A Quantum-Inspired Ant Colony Optimization Approach for Exploring Routing Gateways in Mobile Ad Hoc Networks

Abstract

Establishing internet access for mobile ad hoc networks (MANET) is a job that is both vital and complex. MANET is used to build a broad range of applications, both commercial and non-commercial, with the majority of these apps obtaining access to internet resources. Since the gateways (GWs) are the central nodes in a MANET’s ability to connect to the internet, it is common practice to deploy numerous GWs to increase the capabilities of a MANET. Current routing methods have been adapted and optimized for use with MANET through the use of both conventional routing techniques and tree-based network architectures. Exploring new or tacking-failure GWs also increases network overhead but is essential given that MANET is a dynamic and complicated network. To handle these issues, the work presented in this paper presents a modified gateway discovery approach inspired by the quantum swarm intelligence technique. The suggested approach follows the non-root tree-based GW discovery category to reduce broadcasting in the process of exploring GWs and uses quantum-inspired ant colony optimization (QACO) for constructing new paths. Due to the sequential method of execution of the algorithms, the complexity of ACO grows dramatically with the rise in the number of paths explored and the number of iterations required to obtain better performance. The exploration of a huge optimization problem’s solution space may be made much more efficient with the help of quantum parallelization and entanglement of quantum states. Compared to other broad evolutionary algorithms, QACO s have more promise for tackling large-scale issues due to their ability to prevent premature convergence with a simple implementation. The experimental results using benchmarked datasets reveal the feasibility of the suggested approach of improving the processes of exploring new GWs, testing and maintaining existing paths to GWs, exploring different paths to existing GWs, detecting any connection failure in any route, and attempting to fix that failure by discovering an alternative optimal path. Furthermore, the comparative study demonstrates that the utilized QACO is valid and outperforms the discrete binary ACO algorithm (AntHocNet Protocol) in terms of time to discover new GWs (27% improvement on average), time that the recently inserted node takes to discover all GWs (on average, 70% improvement), routing overhead (53% improvement on average), and gateway’s overhead (on average, 60% improvement).

1. Introduction

Mobile ad hoc networks (MANET) are transient wireless networks that are formed out of a collection of mobile nodes (see Figure 1) that are capable of dynamic self-organization and self-configuration [1]. Due to its unique properties, MANET has found usage in a variety of fields, both commercial (e.g., smart agriculture) and non-commercial (e.g., military applications), and the vast majority of MANET applications and users rely on internet resources [2]. For optimal speed and efficiency while connecting to the internet, it is recommended that multiple gateways (GWs) be established. The process of locating gateways that have joined or left the network, as well as failures or new connections to existing gateways, is complex due to the evident architecture and features of the MANET and the lack of permanent infrastructure services [1]. This adds unnecessary burden and complexity to the network. Several existing routing technologies work to enhance and expand MANET internet access [2,3].

Three types of MANET routing protocols exist: reactive (on-demand), proactive (table-driven), and hybrid. To begin, reactive protocols only create connections when a source node actively requests data packets from an end node [3]. Until data packets reach the destination node, this route is preserved. These protocols delay source-to-destination communication yet decrease network overhead and broadcasts. Ad hoc on-demand distance vector (AODV) and dynamic source routing (DSR) are two such examples [4]. The second is that proactive protocols construct and disseminate routing tables for all network nodes. These protocols link sources and destinations with just a short lag time, but they use more resources and cause network loops. Destination sequenced distance vector (DSDV) and optimized link state routing protocol (OLSR) are examples [5].

Third, hybrid protocols combine reactive and proactive techniques, setting the route from the routing table (proactively) and reacting to changes and new requests (reactively). An example of this is the zone routing protocol (ZRP) [4,5,6]. However, AODV and the OLSR are used to construct such protocols, and they do not support multiple paths. Other protocols, such as the hybrid wireless mesh protocol (HWMP), may only support a single GW, or they may use a tree-based routing solution (discovering the GW mechanism by broadcasting its presence) [3,7,8,9,10]. In order to discover new GWs or create new path, this tree-based approach relies heavily on broadcasting, which may slow down the process significantly [11].

Swarm intelligence-based algorithms such as ant colony optimization (ACO) provide loop-free, energy-aware, and multi-path MANET routing [12,13,14]. The packet delivery ratio, average end-to-end latency, and routing overhead are all improved as a result [15,16]. Artificial ants that imitated real ants communicated to find an ideal optimization solution using the ACO technique. The ants’ pheromone concentration dictated the ideal route between the source and destination. Compared to other optimization methods, ACO is more effective at finding the shortest path to the target node. By acting as echoes, the artificial ants in ACO are able to reflect the control packets that are utilized to gather data between the source and the destination nodes. Each network node has a routing table containing information about its neighbors. When a node has numerous possible pathways between a source and a destination, it uses the pheromone values associated with each path to determine which ones are best [17].

Classical ACO algorithms may provide more desirable optimum solutions, but they do so at the expense of an excessively high computational cost. Through the parallelism of quantum computing, algorithmic speedups are possible. Quantum algorithms now in use for ACO solutions fall into one of two categories: classical algorithms influenced by quantum mechanics or hybrids of classical and quantum approaches [18]. Quantum ant colony optimization (QACO) is an approach that builds on quantum evolutionary algorithms (QEA), where a Q-bit is utilized to represent the pheromone and a quantum rotation technique is used to update the pheromone in a discrete binary combinatorial optimization domain [18,19,20]. According to the simulation results in the literature, QACO outperforms ACO, even with a small population size, and its search and optimization capabilities are superior [21].

An improved routing approach inspired by quantum-inspired ant colony optimization is suggested in this work. The exploration of new GWs, testing and maintenance of existing GW routes, exploration of new paths to existing GWs, identification of any connection failure in any route, and attempts to rectify that failure are all enhanced by the proposed approach. A multi-route, multi-gateway system that incorporates QACO eliminates conventional procedures’ disadvantages while reducing network overhead and accelerating discovery over tree-based approaches. Specifically, the employed QACO uses a combination of Grover’s amplitude amplification approach and time-driven quantum evolution to encode the potential paths through a continuous update to the pheromone distribution’s probability density function. Global convergence of the optimization issue in the solution space is achieved when more and more pheromones are deposited along the shortest route.

This article continues as follows: The current MANET routing protocols and their shortcomings are discussed in Section 2. Section 3 provides an outline of the recommended approach. Section 4 tests the suggested approach and reviews the results. Section 5 summarizes the presented work and recommends next directions.

2. Related Works

Here, we give a quick overview of previous research that compared and contrasted the performance of several routing protocols used in MANETs and their drawbacks. Furthermore, the results of studies that highlight the positive aspects of including ACO into MANET routing systems are provided. In [22], the authors reviewed AODV’s performance in terms of route exploration and maintenance. According to the results of their study, the routing expiry period is difficult to predict without receiving data, and it does not permit the discovery of alternative routes or the investigation of other gateways after finding the first path to the current gateway [8,9]. In [23], the authors evaluated upgraded AODV protocols such as ad hoc on-demand distance vector routing from Uppsala University (AODV-UU), which supports IPv6 and multicasting, and ad hoc on-demand multiple distance vector routing (AOMDV), which is a multi-path addition to AODV. AOMDV employs many channels to convey data, which increases routing overhead. This extra routing reduces network efficiency [24].

In [25], a comparison was made between the destination-sequenced distance vector (DSDV) protocol and its enhanced variant, known as I-DSDV, which utilizes OLSR proactive routing. OLSR has better packet delivery and latency. OLSR uses multi-point relay (MPR) nodes to optimize pure LSR for MANETs by reducing control traffic overhead. Due to frequent routing table updates, the bandwidth utilization increases, and MPR is hard to identify [5]. In [26], research was conducted on ZRP as well as its several versions, which include the independent zone routing protocol (IZRP), the two-zone routing protocol (TZRP), and the fish-eye zone routing protocol (FZRP). ZRP utilizes proactive link-state routing within the radius (zone) and reactive routing outside the zone. These protocols decrease communication overhead by re-transmitting routes quicker than reactive protocols such as DSR. They are reactive when the routing zone value is small but proactive when the value is large [27]. In [28], the authors analyzed HWMP, IEEE 802.11’s default routing protocol. HWMP requires frequent route rebuilding owing to unpredictable wireless connections; single-path routing does not properly leverage path diversity; as a tree-based proactive type, this results in a bottleneck, since it is entirely concentrated and cannot expand beyond the root node. In [3], the authors offered a multi-gateway multi-path protocol (MGMP) as a solution of problems with HWMP. It discovers a variety of routes inside the multi-gateway MANET. The HWMP has a tree-based design, which results in broadcasting and a bottleneck at the root node.

The widespread ACO routing algorithm uses ant behavior as a learning model. As an effective swarm intelligence algorithm, it has been used in MANET design [29]. In [30], the authors found that ACO improves the overhead and connectivity of MANET routing protocols. Researchers have sought to improve classic MANET routing systems using ACO [28]. Ant-AODV reduces end-to-end latency and improves connection as contrasted with the conventional AODV. The ant dynamic source routing-based procedure enabled proactive route optimization by constantly verifying cached routes. This method enhances the chance that a cached route reflects network reality. The hybrid ACO routing algorithm employs the zone routing protocol, which combines proactive and reactive benefits [29,30,31,32]. Routing methods that consider power, QoS, and security are discussed in [17]. This article found that the ACO algorithm is one of the most effective route finding approaches for MANET.

In [33], the authors presented the bio-inspired hybrid routing protocol (B-iHTRP) system with a smart perception and autonomic optimization routing protocol for MANET, based on trusted assessment, ant colony optimization (ACO), and physarum autonomic optimization (PAO). It considered a large-scale multi-hop MANET whose nodes are randomly distributed in a two-dimensional area, subjectively dividing the network into a set of zones where each node has one zone, and each zone has a central node and other nodes. B-iHTRP is made up of routing within a zone, routing among zones, and other basic models. Proactive routing is implemented for each zone, while reactive routing is implemented within zones. Path discovery and path failure maintenance are performed by process, automation, control and optimization (PACO). PAO is used to pick the best route from the source node paths identified and to optimize local routes during multi-zone communication sessions. B-iHTRP is committed to combining the advantages of both ACO and PAO in order to boost effective efficiency, but it does not consider the actual mobility model of nodes that do not fit into the real MANET environment.

To boost QoS in MANETs, the authors in [34] presented a novel technique for route selection by fusing the AODV protocol with ACO. AODV is based on the ant colony’s method for selecting the most efficient way for data transmission based on the pheromone value of that path. The pheromone value of a path is determined by considering its end-to-end dependability, congestion, number of hops, and residual energy of the nodes along the way. The data packet will be sent along the route with the greatest pheromone value. In comparison to AODV, DSR, and Enhanced-Ant-DSR, their approach performs better in simulations. In [35], the authors presented AntHocNet, which is an ACO-inspired hybrid routing scheme that allows multiple paths and gateways data transmission. Similar to previous ACO algorithms, it stores routing data in a pheromone table and deals with connection failure by repairing routes locally and sending out warning signals. AntHocNet speeds up network discovery in high-data-rate networks. However, it loops in certain cases and is an energy hog [36,37].

In [38], by incorporating quantum computing and a multi-objective fitness function into the routing research method, a novel WSN routing algorithm called quantum ant colony multi-objective routing (QACMOR) may be employed for monitoring in such industrial contexts. Quantum bits stand in for the pheromone at each node, and quantum gate rotation is utilized to refresh the pheromone along the search route. Search paths are optimized using fitness functions that take into account node energy use, latency in data transmission, and the load-balancing capability of the underlying network. With reference to the peculiarities of industrial continuous steel casting production, this article investigated two performance metrics: convergence rate and network lifetime. The simulation results showed that the suggested approach can quickly find the ideal path with a high convergence rate while also extending the network’s lifetime. Based on their earlier work [39,40], physical WSN deployment and testing have shown that the proposed QACMOR method is reliable in such situations. More research on the use of optimization algorithms in MENT routing and related scheduling problems can be found in references [39,40,41,42,43].

Table 1. Existing MANETs routing protocols comparison.

	Classification	Algorithm-Based	Multi-Path Multi-GW	Advantages	Disadvantages
AODV	Reactive	Non-root	Single-path Single-GW	1- Low routing overhead over time 2- Widely used and easy to implement	1- Single-path single-GW 2- No mechanism to find new GW 3- Packet delivery, and node energy need improvement
AODV-UU	Reactive	Non-root	Single-path Single-GW	1- Supports IPv6	1- Same as AODV except supports IPv6
AOMDV	Reactive	Non-root	Multi-path Multi-GW	1- Supports multi-path data transmission	1- Same as AODV except supporting multi-path 2- Increase the routing overhead
DSDV and I-DSDV	Proactive	Non-root and broadcast	Single-path Single-GW	1- A table-driven routing protocol 2- Suitable for a small number of nodes	1- Needs enhancement in end-to-end delay 2- Increases the broadcast caused by periodically routing updates sent by each node 3- Single-path single-GW
OLSR	Proactive	Non-root and broadcast	Single-path Single-GW	1- A table-driven routing protocol 2- Better in end-to-end delay and packet delivery	1- Increase the broadcast caused by periodically routing updates sent by each node 2- Requires more bandwidth 3- Single-path single-GW
ZRP, IZRP, TZRP and FZRP	Hybrid	Non-root and Broadcast with zone separation	Single-path Single-GW	1- Divided the network to zones 2- Decreases the quantity of communication overhead 3- Works well with a large number of zones	1- In a small number of zones behaves like reactive protocols 2- Creates overlapping zones 3- Single-path single-GW
HWMP	Hybrid	Tree-based	Single-path Single-GW	1- Addresses mobility using tree-based routing and on-demand routing.	1- Due to unreliable connection, requires frequent route reconstruction. 2- The tree-based proactive mode creates a root node bottleneck 3- Single-path single-GW
MGMP	Hybrid	Tree-based	Multi-path Multi-GW	1- It seeks many paths in order to address the shortcomings HWMP	1- Built-in tree-based method causes a bottleneck to the root node and more broadcast
Ant-AODV	Reactive	AODV and ACO	Single-path Single-GW	1- Developed to overcome the limitations of AODV	1- Still single-path single-GW
Ant-DSR	Reactive	DSR and ACO	Single-path Single-GW	1- Developed to overcome the limitations of DSR and DSDV	1- Still single-path single-GW
HOPNET	Hybrid	ACO and zones	Single-path Single-GW	1- Developed to overcome the limitations of ZRP	1- Still single-path single-GW
B-iHTRP	Hybrid	ACO, PAO and zones	Single-path Single-GW	1- It is committed to combining the advantages of both ACO and PAO in order to boost effective efficiency	1- It does not consider the actual mobility model of nodes that do not fit into the real MANET environment 2- Single-path single-GW
AntHocNet	Hybrid	ACO	Multi-path Multi-GW	1- Low network overhead 2- Fast network discovery 3- Multi-path multi-GW	1- Suffer from looping in some scenarios 2- Large energy consumption
QACMOR	Proactive	QACO	Optimal Path	1- It is committed to combining the advantages of both ACO and quantum computing in order to select the best route.	1- Single path (best route)

lists the benefits and downsides of MANET routing protocols. Previous research combined ACO with pre-existing routing protocols to mitigate their drawbacks, using the latter as a proactive phase and the former as a reactive one. Our suggested protocol was based on QACO to deal with the increasing ACO complexity as more paths are studied and more iterations are needed to improve performance. Quantum parallelization and the entanglement of quantum states may greatly improve the efficiency with which the solution space of a massive optimization problem is explored. In contrast to the work presented in Ref. [38], which deals with the use of quantum-inspired ACO in choosing the best path in WSN, the suggested approach uses the QACO paradigm to find the best alternative path if any route’s connection fails. This is in addition to other tasks such as exploring new GWs, testing and maintaining existing GW paths, and exploring different paths to existing GWs. The aim of the current research is to find the Internet gateways without overloading the network, not to find the optimal routing path.

3. The Suggested QACO-Based GW Discovery Approach

The suggested approach was created so that nodes in MANET could automatically and efficiently search for GWs that were connected to the Internet. It is a three-step process that resulted in a hybrid protocol. During the offloading phase, a method was used that significantly reduced the extra work required by GWs due to control packet broadcasting by the GW in response to nodes in order to either find new paths or maintain the ones already established. During the reactive phase, new or already connected GWs were found by utilizing the QACO technique. During the proactive phase, established paths were monitored, novel connections were investigated, and problems with already established links were identified.

An array known as a pheromone table ($PH\_TABLE)$ contained the data structures generated by each node. Each path’s Neighbor ID $\left( N_{ID}\right)$, to which the MAC address of the node corresponds, Gateway ID ($G{W}_{ID})$ to which the GW MAC address corresponds, next node ID $(N{N}_{ID})$ that specifies the GW path’s next node identifier, the level (quantity) of pheromones ($PHQ)$ that measures the quality of the GW path through $N{N}_{ID}$, and Evaporation variable $\left(EV\right)$ that denotes the evaporation value of the $PHQ$, were recorded in this data structure. For each GW’s route, we determined the $PHQ$ by considering the lowest bandwidth $B{W}_{min}$ connection along the path and maximum queue length at any node along the route for all $N_{path}$.

$$B{W}_{min}=min\left(B{W}_I, B{W}_{I-1}\right)$$

(1)

$$Q_{max}=max\left(Q_I, Q_{I-1}\right)$$

(2)

where $B{W}_I$ and $B{W}_{I-1}$ represent the current and previous node’s bandwidth link. $Q_{max}$ is the queue length of the maximum node’s queue among the path, $Q_I$ and $Q_{I-1}$ are the current and preceding node’s queue sizes. $N_{path}$ symbolizes the total amount of route nodes.

In our case,$EV\in \left(0,0.5,1\right),$ in which 1 indicates that the route has been confirmed and may be used to send and receive data as well as update neighbors’ $PH\_TABLE$. A path status of 0.5 indicates that it needs to be verified and that a proactive procedure be launched to update that route, while a path status of 0 indicates that the path has expired and is not valid. The suggested protocol is a routing paradigm without the need of building nodes’ tree representation, in which each node discovers GWs instead of the GW broadcasting announcements. In the proposed approach, the QACO technique is employed to achieve this task. In QACO, an electronic packet represents the ant. Forward ant $FW\_ANT$ finds and explores all GW’s paths, while backward ant $BW\_ANT$ gathers the data needed to build the $PH\_TABLE$. Each step is explained below.

3.1. Offloading Phase

In the reactive and proactive stages of existing routing protocols, each network node transmits a control packet on a constant schedule to research the gateway or confirm its presence, and the gateway replays all of the packets, burdening the gateway to explore the network. To allow gateways to concentrate on internet access, we moved this effort to its neighbors. Every gateway sends periodic broadcast packets to its neighbors in this phase. To guarantee the broadcast stops at the next neighbor, it sets the TTL (time-to-live) counter to 1. Each neighbor may evaluate the GW’s quality and status based on this packet’s response and declare it down if it does not receive it. A gateway’s broadcast notification is sent out, neighbors identify themselves as GW neighbors (GWNs), and every node that verifies the GW’s availability receives a replay.

Much research has been conducted in the past years to determine an optimal path between source and destination nodes, which will result in maximizing the energy conservation of a network. However, the challenge is to create a routing algorithm that takes into consideration the major issues of minimizing energy consumption and maximizing network lifetime. Various optimization techniques are available to determine a routing path between a source node and destination node. In this paper, the goal of utilizing a quantum-inspired ant colony optimization procedure is to select the best route for internet gateways in case of detecting any connection failure in any route and attempting to fix that failure by discovering an alternative optimal path.

In its simplest form, ACO may move either forward (away from the nest and toward the food) or backward (from food back to the nest). In order to construct a solution, forward ants use a random number generator to choose a node from the set of neighbors of the current node. Pheromone trails left behind by other ants affect this probability decision. When coupled with predictable backwards movements, the lack of pheromone deposits made by forward ants aids in the elimination of loop development. Step by step, each ant constructs a solution to the problem using just the information available to it at the current node or along its outgoing arcs. The search procedure starts with priming all arcs with the same quantity of pheromone (${\mathcal{T}}_{ij}$ = 1). If ant k is currently at node i, it may use the pheromone trail ${\mathcal{T}}_{ij}$ to determine its likelihood of moving on to node j [18,19,44].

$$p_{ij}{}^k=\left\{\begin{array}{c}\frac{{\mathcal{T}}_{ij}^{\alpha }}{{\sum }_{j\in N_i^k}{\mathcal{T}}_{ij}^{\alpha }} if j\in N_i^k\\ 0, if j\notin N_i^k\end{array}\right.$$

(3)

$$f\left(j\right)=\left\{\begin{array}{c}arg\left\{\begin{array}{c}max\\ d=feasibl{e}_{k^{\left(t\right)}}{}^{\left[{\mathcal{T}}_{id}{\left(t\right)}^{\alpha }.{\eta }_{id}^{\beta }\right] } when r\le r0\end{array}\right\}\\ j^{\prime } when r>r0\end{array}\right.$$

(4)

$$P_{ij}^k\left(t\right)=\left\{\begin{array}{c}\frac{{\left[{\mathcal{T}}_{ij}\left(t\right)\right]}^{\alpha }.{\eta }_{ij}^{\beta }}{{\sum }_{d\in feasibl{e}_{k^{\left(t\right)}}}{\left[{\mathcal{T}}_{ij}\left(t\right)\right]}^{\alpha }.{\eta }_{ij}^{\beta }} if j\in feasibl{e}_{k^{\left(t\right)}} \\ 0, otherwise\end{array}\right.$$

(5)

$N_i^k$ is the neighborhood of ant k when located on node i (leaving out the node before i). From node i to node j, the transition function must satisfy the constraint $f\left(j\right)$. ${\mathcal{T}}_{id}\left(t\right)$ is the pheromone trail at time t, ${\eta }_{id}$ symbols the problem specific heuristic information, $\alpha$ is the impact of heuristic information, $r$ represents a random number with uniform distribution in [0, 1], $r0$ is the pre-specified parameter ranging from 0 to 1, inclusive, $feasibl{e}_{k^{\left(t\right)}}$ is the collection of possible nodes that the k-th ant might go before going to node i eliminating nodes that the k-th ant has previously visited (predecessor nodes) to avoid loop creation, and $j^{\prime }$ is the target location based on the probability distribution $P_{ij}^k\left(t\right)$.

Each ant deposits $\Delta {\mathcal{T}}^k$ units of pheromone before beginning a step-by-step retracing of the same path in reverse mode. The scanning procedure eliminates any established loops. This is how the pheromone value would change if ant k were to go backwards along the $arc\left(i,j\right)$. This process of upgrading pheromones increases the likelihood that subsequent ants will follow the same route.

$${\mathcal{T}}_{ij}^{\prime }={\mathcal{T}}_{ij}+\Delta {\mathcal{T}}^k$$

(6)

Exploration mechanisms such as pheromone trail evaporation ${\mathcal{T}}_{ij}^{\ast }$ help ants avoid quickly settling on a local best solution or a suboptimal approach. Pheromone trail attenuation is a process that encourages branching off into new directions over the whole search area.

$${\mathcal{T}}_{ij}^{\ast }\leftarrow \left(1-\rho \right). {\mathcal{T}}_{ij} \forall \left(i,j\right)\in E\left(G\right)$$

(7)

$E\left(G\right)$ represents the set of all arcs of the graph, and $\rho \in \left[0,1\right]$ is a parameter. To ensure that all arcs receive the same $\Delta {\mathcal{T}}^k$ quantity of pheromones, the evaporation and deposition processes are layered upon one another. However, in certain cases, the value of depositing extra pheromones to influence the search process from a non-local perspective is dependent on activating a local optimization technique to apply centralized actions.

Due to the sequential method of execution of the algorithms, the complexity of ACO grows dramatically with the rise in the number of paths explored and the number of iterations required to obtain better performance. The computational difficulty of searching a large optimization problem’s solution space may be greatly reduced with the use of quantum parallelization and entanglement in a quantum state [19,20]. Currently, Quantum Ant Colony Optimization (QACO) research utilizes Quantum-inspired Evolutionary Algorithms (QEA), which are fed by the probabilistic process of quantum computing.

Q-bits, the fundamental unit of data storage in QEA, is defined as ${\left[\alpha ,\beta \right]}^T$ where $\alpha$, and $\beta$ are complex integers representing the normalization condition ${\left|\alpha \right|}^2+{\left|\beta \right|}^2=1$. Each Q-bit may be translated into a single binary bit by a process of probabilistic observation. Equation (6) illustrates how a Q-bit representation, in which a single Q-bit is used to characterize a probabilistic linear superposition, may be generalized to a system with many Q-bits.

$$Q=\left[\left.\begin{array}{c}{\alpha }_1\\ {\beta }_1\end{array} \right|\left.\begin{array}{c}{\alpha }_2\\ {\beta }_2\end{array} \right|\dots \left|\begin{array}{c}{\alpha }_m\\ {\beta }_m\end{array}\right.\right]=\left[\left.\begin{array}{c}\frac{-\sqrt{3}}{3}\\ \frac{\sqrt{6}}{3}\end{array} \right|\left.\begin{array}{c}\frac{\sqrt{2}}{3}\\ \frac{\sqrt{7}}{3}\end{array} \right|\dots \left|\begin{array}{c}\frac{-\sqrt{5}}{3}\\ \frac{-2}{3}\end{array}\right.\right]$$

(8)

The superposed state of the 2³ = 8 states represented by $\left|000\right.〉$, $\left|001\right.〉$, $\left|010\right.〉,$ $\left|011\right.〉$, $\left|100\right.〉$,$\left|101\right.〉$, $\left|110\right.〉$, and $\left|111\right.〉$ in the previous example may be characterized as:

$$\begin{gathered} \left|\psi \right.〉=\frac{\sqrt{30}}{27}\left|000\right.〉+\frac{\sqrt{24}}{27}\left|001\right.〉-\frac{\sqrt{105}}{27}\left|010\right.〉+\frac{\sqrt{84}}{27}\left|011\right.〉+\frac{\sqrt{60}}{27}\left|100\right.〉-\frac{\sqrt{48}}{27}\left|101 \right.〉 \\ +\frac{\sqrt{210}}{27}\left|110\right.〉-\frac{\sqrt{168}}{27}\left|111\right.〉 \end{gathered}$$

(9)

Q-bit observation is used to build a standard binary solution by comparing each bit (or “observable”) of a binary individual (r) with the corresponding bit (or “observable”) of a Q-bit individual (P). To encode a message in binary, you would use the following:

$$\left\{\begin{array}{c}{r}_i=0, if {\left|{\alpha }_i\right|}^2>\eta \\ r_i=1, if {\left|{\alpha }_i\right|}^2\le \eta \end{array}\right.$$

(10)

where for a bit $r_i$ of a binary individual r, a chosen value of random number $\eta \in \left[0,1\right]$ is compared with ${\alpha }_i$. The output of the generation stage is then put through a quantum rotation gate $R\left(\theta \right)$ with the following operation:

$${\left[\begin{array}{c}{\alpha }_i\\ {\beta }_i\end{array}\right]}^{\prime }R\left(\theta \right)\left[\begin{array}{c}{\alpha }_i\\ {\beta }_i\end{array}\right]=\left[\begin{array}{cc}\cos {\theta }_i& -\sin {\theta }_i\\ \sin {\theta }_i& \cos {\theta }_i\end{array}\right]\left[\begin{array}{c}{\alpha }_i\\ {\beta }_i\end{array}\right]$$

(11)

A fitter state is reached by updating the quantum rotation gate. The rotation angle ${\theta }_i$ plays a crucial role in the effectiveness of EAs influenced by quantum mechanics.

$${\theta }_i=sign\left({\alpha }_i,{\beta }_i\right)\Delta {\theta }_i$$

(12)

Direction is indicated by the sign of the rotating angle ${\theta }_i$, which is represented by $sign\left({\alpha }_i,{\beta }_i\right)$. A table is used to search up the value of $sign\left({\alpha }_i,{\beta }_i\right)$ and $\Delta {\theta }_i$ based on how well the solution supplied by the current individual compares to the best solution so far.

The biggest drawback arising during the process of quantum state rotation comes in the reliance on employing a lookup table for setting the quantum rotation angle. A large reduction in search performance for an adaptive network due to a fixed rotating angle might severely limit the search’s applicability. Improving the inefficiency of a rotating-angle-updating method by increasing its local searching capabilities and locating an exit from local optima may be difficult [44].

3.2. Reactive Phase

In two cases, the reactive phase discovers previously undiscovered GWs. Whether a node does not already has a GW in its $PH\_TABLE$, it sends $FW\_ANT$ to all of its neighbors, asking if any of them have a GW. The second circumstance is continual discovery, when it has GWs but explores others. On this phase, it sends an $FW\_ANT$ to any neighbor that is not the next node in any GW’s route. Each neighbor receives an $FW\_ANT$, searches its $PH\_TABLE$, and verifies the $PHQ$ and $EV$ of any GWs. If the $EV$ = 1 for each $PHQ$, the route is confirmed and updated, the $FW\_ANT$ tour terminates, and it becomes a $BW\_ANT$. If $EV$ is equal to 0.5, the route is legitimate yet not up-to-date, and the route’s node updates it proactively [45].

After the proactive process for that route is complete, the $FW\_ANT$ is transformed to a $BW\_ANT$ and returned to the sending node. In case of $EV=0.5$, paths are skipped. If the received node’s $PH\_TABLE$ has no GW, to prevent loops, the $FW\_ANT$ sends to all its neighbors except the one it just received from. This procedure continues pending a node receives an $FW\_ANT$ with GW in its $PH\_TABLE$ or a GWN, at which point the $FW\_ANT$ is transformed to a $BW\_ANT$ and returned to the source node. The $BW\_ANT$ updates each node’s $PH\_TABLE$ with its $G{W}_{ID}$, $N{N}_{ID}$, and $PHQ$ based on its $B{W}_{min}$, $Q_{max}$, and $N_{path}$. The path with $EV=1$ is also updated.

3.3. The Proactive Phase

Maintaining the GW path(s) in the $PH\_TABLE$ is the responsibility of the proactive phase of the process. In this context, “maintain” refers to ensuring the route is available and collecting data on its quality. Each node’s $PH\_TABLE$ may include many GWs under typical conditions, and several possible routes may exist between each GW. The proactive procedure thus refreshes these routes, and the $EV$ rate establishes whether paths are active and up-to-date, which paths are active but need to be checked, and which paths have expired. Additionally, “if there are numerous GWs and their paths cross via the same neighbor node, only the $G{W}_{ID}$ with the greatest $PHQ$ will be stored in the $PH\_TABLE$” at the stage of proactive preparation, which finds better related GWs among present GW paths.

During the problematic discovery phase, the node made use of its neighbor nodes in an effort to find new connected GWs not registered in the $PH\_TABLE$ as $N{N}_{ID}$, and initially, when the node lacked GW, it was discovered via the reactive phase in its $PH\_TABLE$ and required to locate active GWs in the network. Every newly uncovered GW’s route is first recorded in the $PH\_TABLE$ with a $EV$ value of 1, indicating that it is valid and up-to-date. However, a node will set the $EV$ value to 0.5 if the route is not used for a while, indicating that it is not up-to-date and should be verified. The first step in this proactive procedure is to send an $FW\_ANT$ to the node containing the $N{N}_{ID}$ along the route in consideration, requesting an update on the $G{W}_{ID}$ in examination.

It then looks up the route in its $PH\_TABLE$, and if it finds the $EV=1$ of that path, it updates itself, changes the $FW\_ANT$ to a $BW\_ANT$, and transfers it back to the source node with the path’s $PHQ$. If the $EV$ is equal zero, the route is considered invalid, and the source node is notified through $BW\_ANT$ to terminate the connection. If the EV is 0.5, this node must likewise be verified and updated for that GW’s route, and it will continue to use the $N{N}_{ID}$ from its $PH\_TABLE$ to do the same process until the $FW\_ANT$ is converted to a $BW\_ANT$ by a node along the path with an $EV$ of 1 or until it reaches the GWN. At that point, no more $FW\_ANTs$ are sent to the GW as a result of the offloading procedure. After updating the $PH\_TABLE$ of each node along the $PH\_TABLE$ route, the $BW\_ANT$ then returns along the same path.

Finally, if the receiving node has a higher-quality new connected GW than the one requested by the source node, it will send the latter a $BW\_ANT$ by way of $EV$ equals 0 for the original $G{W}_{ID}$ route and the fresh $G{W}_{ID}$ and its assessment. In order to reflect the new $G{W}_{ID}$, the original node deletes the old $G{W}_{ID}$’s path from the $PH\_TABLE$ and adds a new record to the new $G{W}_{ID}$. Due to the multi-GW multi-path nature of the proposed model, its efficacy is conditional on the quality of the paths currently at hand in the $PH\_TABLE$, many gateways (GWs) and multiple pathways inside a single GW may be used by a node to transmit data to the internet. The best paths, or the subsequent $N{N}_{ID}$, are chosen by the node with a certain probability $P_{N{N}_{ID}}$ when picking a path to send the data [46].

$$P_{N{N}_{ID}}=\frac{{\left(PH{Q}_{GN}\right)}^{{\beta }_1}}{{\sum }_{j\in N{N}_{ID}^I}{\left(PH{Q}_{GJ}\right)}^{{\beta }_1}} {\beta }_1\ge 1$$

(13)

where $P_{N{N}_{ID}}$ is the likelihood that the $N{N}_{ID}$ will lead to the GW, $N{N}_{ID}^I$ is the collection of all possible $N{N}_{ID}$ paths leading to the GW, $PH{Q}_{GN}$ represents the pheromone level of the gateway’s rout via $N{N}_{ID}$, and ${\beta }_1$ denotes a threshold rate, which regulates the ants’ exploratory activity.

For QACO, quantum state preparation is performed to encode all potential routes traveled by ants on their way from food source to colony. In order for the quantum ants to choose between the encoded pathways uniformly at first, they will experience a process of uniform superposition. Moreover, before being executed, the algorithm assumes that no pheromone has been deposited along any potential routes. The suggested model uses a function to iteratively choose paths and modify the pheromone. During each cycle, pheromones will be deposited along the routes that were chosen and evaporated along the routes that were not. Convergence-criterion-satisfied paths are the only ones where pheromone updates are allowed. Maximum pheromone deposition will occur naturally along the “best-path” discovered after enough repetitions. Once we discover the path, we will measure the route in classical registers and then apply a phase shift and amplitude boost to pick it out of the original superposition of paths [44].

The quantum and classical registers for the ant colony optimization problem are initialized (Algorithm 1: the Establishment of Classical Constraints) to begin the procedure. After the problem is encoded and set up in the first stage, an iterative process (Algorithm 2: Quantum ants explore potential routes) is performed. With the use of Multiple Control Toffoli (MCT) gates, the Ant_ Execute () process selects pathways to be investigated next, and Update_ Pheromone () keeps the pheromone box up to date in which (Algorithm 3: the pheromone density revisions based on current travel routes). We avoid pheromone deposition along the route, with a density meaning that the pheromone box for that route is already at capacity. Furthermore, the paths with a pheromone density of 000…00 do not lose their pheromones, since the pheromone box for those routes is empty. In Algorithm 4, the pheromone density along the route of choice increases incrementally by unit. In Algorithm 5, excluding the “selected path,” “paths with a full pheromone density” and “paths with an empty pheromone density”, the pheromone density of all other paths decreases by one unit. The qubit expansion approach linked to pheromone box updating allows the utilized QACO algorithm (Algorithm 6: QACO Procedure) to display behavior that is similar to that of real ants. See [44] for more information.

Algorithm 1: Initialization

K → Number of iterations constant; n → Total possible routes; $W\left[n\right]$ → Weights along each path; $x\to \lceil lo{g}_{2}n\rceil$ Path encoding qubit count $Q\left[p_0\dots \dots p_{x-1}\right]$ → Qubits corresponding to paths; $Q\left[a_1\left],Q\right[a_2\left],Q\right[a_{target}\right]$ → Supplementary qubits d → Pheromone distribution encoding qubit count; $Q\left[p{h}_0\dots \dots p{h}_{d-1}\right]$ → Quantum bits for encoding pheromone distribution; $C\left[0\dots \dots x-1\right]$ → Classical register count for measurement purposes; Set $Q\left[p_0\dots \dots p_{x-1},a_1,a_2, p{h}_0\dots \dots p{h}_{d-1},a_{target}\right] as |0\rangle$ $H\left(Q\left[p_0\dots \dots p_{x-1}\right]\right)$ → The qubits along x encoded pathways are quantum superposed.

Algorithm 2: Ant _Execute ( )

While I in (0; n − 1) do If $t \% W\left[i\right]==0$ then $\mathrm{While} l in (p_0, p_{x-1)}$ do If $i \% 2==0$ then $NOT\left(Q\left[l\right]\right)$; End End $C^{x}NOT\left(Q\left[p_0,\dots \dots p_{x-1}\right], Q\left[a_1\right]\right)$; $C^{x}NOT\left(Q\left[p_0,\dots \dots p_{x-1}\right], Q\left[a_2\right]\right)$; While $l in (p_0$,$p_{x-1)}$ do If $i \% 2==0$ then $NOT\left(Q\left[l\right]\right)$ End End End End $NOT\left(Q\left[a_2\right]\right)$; Call Algorithm 3: Update_ Pheromone ( ) Reset $Q\left[a_1\right]$; Reset $Q\left[a_2\right]$;

Algorithm 3: Update_ Pheromone ( )

$C^{d}NOT\left(Q\left[p{h}_0,\dots \dots p{h}_{d-1}\right], Q\left[a_1\right]\right)$; Call Algorithm 4: Pheromone_ Deposition ( ) $C^{d}NOT\left(Q\left[p{h}_0,\dots \dots p{h}_{d-1}\right], Q\left[a_2\right]\right)$; $NOT\left(Q\left[p{h}_0,\dots \dots p{h}_{d-1}\right]\right)$ $C^{d}NOT\left(Q\left[p{h}_0,\dots \dots p{h}_{d-1}\right], Q\left[a_2\right]\right)$; $NOT\left(Q\left[p{h}_0,\dots \dots p{h}_{d-1}\right]\right)$ Call Algorithm 5: Pheromone_ Evaporation ( )

Algorithm 4: Pheromone_ Deposition ( )

$set r=p{d}_d-2$ While $m in \left(r,p{d}_0\right) do$ $C^{2}NOT\left(Q\left[a_1\right], Q\left[m\right], Q\left[m+1\right]\right)$; End $CNOT\left(Q\left[a_1\right], Q\left[m\right]\right)$

Algorithm 5: Pheromone_ Evaporation ( )

$set r=p{d}_d-2$ $CNOT\left(Q\left[a_2\right], Q\left[p{d}_0\right]\right)$; While $m in \left(p{d}_0, r\right) do$ $C^{2}NOT\left(Q\left[a_2\right], Q\left[m\right], Q\left[m+1\right]\right)$; End

Algorithm 6: QACO Procedure

Call Algorithm 1: Initialization While $t in \left(1,K\right)$ do Call Algorithm 2: Ant _Execute ( ) End $C^{d}NOT\left(Q\left[p{h}_0,\dots \dots p{h}_{d-1}\right], Q\left[a_{target}\right]\right)$; $Phase \left(Q\left[a_{target}\right],Q\left[P_{x-1}\right],\pi \right)$, //Target phase-shifting for the best achievable route $Amplification \left(Q\left[p_0,\dots \dots p_{x-1}\right]\right)$ //Quantum Amplitude Amplification $Measure Q\left[p_0,\dots \dots p_{x-1}\right] to C\left[0\dots \dots x-1\right]$ //global path convergence measurement

4. Results

In these simulations, we used the simulation package of MATLAB 9.1 (R2016B) to construct our routing approach. The simulation is run on a machine with a 64-bit UBUNTU operating system (Linux), 16 GB of RAM, and an Intel Core i7-11700K processor running at 3.6 GHz. AODV and HWMP were deployed and compared to our approach. AOVD was selected since MANET uses it widely and HWMP is the standard IEEE routing procedure. We then employed AntHocNet protocol as a BlackBox with default parameters to compare with our technique. AntHocNet is a biological algorithm based on ant colony optimization (ACO) for routing that can handle the dynamic nature of ad hoc networks, which is a hybrid routing protocol with multi-path multi-GW. In addition, it is frequently used, and all studies concur that it is one of the most efficient routing protocols in MANET. Several iterations and phases were used to conduct the simulation. As shown in

Table 2. MATLAB 9.1 simulation parameters.

Parameter	Value
1- Area	1000 × 1000 m
2- No of nodes	100, 100+
3- No of GWs	10 to 30
4- Radio type	802.11 b
5- Data Rate	2 Mbps
6- Channel frequency	2.4 GHz
7- No. of channel	1
8- Antenna model	Omni-directional
9- Application type	HTTP and video streaming
10- Packet size (byte)	512
11- Simulation time	5, 10, 50, 100, and 500 s

, we adjusted the number of nodes, GWs, and simulation periods in each cycle to evaluate and validate the stability of our approach under various settings and scenarios.

We presented the goals and results of three simulated rounds after executing each technique. We computed the outcome of each protocol’s reactive stage and analyzed the amount of time required for all nodes to identify all gateways throughout all accessible pathways in the first iteration. As shown in

Table 3. Initial discovery time for distinct routing techniques.

Routing Protocols	Discovery Times (s)
AODV Protocol	0.53
HWMP Protocol	0.55
AntHocNet Protocol (ACO-based routing)	0.51
Proposed Protocol (QACO-based routing)	0.39

, the suggested protocol enables network nodes to find all network gateways and paths to the matching gateway faster than other protocols. This is because, although other protocols began the exploration stage by broadcasting, only the suggested one required the packet of discovery to reach the gateway. The suggested approach terminates the delivery of the packet of discovery to any network’s node that has previously identified the GW, making it somewhat quicker than the alternatives.

The simulation was run three times with various numbers of new GWs (1, 3, 5, and 10 GWs) in the subsequent iteration to examine each protocol’s discovery time. According to

Table 4. Time to discover new GWs for distinct routing techniques.

Routing Protocols	Discovery Times of All Newly Connected GWs (s)
	1 GW	3 GWs	5 GWs	10 GWs
AODV Protocol	1.00	2.00	2.50	2.95
HWMP Protocol	0.65	0.64	0.67	0.68
AntHocNet Protocol(ACO)	0.72	0.73	0.75	0.79
Proposed Protocol (QACO)	0.50	0.39	0.40	0.41

, AODV requires a considerable amount of time to explore newly connected GWs due to the fact that it is a reactive or on-demand protocol that lacks a method for finding new GWs if it has one. In Table 3, as the protocols from the second to the fourth are hybrid protocols, they examined the GWs more quickly during the proactive phase. The discovery procedure takes less time with HWMP than with AntHocNet, since it may receive an announcement from the new GW. AntHocNet’s lengthy discovery time is the result of its need to traverse the whole forward and backward route to reach the GW. The suggested protocol, however, does not need direct communication with the GW, since it may instead obtain the GW’s location from any of the path’s neighboring nodes that have already located the GW. Therefore, the suggested approach outperformed the alternatives in terms of speed.

In the last iteration, we calculated the time needed to discover all GWs after adding the new node to the network. The discovery time for all GWs using the proposed protocol is shown to be extremely good in

Table 5. Time of new node to discover all GWs.

Routing Protocols	Discovery Times (s)
AODV Protocol	0.53
HWMP Protocol	0.30
AntHocNet Protocol (ACO)	0.50
Proposed Protocol (QACO)	0.07

for each newly joined node to the network. The newly inserted node in case of AODV and AntHocNet protocols initiates the first finding operation from the source (root) node to the GWs and inversely, whereas in HWMP, it waits until all GWs announce. However, the suggested procedure eliminates the requirement to contact every GW in the network; instead, when a new node initiates discovery, its neighbors instantly reply with a list of all available GW.

In addition, we took the following measurements at each iteration: the routing overhead, defined as the percentage of control packets sent in comparison to the total number of packets sent across the network, and the GW’s overhead, defined as the percentage of control packets sent in comparison to the total number of packets handled by the GW in both directions [40].

Table 6. Simulation running time-variant routing overhead.

Routing Protocols		Routing Overhead %
	5 s	10 s	50 s	100 s	500 s
AODV Protocol	16	11	9	10	11
HWMP Protocol	21	18	19	19	18
AntHocNet Protocol (ACO)	18	13	12	13	14
Proposed Protocol (QACO)	18	12	8	6	6

shows that all protocols started with broadcast, so their routing overhead was similar. Two broadcast packets were requested by HWMP—one starting from the node to learn about the network structure and one transmitting from the gateway to declare itself—which increased the routing cost. In case of AntHocNet protocol, by moving ants all the way frontward and backward, the GW’s availability is increased, increasing the routing control packets throughout the network, whereas HWMP used announcement (broadcast) in the reactive stage, increasing overhead. On the other hand, the proposed protocol negotiated with its neighbors to update its routing table. Due to the lack of proactive method, AODV’s overhead was reduced.

The benefits of the proposed protocol, including GW offloading, are listed in

Table 7. GW overhead over simulation running time.

Routing Protocols		Gateway Overhead %
	5 s	10 s	50 s	100 s	500 s
AODV Protocol	21	23	22	19	19
HWMP Protocol	23	16	14	14	15
AntHocNet Protocol (ACO)	21	23	18	17	17
Proposed Protocol (QACO)	4	3	5	4	4

. Depending on the volume of data flowing across the network, the GW overhead ranged from about 20% in AODV to about 17% in HWMP and from about 17% to about 23% in AntHocNet. In contrast, under the suggested protocol, it was only approximately 5%, since the GWN answered on behalf of the GW, drastically reducing the GW’s cost to an absolute minimum. We ended by following the steps taken to implement the suggested protocol. The final outcomes of each stage and iteration are shown in

Table 8. Protocol tracing result.

Tracing Parameter (s)	Result
1- Initial discovery time	0.93
2- Time to discover GWs	1 GW = 0.5, 3 GWs = 0.39, 5 GWs = 0.40, and 10 GWs = 0.41
3- Time of new node to discover GWs	0.07
4- Routing overhead over simulation running time	18% in 5, 10% in 10, 8% in 50, 6% in 100, and 6% in 500 s
5- Gateway’s overhead over simulation running time	4% in 5, 3% in 10, 5% in 50, 4% in 100, and 4% in 500 s

.

Table 9. Overhead routing results for different metaheuristics-based MENT routing protocols over various simulation node counts.

Routing Protocols		Routing Overhead %
	100 Node	200 Node	300 Node	400 Node	500 Node
GA_HocNet Protocol	10	13	17	22	27
PSO_HocNet Protocol	8	10	14	18	20
ABC_HocNet Protocol	7	8	12	16	17
QACO_HocNet Protocol	5	6	9	14	15

compares the performance of the built-in MENT routing protocol versions based on the genetic algorithm (GA_HocNet Protocol), the particle swarm optimization algorithm (PSO_HocNet Protocol), the artificial bee colony algorithm (ABC_HocNet Protocol), and the suggested routing algorithm based on QACO (QACO_HocNet Protocol). All routing protocols studied were run as black boxes with their default settings; for additional information on these protocols, see [47,48,49,50,51,52]. The comparison is based on their relative routing overhead as a function of node count. Despite a slight increase in the QACO_HocNet Protocol, packet receiving efficiency has improved. The routing balancing of the network’s load is causing the overhead promenade. According to the table, the routing overhead of the QACO_HocNet Protocol is less than that of the GA_HocNet Protocol, the PSO_HocNet Protocol, and the ABC_HocNet Protocol as the network size increases.

5. Conclusions

In this study, we provide a novel QACO-based, non-root-base routing protocol inspired by quantum mechanics. Initiating both reactive and proactive phases at the source node with the help of the QACO approach, this multi-gateway multi-path protocol requires few network broadcasts. Since algorithms are executed sequentially, ACO becomes more difficult to use as the number of pathways studied and the number of iterations needed to improve performance both increase. Quantum parallelization and entanglement of quantum states may significantly improve the efficiency with which the solution space of a large optimization problem is explored.

According to the incremental results, the proposed protocol performs better than the two typical state-of-the-art traditional protocols, AODV and HWMP, regarding the gateway’s time of discovery during the exploratory phase and the proactive path. The results also showed that this GW-discovering protocol is superior to other current bio-inspired routing systems such as AntHocNet. As opposed to sending the ant along the whole route, the proposed protocol instead enquires about the presence and quality of any nearby GWs, and it also introduces a new gateway’s offloading technique that considerably reduces the overhead of the gateways routing.

6. Future Work

Discovering GWs and their various routes while maintaining their dependability, quality, and efficiency were all addressed by the suggested protocol. In order to afford a comprehensive wireless routing protocol, we want to in the future provide support for discovery of the internal network. This involves locating nodes and their associated pathways inside the network. Future research will also need to address the issue of how to make a rotating-angle-updating approach more effective in QACO by enhancing its local searching skills and finding an escape from local optima.