figure 3. MANETs security schemes 

To provide a secure relationship between nodes, security 
schemes used in MANETs must provide the following 
services, as illustrated in Figure 4: authentication, 
authorization, availability, integrity, anonymity, non-
repudiation, and confidentiality [14]. 
• Authentication: Authentication ensures that only 

authorized nodes are involved in the exchange of 
information, preventing malicious nodes from 
impersonating trusted ones and disrupting communication 
within the network [15]. 

• Authorization: Authorization involves providing entities 
with credentials that detail their granted privileges and 
permissions, ensuring their authenticity and non-
repudiation by the certificate authority [16]. 

• Availability: A node consistently offers the services it’s 
intended for, with a significant focus on thwarting denial-
of-service attacks, while certain self-serving nodes render 
specific network services inaccessible [14]. 

• Integrity: Integrity ensures that message content can only 
be altered by authorized users, maintaining message 
integrity during transmission. Unauthorized actions, such 
as modifying messages, removing data streams, or 
unnecessary data replication, compromise integrity [14]. 

• Anonymity: Anonymity conceals any data that could 
identify present or owning client nodes, ensuring that such 
information remains private and is not disclosed by the 
network device/software or the node itself [17]. 

• Non-repudiation: Non-repudiation ensures that both the 
sender and receiver of a message cannot deny having 
transmitted or received the message, which is crucial for 



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determining whether a node within a network has been 
compromised or not [15]. 

• Confidentiality: Confidentiality guarantees authorization 
by limiting access to legitimate information to authorized 
users, thereby safeguarding data privacy [14]. 

 
Figure 4. MANETs security schemes 

2. Related work  

Early Research on secure and adaptive routing in 
MANETs has evolved across several methodological 
directions, each with specific strengths and limitations. For 
foundational trust-based routing without metaheuristics or 
adaptiveness, early approaches focused on evaluating node 
behavior through forwarding reliability and historical 
interactions. Sivaranjani et al. [18] proposed FLEATM, a fuzzy 
logic-based decision rule framework that updates trust 
ratings using direct observations and neighbor 
recommendations, but lacks adaptive routing and 
metaheuristic optimization. Sen [19] introduced a distributed 
trust-reputation framework that emphasizes malicious node 
detection while remaining non-adaptive and not energy-
aware. Govindaraj and Arumugam [20] enhanced AOMDV 
using a trust-based next-hop selection model to counter 
blackhole attacks, yet the technique does not support energy 
efficiency or adaptiveness. Cordasco et al. [21] promoted 
trust-based routing as an alternative to cryptographic 
mechanisms, although it retains static behavior. Pathan et al. 
[22] developed TSQRS, which employs social and QoS trust 
metrics to secure routing but is non-adaptive and lacks 
metaheuristic mechanisms. These solutions demonstrate that 
static trust-based routing cannot cope with dynamic and 
adversarial MANET environments. 

In the context of machine learning and hybrid 
optimization approaches, Hassan et al. [23] introduced 
FLSTMT-LAR, incorporating federated learning, LSTM-based 
trust prediction, and NSGA-III optimization. Despite high 
detection capability and energy efficiency, the model exhibits 
high computational complexity and partial adaptiveness. 
Arulselvan and Rajaram [24] integrated deep reinforcement 
learning with a dolphin-cat optimizer, achieving improved 
delay and trust estimation but limited real-time adaptiveness. 
Priya et al. [25] combined GA, PSO, reinforcement learning, 
and quantum-resistant cryptography to enhance security, 
though the approach remains centralized, heavy, and only 
partially adaptive. These hybrid approaches highlight gains in 
intelligence but struggle to deliver fully dynamic, lightweight, 
and distributed adaptiveness. 

A distinct category involves metaheuristic routing with 
trust but partial adaptiveness, where trust mechanisms exist 
but are only loosely connected to the optimization process. 
Veeramani et al. [2] used FFWHO with LF-SSO-DSR, 
incorporating intelligent dynamic trust yet keeping trust 
static and disconnected from metaheuristic decision-making. 
Kondaiah and Sathyanarayana [26] integrated fuzzy-firefly 
and PSO for intrusion detection, but trust is applied post-
selection rather than proactively guiding routing decisions. 
Prabaharan and Ponnusamy [27] proposed a hybrid ACO that 
improves energy consumption and mitigates selfish behavior, 
although the lack of structured trust limits security. 
Krishnaveni and Angel [28] used IHSO for trusted-node 
identification but without adaptive reactivity. Dudala et al. 
[29] combined WOA with differential evolution to mitigate 
Byzantine and wormhole attacks, remaining detection-
oriented and partially adaptive. Alappatt and Prathap [30] 
employed LF-SSO and SH2E encryption for secure multipath 
routing, but adaptiveness is still limited. In these works, trust 
and metaheuristics coexist but do not interact deeply, limiting 
proactive routing resilience. 

A related yet more advanced category consists of trust-
integrated metaheuristic mechanisms with partial 
adaptiveness, where trust is directly embedded into the 
optimization process. These approaches differ from the prior 
category because trust actively influences the metaheuristic 
cost, selection, or fitness functions, even though adaptiveness 
remains incomplete. Veeraiah et al. [31] integrated fuzzy trust 
clustering with C-SSA, improving energy and security but 
using trust mainly for detection rather than preventive 
adaptiveness. Vishwakarma et al. [32] combined fuzzy 
butterfly optimization with chaotic grey wolf optimization, 
embedding trust values and encryption, but retaining partial 
adaptiveness. Brar et al. [33] used TrustOpt (ACO-WOA 
hybrid) with dynamic trust updating, yet the method remains 
detection-heavy. Vellingiri et al. [34] applied fuzzy trust 
evaluation with harmony search, GA, and cuckoo search for 
DSR, but trust integration is still limited. Karanje and Eklarker 
[35] developed GLBO, which combines energy and trust 
metrics in optimization, but lacks a full adaptiveness model. 
Sankaran and Hong [36] used cuckoo search for trust-aware 
routing, but static RSSI restricts dynamic response. These 
strategies demonstrate progress toward integrating security 
with optimization, but still lack continuous state-based 
adaptiveness. 

Another relevant category includes metaheuristic 
clustering-based trust routing with partial adaptiveness, 
where metaheuristics optimize cluster formation rather than 
end-to-end routing. Kumari et al. [37] proposed RTO-TV, 
using modified group optimization and trust-based security 
for cluster-head selection, achieving partial adaptiveness but 
lacking dynamic path re-evaluation. Aravindan and Rajaram 
[38] combined reinforcement learning with spider monkey 
optimization for secure cluster routing, offering trust support 
but limited dynamic re-routing. These methods provide 
security and energy efficiency, but do not deliver a 
metaheuristic, trust-adaptive path selection framework. 
Toward full integration, adaptive trust–metaheuristic 
mechanisms have emerged. Prasanna and Ramesh [39] used 
ASO and hybrid cat swarm optimization for trust-aware 
routing, offering a degree of adaptiveness but suffering 
encryption overheads. Kamboj and Dalip [40] incorporated 
grey wolf optimization and cuckoo search with machine 
learning for malicious detection, but the strategy remains 
partially adaptive and threat-detection-focused rather than 
preventive. These works signal a shift towards adaptiveness 



AD. Agor et al. /Future Technology                                                                                   February 2026| Volume 05 | Issue 01 | Pages 168-179 

172 

 

but still do not achieve continuous trust-driven dynamic 
optimization. Finally, the RFD-based baselines from which the 
proposed method derives show key limitations. Amin et al. [6] 
presented RFDTrust, embedding trust into the RFD paradigm 
using trust_forwarding and trust_goodness scores. However, 
path selection is restricted to lower-altitude neighbors, 
preventing full exploitation of the network topology and 
limiting both energy efficiency and trust propagation. Agor et 
al. [1] improved this with PRFDRA, enabling selection among 
higher, equal, and lower altitudes to enhance network 
longevity. However, PRFDRA remains non-secure and only 
partially adaptive. These limitations collectively motivate the 
proposed TA-PRFDRA, which integrates multi-stage trust 
evaluation directly into the RFD metaheuristic, employs 
adaptive SFD-MFD switching, and enables dynamic, 
preventive, and energy-efficient path selection beyond the 
capabilities of prior methods. Table 1 presents a comparative 
summary of representative MANET routing protocols, 
highlighting trust mechanisms, metaheuristic integration, 
adaptiveness, and key limitations relative to TA-PRFDRA. 

3. Methodology 

3.1 Overview and framework of TA-PRFDRA 
The proposed TA-PRFDRA is developed as an 

enhancement of the PRFDRA proposed by Agor et al. [1]. 
PRFDRA itself is derived from the RFD model introduced by 
Rabanal et al. [5]. TA-PRFDRA retains the energy-aware and 
delay-optimized structure of PRFDRA but integrates trust 
into all routing computations. It also presents an adaptive 
SFD-MFD switching mechanism to improve resilience under 
dynamic and deceptive network conditions. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.2 Trust estimation module 
This module evaluates node reliability through four 

dimensions: forwarding ratio, route participation, energy 
reputation, and routing metric consistency. Each submetric 

contributes to a composite trust score 𝑇𝑖𝑗  for neighbour 𝑗 as 

perceived by the node 𝑖 defined in equations 1 to 4:  

Forwarding ratio (𝛼𝑖𝑗):  

𝛼𝑖𝑗 =
𝐹𝑖𝑗

𝑅𝑖𝑗
⁄             (1) 

where 𝐹𝑖𝑗  is the number of packets forwarded by the node 𝑗 

from node 𝑖, and 𝑅𝑖𝑗 is the number of packets received by 𝑗 

from node 𝑖. This metric, rooted in watchdog and path-rater 
trust frameworks, helps identify packet-dropping behaviors 
associated with blackhole attacks [19]. 

Route Participation Ratio (𝛽𝑗):  

𝛽𝑗 =
𝑅𝑃𝐹𝑗

𝑅𝑃𝑡𝑜𝑡𝑎𝑙
⁄            (2) 

where 𝑅𝑃𝐹𝑗  is the number of valid routes that include the 

node 𝑗 and 𝑅𝑃𝑡𝑜𝑡𝑎𝑙  is the total number of valid routes that are 
observed. This monitors how frequently 𝑗 appears in valid 
routes and penalizes nodes that rarely participate in routing. 
Low participation suggests non-cooperation or instability. 

Energy reputation (𝛾𝑗):  
𝛾

𝑗=
𝐸𝑗

𝐸𝑖𝑛𝑖𝑡
⁄

            (3) 

where 𝐸𝑗  is the residual energy and  𝐸𝑖𝑛𝑖𝑡 is the initial energy. 

This extends the energy-aware metrics of PRFDRA [1]. 

Routing metric consistency (𝛿𝑗):  

𝛿𝑗 = 1 −
(|𝑟𝑒𝑝𝑜𝑟𝑡𝑒𝑑 (𝑇𝐷𝑗) − 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑(𝑇𝐷𝑗)|)

𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 (𝑇𝐷𝑗)
⁄   

             (4) 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 1. Comparative Summary of Representative MANET routing Protocols and key limitations relative to TA-PRFDRA 

Study Trust Mechanism Metaheuristic/ 
Optimization 

Adaptiveness Main Limitation 

Foundational trust-based routing 
(non-adaptive)- 
[18-22]  

Fuzzy,  reputation, or 
social trust None None 

Static trust; lacks 
metaheuristic and 
adaptive behavior 

Hybrid ML/ Optimization trust 
routing (partial adaptiveness)- 
[23-25] Learning-based trust 

Multiobjective or 
hybrid ML-
optimization Partial 

High computational 
overhead; delay; limited 
real-time adaptiveness 

Metaheuristic routing with trust 
but partial adaptiveness 
[26-30] 

Static or loosely 
coupled trust Nature-inspired Partial 

Trust not embedded in 
optimization; largely 
detection-based 

Trust-integrated metaheuristic 
routing with partial adaptiveness 
[31-36] 

Fuzzy or behavioural 
trust 

Hybrid 
metaheuristics Partial 

Limited preventive 
adaptiveness; static 
elements restrict 
dynamic response 

Metaheuristic clustering-based 
trust routing (partial 
adaptiveness) 
[37,38] 

Cluster or RL-based 
trust Nature-inspired Partial 

Adaptiveness limited to 
cluster management 

Adaptive trust metaheuristic 
routing (partial adaptiveness) 
[39,40] 

Behavioral and ML-
assisted trust 

Hybrid 
metaheuristics Partial 

Detection-focused; lacks 
continuous pre-emptive 
adaptiveness 

RFD variant without trust [1] 
 None RFD metaheuristic Partial Energy-aware; no trust 

RFD variant with trust [6] Behavioral trust RFD metaheuristic Partial 

Trust propagation 
constrained; limited 
energy efficiency 

Proposed TA-PRFDRA 
Continuous multi-stage 
trust integration 

RFD metaheuristic 
with SFD-MFD 
switching Dynamic 

Adaptive, preventive, 
trust, and energy-
efficient route selection 

 



AD. Agor et al. /Future Technology                                                                                   February 2026| Volume 05 | Issue 01 | Pages 168-179 

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This validates reported delay values to identify 
manipulation of common wormholes and grey hole attacks. 

Here, 𝑟𝑒𝑝𝑜𝑟𝑡𝑒𝑑 (𝑇𝐷𝑗) refers to the delay value that the node 𝑗 

advertises its current packet transmission time. 

𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑(𝑇𝐷𝑗), on the other hand, represents the actual 

time delay inferred by the node 𝑗 through empirical 

observation. 𝑇𝐷𝑗  captures the queuing and forwarding 

latency of the node 𝑗, which rises with congestion. Therefore, 
consistent discrepancies between reported and observed 
delays may indicate intentional misreporting, as observed in 
wormhole or grey hole attacks. 

The composite trust score is computed as: 

𝑇𝑖𝑗
𝑛𝑒𝑤 = 𝑤1. 𝛼𝑖𝑗 + 𝑤2. 𝛽𝑗 + 𝑤3. 𝛾𝑗 + 𝑤4. 𝛿𝑗         (5)  

with weight vector [𝑤1, 𝑤2, 𝑤3, 𝑤4] = [0.4, 0.2, 0.2, 0.2], 

emphasizing forwarding reliability while balancing 

participation, energy and consistency. The exponentially 
weighted moving average (EWMA), 𝑇𝑖𝑗(𝑡) is computed as: 

𝑇𝑖𝑗(𝑡) = 𝜆. 𝑇𝑖𝑗(𝑡 − 1) + (1 − 𝜆). 𝑇𝑖𝑗
𝑛𝑒𝑤, 𝜆𝜖[0.6, 0.9]       (6) 

𝜆 is a smoothing factor that determines the weight 

given to historical data. The EWMA produces smoothed trust 
scores to prevent rapid fluctuations and improve decision 
stability. Equations (1) to (6) are original formulations 
developed in this study to quantify node trust. They are 
conceptually informed by trust models in wireless networks 
[41–46], but mathematically defined for the TA-PRFDRA 
framework. 

3.3 Trust-augmented gradient computation 
In PRFDRA, the neighbour 𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡(𝑖, 𝑗) is based on 

altitude difference, time delay (𝑇𝐷) energy (E) and number of 
hops (𝑁𝐻𝑜𝑝𝑠). TA-PRFDRA modifies it to account for trust in 
equation 7. 

𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗) =

[(𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒𝑡𝑟𝑢𝑠𝑡(𝑖) − 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒𝑡𝑟𝑢𝑠𝑡(𝑗)). 𝑇𝐷𝑗.𝑇𝑖𝑗]
[E𝑗 . 𝑁𝐻𝑜𝑝𝑠(𝑖, 𝑗)]

⁄        (7) 

This formulation penalises low-trust neighbors while 
maintaining the energy, hop count and latency considerations 
inherited from PRFDRA.  

3.4 Adaptive SFD–MFD switching logic  
Whereas PRFDRA employs only an SFD strategy, TA-

PRFDRA introduces a variance-driven switching mechanism, 
as defined in equations 8 and 9.  

𝜇𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡
= 1

|𝑁(𝑖)|⁄  ∑ 𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗)𝑗∈𝑁(𝑖)              (8) 

𝜎𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡

2 = 1
|𝑁(𝑖)|⁄ ∑ (𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗) − 𝜇𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡

)2
𝑗∈𝑁(𝑖)

               (9) 

If 𝜎𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡

2 < 𝜃 the algorithm switches to MFD mode; 

otherwise, it remains in SFD mode as defined in equations 
(10) to (11). This allows dynamic control of forwarding 
strategies based on local variation in gradients. In SFD mode, 
the node with the highest 𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗) is 
deterministically chosen.  

If 𝜎𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡

2 < 𝜃 → MFD mode (gradients are similar)

           (10) 

Else → SFD mode (one clear path dominates)                              (11)
  

3.5 Trust-Based Probabilistic Flow Assignment in MFD 
Mode 
When MFD mode is active, forwarding probabilities for 

each neighbor are calculated using the normalized formulae 
defined in equations 12 to 14 of Table 2. 

Table 2. Trust-based probabilistic flow assignment under MFD 

 

These probabilistic assignments extend PRFDRA’s 

neighbour selection mechanism by introducing trust-

weighted flow control. 

3.6 Trust-conscious erosion mechanism 
Erosion is adjusted based on the selected mode defined 

in equations 15 to 17 of Table 3. 
• SFD: Apply erosion to the selected neighbor only. 
• MFD: Distribute erosion proportionally to each neighbour.  
This ensures reinforcement of trusted paths and degradation 
of malicious ones.  

Table 3. Trust-weighted erosion distribution formulas 

Neighbor Set  Erosion Equation Equation 

Vk(i) [εV.gradienttrust(i,j).TDj]/[(N−1). 

M.Ej.NHops(i,j)] 

(15) 

Uk(i) [εU.TDj]/[|𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗)|. (𝑁 −

1). E𝑗 . 𝑁𝐻𝑜𝑝𝑠(𝑖,𝑗)] 

(16) 

Fk(i) [εF.TDj] / [(N−1).M.Ej.NHops(i,j)] (17) 

 

3.7 Trust-conscious altitude mechanism 
Altitude reduction is scaled based on the target node's 

trustworthiness. Nodes with lower trust scores cause less 
erosion, discouraging traffic through untrusted nodes and 
vice versa. The amount of sediment deposited is influenced by 
the trust level of the node 𝑗. Less sediment is transferred to 
low-trust nodes, reflecting reduced confidence in their long-
term reliability. Equation 18 computes 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒𝑡𝑟𝑢𝑠𝑡(𝑖) 𝑎𝑠:  

𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒𝑡𝑟𝑢𝑠𝑡(𝑖) = 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒𝑡𝑟𝑢𝑠𝑡(𝑖) ±

(
(𝑒𝑟𝑜𝑠𝑖𝑜𝑛𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗). 𝑇𝑖𝑗)

𝑁
⁄ )        (18) 

In Equation 19, blocked drops increase a node’s altitude more 
when the node is untrustworthy, discouraging future 

selection. 

𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒𝑡𝑟𝑢𝑠𝑡(𝑙) = 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒𝑡𝑟𝑢𝑠𝑡(𝑙) +
𝑝𝑎𝑟𝑎𝑚𝐵𝑙𝑜𝑐𝑘𝑒𝑑𝐷𝑟𝑜𝑝. 𝑐𝑎𝑟𝑟𝑖𝑒𝑑𝑠𝑒𝑑𝑖𝑚𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡. 𝑇𝑖𝑗               (19) 

3.8 Trust-focused sedimentation process 
Trust modulates the erosion contribution to carried 

sediment, further limiting the role of low-trust nodes in the 
sediment transportation process.  

Neighbor Set Probability Equation Equations 

Vk(i) [𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗).TDj]/Σ Ej. NHops(i,j) (12) 

Uk(i) [ω /𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗)|). 𝑇𝐷𝑗] (13) 

Fk(i) [δ.TDj] / Σ Ej.NHops(i,j) (14) 



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174 

 

Equations 20 and 21 compute 𝑠𝑒𝑑𝑖𝑚𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗) and 
𝑐𝑎𝑟𝑟𝑖𝑒𝑑𝑆𝑒𝑑𝑖𝑚𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗). 

𝑠𝑒𝑑𝑖𝑚𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗) = (𝛽. (𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒𝑡𝑟𝑢𝑠𝑡(𝑖) −

𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒𝑡𝑟𝑢𝑠𝑡(𝑗)). 𝑐𝑎𝑟𝑟𝑖𝑒𝑑𝑆𝑒𝑑𝑖𝑚𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗). 𝑇𝐷𝑗. 𝑇𝑖𝑗)/
(E𝑗. 𝑁𝐻𝑜𝑝𝑠(𝑖, 𝑗))         (20) 

𝑐𝑎𝑟𝑟𝑖𝑒𝑑𝑆𝑒𝑑𝑖𝑚𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗) = 𝑐𝑎𝑟𝑟𝑖𝑒𝑑𝑆𝑒𝑑𝑖𝑚𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗) +
𝑒𝑟𝑜𝑠𝑖𝑜𝑛𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗). 𝑇𝑖𝑗 − 𝑠𝑒𝑑𝑖𝑚𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗)                         (21) 

3.9 Route cost with trust penalty 
To discourage untrusted paths, the final cost function 

includes a trust-based penalty. Equation 22 defines 
cost𝑡𝑟𝑢𝑠𝑡(i, j) as: 

cost𝑡𝑟𝑢𝑠𝑡(i, j) = σ ∙ TD + μ ∙ [1 Min(E)⁄ ] + 𝜏 ∙ [1 𝑁𝐻𝑜𝑝𝑠⁄ ] +

φ. [1 𝑇𝑚𝑖𝑛⁄ ]                       (22) 

In which  𝑇𝑚𝑖𝑛 = 𝑚𝑖𝑛ℓ∈P𝑇ℓ to severely punish routes that 
have even an untrusted link.  

3.10 Trust-embedded iteration is the best solution  
Solutions passing through high-trust nodes are 

preferred. Low-trust paths incur a higher normalized cost and 
are less likely to be selected as the best path. This ensures that 
trust governs not only local forwarding but also global route 
convergence. The iteration-best trust-weighted solution is 

computed as 𝑇𝑡𝑟𝑢𝑠𝑡
𝐼𝐵 in equation 23.  

𝑇𝑡𝑟𝑢𝑠𝑡
𝐼𝐵 = 𝑎𝑟𝑔 𝑚𝑖𝑛 ∀𝑇𝐷𝑟𝑜𝑝𝑐𝑜𝑠𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗)       (23) 

3.11 Provenance of equations and notation 
Equations (1) to (11) are original formulations 

developed in this study to model trust computation and 
adaptive SFD-MFD control. Equations (12) to (23) are 
adapted and extended from PRFDRA [1]. Trust scaling and 
adaptive logic represent new extensions. Table 4 summarizes 
the symbols and parameters used in the TA-PRFDRA 
formulations. Parameters already defined in the text are not 
repeated. 

4. Results and discussion  

This section presents a comparative evaluation of TA-

PRFDRA against PRFDRA, RFDTrust, RFDManet, and TORA 

using four performance metrics: packet delivery ratio (PDR), 

average end-to-end delay (AE2ED), detection rate (DR), and 

energy consumption (EC). Simulations were conducted 

across varying source node densities (10–60 active sources) 

to represent diverse traffic conditions in MANETs. A hybrid 

adversary model was employed to assess robustness under 

internal threats, with 10–20% of nodes randomly designated 

as malicious during initialization. Blackhole nodes dropped 

all data packets after path establishment, while grayhole 

nodes selectively forwarded ~70% and dropped 30% of 

packets. These behaviors were implemented via packet-

forwarding suppression events in NS-3, affecting path 

selection without altering metric computations. 

The trust-based framework mitigated malicious 

influence through distributed neighbor evaluation, where 

each node computed its local trust based on the forwarding 

ratio, residual energy reliability, reporting consistency, and 

route participation frequency. Nodes with cumulative trust 

below the threshold τ = 0.5 were penalized in gradient, 

erosion, and flow probability calculations, reducing their 

impact on subsequent path selection. Statistical significance 

testing was performed between TA-PRFDRA and the trust-

based baseline (RFDTrust) for all four metrics using paired t-

tests at a 95% confidence level. This focused comparison 

aligns with established evaluation practices, avoiding 

redundant pairwise testing [47,48]. Tables 4–6 present the 

key simulation parameters, averaged results, and statistical 

test outcomes, respectively. 

Table 4. Simulation parameters 

 

4.1 Packet delivery ratio (PDR) 
As shown in Figure 5, TA-PRFDRA maintains a 

consistently high PDR across all source counts, recording 
99.64 % at 10 active sources and remaining above 98 % 
throughout, achieving 98.87 % at 60 sources. The average 
PDR values for TA-PRFDRA, PRFDRA, RFDTrust, RFDManet, 
and TORA are 99.54 %, 99.42 %, 99.34 %, 99.20 %, and 
98.21 %, respectively. Accordingly, the corresponding 
improvement rates of TA-PRFDRA over PRFDRA, RFDTrust, 
RFD, and TORA are 0.12 %, 0.20 %, 0.33 %, and 1.33 %. The 
paired t-test confirms that the improvement over RFDTrust is 
statistically significant (p = 0.022, Table 6). 

 
Figure 5. Packet delivery ratio against the number of sources 

4.2 Average end-to-end delay (AE2ED) 
Figure 6 illustrates the AE2ED performance of all 

algorithms. TA-PRFDRA achieves an average end-to-end 
delay of 0.087 s, compared with 0.113 s, 0.128 s, 0.137 s, and 
0.225 s for PRFDRA, RFDTrust, RFDManet, and TORA, 
respectively. The corresponding improvement rates of TA-
PRFDRA over PRFDRA, RFDTrust, RFD, and TORA are 0.026 s, 
0.041 s, 0.050 s, and 0.138 s. The paired t-test confirms that 
the delay reduction relative to RFDTrust is statistically 
significant (p = 0.010). 

 

Simulator NS-3 

Routing Protocols  TA-PRFDRA, PRFDRA, 
RFDTrust, RFDManet, TORA 

Simulation Time (S) 1500 

Simulation Area 1500 m x1500 m 

Mac Layer Protocol IEEE 802.11 

Nodes Number 250 

Transmission Range (m) 250 

Mobility Model RWP 

Highest Node Speed 10 m/s 

Data Packet Size 512 bytes 

Traffic CBR 

Initial Node Energy (J) 100  



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Table 5. Averaged performance metrics of TA-PRFDRA and baseline protocols under varying numbers of active sources 

Scenario 

Number of Active 
Sources 

PDR in percent 

TA-PRFDRA RFDTrust PRFDRA RFD TORA 

10 99.64 99.93 99.84 99.53 98.75 

20 99.71 99.68 99.58 99.33 98.51 

30 99.67 99.47 99.63 99.45 98.26 

40 99.69 99.53 99.4 99.13 98.03 

50 99.63 99.23 99.65 99.12 98.24 

60 98.87 98.2 98.41 98.65 97.47 

Number of Active 
Sources 

AE2ED in seconds 

TA-PRFDRA RFDTrust PRFDRA RFD TORA 

10 0.07 0.1 0.07 0.09 0.19 

20 0.07 0.12 0.09 0.11 0.2 

30 0.08 0.13 0.11 0.12 0.21 

40 0.08 0.14 0.13 0.16 0.25 

50 0.09 0.11 0.09 0.15 0.22 

60 0.13 0.17 0.19 0.19 0.28 

Number of Active 
Sources 

DR in percent 

TA-PRFDRA RFDTrust PRFDRA RFD TORA 

10 60.4 55.02 51.13 46.7 39.6 

20 63.25 58.5 52.66 47.65 41.63 

30 69.53 63.22 57.32 48.01 42.08 

40 78.02 75.57 58.19 49.3 44.3 

50 81.65 75.9 59 49.88 44.92 

60 81.95 80.06 59.77 50.25 44.98 
Number of Active 

Sources 
EC in joules 

 TA-PRFDRA RFDTrust PRFDRA RFD TORA 

10 46.34 50.81 48.38 53.14 63.16 

20 48.51 52.22 49.95 54.08 62.77 

30 48.69 51.8 49.8 53.21 61.5 

40 48.47 53.31 51.41 55.3 63 

50 49.1 54.88 51.69 55.99 62.43 

60 46.62 50.17 46.82 51.4 64.91 
 

 

Table 6. Statistical significance of TA-PRFDRA compared with the trust baseline protocol  

Metric Compared 

Strategy 

Mean difference 

(TA-baseline) 

RFDTest used P_value Significant (α 

=0.05) 

PDR (%) RFDTrust +0.20 Paired t 0.022 Yes 

AE2ED (s) RFDTrust -0.04 Paired t 0.010 Yes 

DR (%) RFDTrust +4.10 Paired t 0.008 Yes 

EC (J) RFDTrust -4.84 Paired t 0.006 Yes 

 



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176 

 

 
Figure 6. Average end-to-end delay against the number of sources 

4.3 Detection rate (DR) 
As shown in Figure 7, TA-PRFDRA consistently achieves 

higher DR across all source counts. The average DR is 

72.47 %, compared with 55.51 %, 68.05 %, 48.30 %, and 

42.09 % for PRFDRA, RFDTrust, RFDManet, and TORA, 

respectively. The improvement rates of TA-PRFDRA over 

PRFDRA, RFDTrust, RFD, and TORA are 16.96 %, 4.42 %, 

24.17 %, and 30.38 %. The paired t-test indicates that the 

improvement over RFDTrust is statistically significant (p = 

0.008). 

4.4 Energy consumption (EC) 
Figure 8 compares the EC of all algorithms. TA-PRFDRA 

records 47.36 J, while PRFDRA, RFDTrust, RFDManet, and 
TORA consume 49.68 J, 52.20 J, 53.52 J, and 63.63 J, 
respectively. The corresponding improvement rates of TA-
PRFDRA over PRFDRA, RFDTrust, RFD, and TORA are 2.32 J, 
4.84 J, 6.16 J, and 16.27 J. The paired t-test confirms that the 
reduction relative to RFDTrust is statistically significant (p = 
0.006). 

4.5 Discussion 

The combined results validate that the proposed TA-
PRFDRA protocol maintains high delivery reliability, low 
latency, strong security awareness, and energy efficiency 
under dynamic MANET conditions. Its performance 
superiority is especially evident under high source densities, 
indicating excellent scalability and resilience. PRFDRA selects 
paths using residual energy and performance metrics, but 
assumes all nodes behave reliably [1]. Its gradient and flow-
probability computations are energy-aware but trust-neutral. 
This allows unstable or malicious nodes to influence path 
formation, causing route oscillations and packet losses. TA-
PRFDRA integrates a composite trust score into gradient and 
flow-probability calculations. This produces more stable path 
selection and reduced latency compared with PRFDRA. 

RFDTrust evaluates node reputation only prior to node 

selection [6]. Packets primarily follow downhill paths, 

limiting path diversity and restricting adaptiveness in flat or 

deceptive topologies. TA-PRFDRA embeds trust evaluation 

across all RFD stages and applies adaptive switching between 

single-flow and multi-flow modes based on trust-weighted 

gradient variance. This allows rapid isolation of low-trust 

nodes while preserving multiple routing options. RFDManet 

relies solely on altitude differences and erosion dynamics 

without energy or trust weighting [6]. Paths may include 

energy-depleted or malicious nodes, resulting in instability, 

high retransmissions, and increased energy consumption. TA-

PRFDRA combines energy and trust weights in gradient and 

move-probability calculations. This ensures selected paths 

are more reliable and sustainable under dynamic conditions. 

TORA employs a link-reversal mechanism and maintains 

multiple routes, but it treats all links equally and does not 

consider trust [49]. Frequent control messages and uniform 

link treatment increase delay and energy use, especially when 

nodes behave maliciously. TA-PRFDRA concentrates 

forwarding along high-trust links, which reduces unnecessary 

reversals and enhances route reliability. TA-PRFDRA has 

some limitations. The trust update process increases 

computation on nodes with limited resources. The algorithm 

may also scale poorly in very large networks because more 

nodes require more trust and gradient evaluations. Future 

work will reduce this cost through lighter trust updates and 

more efficient gradient processing to support larger 

topologies. 

 

 

Figure 7. Detection rate against the number of sources 

 

 
Figure 8. Energy consumption against the number of sources 

 



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177 

 

5. Conclusion 

This paper presented TA-PRFDRA, a trust and adaptive 
enhanced version of PRFDRA for secure and energy-efficient 
routing in MANETs. TA-PRFDRA incorporated behavioral 
trust evaluation into all PRFDRA stages and applied dynamic 
SFD–MFD switching based on trust-weighted gradient 
variance. Simulation results showed that, compared with 
PRFDRA, RFDTrust, RFDManet, and TORA, TA-PRFDRA 
achieved up to 1.33% higher PDR, reduced AE2ED by 0.14 s, 
increased DR by up to 30.38 %, and lowered EC by up to 
15.94 J. Statistical analysis confirmed that improvements 
over RFDTrust were significant. Future work will extend 
statistical validation to all comparative protocols and 
improve computational efficiency. Additional performance 
metrics such as routing overhead, throughput, and false 
positive rate will also be evaluated in dense MANET settings. 
Future studies may explore the integration of blockchain-
supported trust mechanisms and IoT-based architectures to 
strengthen secure distributed routing.  

Ethical issue 
The authors are aware of and comply with best practices in 
publication ethics, specifically regarding authorship 
(avoidance of guest authorship), dual submission, 
manipulation of figures, competing interests, and compliance 
with research ethics policies. The authors adhere to 
publication requirements that the submitted work is original 
and has not been published elsewhere. 

Data availability statement 
The manuscript contains all the data. However, more data will 

be available upon request from the authors. 

Conflict of interest 

The authors declare no potential conflict of interest. 

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Symbols and parameters 

𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗) Trust-based gradient from node 𝑖 

to 𝑗 

𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒𝑡𝑟𝑢𝑠𝑡(𝑖) Trust-based altitude of node 𝑖 

𝑒𝑟𝑜𝑠𝑖𝑜𝑛𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗) Trust-based erosion of nodes along 

the path from 𝑖 to 𝑗  

𝑠𝑒𝑑𝑖𝑚𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡(𝑖, 𝑗) Trust-based sediment added to 

node 𝑗’s altitude 

𝑐𝑎𝑟𝑟𝑖𝑒𝑑𝑠𝑒𝑑𝑖𝑚𝑒𝑛𝑡𝑡𝑟𝑢𝑠𝑡 Sediment carried from node i to 𝑗 
based on trust 

cost𝑡𝑟𝑢𝑠𝑡(i, j) Trust-integrated route cost 
function 

𝑇𝐷𝑗  Time delay at node 𝑗 

𝑁𝐻𝑜𝑝𝑠(𝑖, 𝑗) Number of hops between node 𝑖 

and 𝑗 

Min(E) Minimum residual energy along the 
evaluated path 

𝐸𝑗  Residual energy at node 𝑗 

𝑝𝑎𝑟𝑎𝑚𝐵𝑙𝑜𝑐𝑘𝑒𝑑𝐷𝑟𝑜𝑝 Parameter indicating a blocked 
sediment drop (1 if blocked) 

𝜎, 𝜇, 𝜏, φ Cost-function weight parameters 

𝑇𝐷𝑟𝑜𝑝 Outcome per iteration 

𝜇𝐺 , 𝜎𝐺
2 Mean and variance of trust-based 

gradients for SFD-MFD switching 

𝜃 Threshold controlling transition 
between SFD and MFD  

εV, εU,, εF Erosion constants for positive, 
negative, and flat gradients 

ω,δ Specific small values in Trust-based 
Probabilistic MFD mode equations 

Vk(i). Uk(i), and Fk(i) Set of neighbors with positive, 
negative and flat gradients 

Sum Sum of numerator weights of all 
neighbors  

𝑖, 𝑗, 𝑙, 𝑛 Node indices  
𝑁(𝑖) Set of neighbors of node 𝑖  
𝑇𝑚𝑖𝑛 Minimum trust among nodes on a 

route 

  

This article is an open-access article distributed under the 

terms and conditions of the Creative Commons Attribution 

(CC BY) license 

(https://creativecommons.org/licenses/by/4.0/). 

https://doi.org/10.34028/iajit/22/3/13
https://doi.org/10.1109/PDGC.2016.7913218
https://creativecommons.org/licenses/by/4.0/

