# Energy-Saving D2D Wireless Networking Based on ACO and AIA Fusion Algorithm

Authors: Jiatong Li; Zhibo Li; Xuanying Li; Cheng Wang
Journal: Security and Communication Networks
 (2021)

---

## Abstract

Lower energy consumption and higher data rate have been becoming the key factors of modern wireless mobile communication for the improvement of user experiences. At present, the commercialization of 5G communications is gradually promoting the development of Internet of things (IoT) techniques. Due to the limited coverage capability of direct wireless communications, the indirect device-to-device (D2D) communications using information relay, in addition to the single 5G base station deployment, have been introduced. Along with the increase of information nodes, the relay devices have to undertake the nonnegligible extra data traffic. In order to adjust and optimize the information routing in D2D services, we present an algorithmic investigation referring to the ant colony optimization (ACO) algorithm and the artificial immune algorithm (AIA). By analyzing the characteristics of these algorithms, we propose a combined algorithm that enables the improved the iterative convergence speed and the calculation robustness of routing path determination. Meanwhile, the D2D optimization pursuing energy saving is numerically demonstrated to be improved than the original algorithms. Based on the simulation results under a typical architecture of 5G cellular network including various information nodes (devices), we show that the algorithmic optimization of D2D routing is potentially valid for the realization of primitive wireless IoT networks.


---

## Body

## 1. Introduction

Since the late eighties of the last century, the Internet has been fast developing along with the progress of personal computers. Meanwhile, a concept of “connecting ubiquitous devices with Internet” emerged [1, 2] and further guided the research of the Internet of Things (IoT) for more comprehensive information sharing [3]. To date, the development of hardware techniques has made great progress. For instance, the fifth generation (5G) broadband communications employing high-frequency wavebands have unprecedentedly enhanced the data traffic performances [4]. However, it also has been noted that higher frequency leads to greater energy consumption due to the path loss of radio wave propagation [5]. As a result, the increasing dataflow requiring higher frequency inevitably encounters a power supply problem, which may lead to the unacceptable deployment density requirement of base stations [6, 7]. Therefore, for the wireless networking of IoTs, the dataflow pressure of central base station is a critical challenge [8, 9]. Under the current hardware development level, the direct routing scenarios using the traditional station-device communication scheme may not be suitable.Focusing on the issues above, we consider that the networking of wireless IoTs may have to fully utilize the current hardware and pursuing energy-efficient scenarios from the algorithm aspect [10]. Following this idea, the algorithmic solutions improving the dataflow without additional energy consumption are commonly related to an indirect device-to-device (D2D) communication architecture, by which the information nodes (e.g., mobile devices) also undertake the message relay missions to reduce the data pressure of the central base station via proper routing solutions [11–13]. Thereby, figuring out an appropriate routing solution via programmed calculations and algorithms is significantly important to the D2D networking [14]. We regard that the D2D routing is somehow similar to a classical mathematic problem which is the location of logistics distribution. To efficiently find out an available routing solution (may not be exactly optimized) under the specific constraint (e.g., energy efficiency in this work), the most well-known algorithms are the ant colony optimization (ACO) and the artificial immune algorithm (AIA) [15, 16]. First, ACO algorithms are usually adopted in wireless networking, which can be divided into two categories, the direct communication and the connectionless networks. In a direct one, all the message packets in the same loop propagate via a common path, which is selected by the preliminary setup state. On the contrary, the connectionless packets in the same loop propagate via different paths [17, 18]. For the routing solution problem, the ACO algorithms envision the even and random manners of the information nodes and update the potentially optimal paths step-by-step [19]. However, these algorithms are still hindered by some limitations to this day, such as the blind search and local optimum problems. To overcome these issues, the routing scenarios employing AIA have been investigated for the fast convergence and the global optimization [20–22]. Although the information feedback in AIA programming is usually inefficient, which may lead to severely redundant iterations, the global optimizing advantage complementary to that of ACO algorithms may potentially open up a novel feasible algorithm appropriate to the iterative calculations for the wireless D2D routing paths [23].Following these ideas, we proposed and a new algorithm, which combines the ACO and AIA principles, and quantitatively discussed the iterative calculation performances via numerical simulations. In particular, the physical environment of the D2D networking was designed based on the existing commercial 5G architecture, and the optimization constraint was accordingly selected as the reduce of energy consumptions [10, 24, 25]. According to the numerical simulation results, we showed that the newly designed algorithm significantly improves the D2D routing solutions, and the energy-saving performance may potentially enable the primitive wireless IoTs for sensor network applications.


## 2. Algorithm

### 2.1. ACO Principle

The ACO algorithm was originally developed for the vehicle routing problems (VRPs). Under this configuration, the feasible routing solutions are regarded as the paths of ants with similar mathematical models [18]. The paths of the entire ant population constitute a solution space. Here, we introduce the ACO algorithm into the D2D routing model. After each iteration, the ant colony in ACO judges the optimization feasibility of each subset in the solution space, according to the newest pheromone concentration, and finds the optimal path. To maintain the universality, we set the number of ants mm∈1,M, the number of nodes nn∈1,N, and the distance between any two nodes i and j as di,ji,j=1,2,…n. At the moment t, the pheromone concentration on a path connecting the nodes i and j is τi,jt. In particular, at the initial time, τi,j0=τ0. Considering that the next visiting node selected by ant k is determined by the pheromone concentration on the connection path between corresponding relay nodes s, the propagation probability denoted Pi,jkt can be expressed as(1)Pi,jkt=τi,jtαηi,jtβ∑s∈Bmτi,jtαηi,jtβ,nodes∈Bm,0,otherwise,where ηi,jt is the heuristic function, representing the expected degree of the ant transfer from node i to node j, and Bm represents the set of relay nodes visited by ant m. Especially, α is the pheromone factor, greater α leads to higher pheromone concentration effect in transfer. Similarly, β is the heuristic function factor; larger β suggests higher probability of a relay node being selected. Regarding the modelling of ACO in path routing, we assume that there are m ants in a quality of service (QoS) routing network, and the global and local pheromone updating rules are adopted [26]. Only the solution belongs to the global optimization path may lead to the increase of pheromone. We then select a constant q0∈0,1 as the transfer factor and define a random variable q∈0,1 to describe the determination of the next node. While an ant i in node r selects the next node s according to the following rules, if q≤q0, the next node maximizes τi,jtαηi,jtβ. In contrast, if q>q0, the state transfer probability determined by equation (1) remains unchanged:(2)ρir,s=maxpheromoner,s,nodes∈Bm0,otherwise.According to equation (2), the ant transfer state determines the output probability results, which ensure the path optimization by searching the local maxima.Following this principle, the ACO algorithms adopt the feedback mechanism and leave more concentrated pheromone in the paths, which indicates the better solutions. The positive feedback makes search processes continuously converging and finally approaching the optima. Any pheromone changes alter the surrounding environment and result in timely updates of the constraint result. Besides, if a suboptimal solution is utilized in the initial of calculation, the iterative convergence could be significantly accelerated. However, the rapid converging advantage may also induce a potential local optimum issue. As a result, other algorithms for the speed-optimum trade-off are necessary.


### 2.2. AIA Principle

To get rid of the local optimum hindrance, the node prediction step planning for the more effective global routing suggests the AIA principle [27]. Under the classical AIA configuration, the antigens represent the subsets of a solution space, and the antibodies represent the coding sets of corresponding relay nodes. The antigen-antibody affinity indicates the recognition strength of a target node. Thus, the affinity function could be designed as a location model of the transmission of the node:(3)Av=1Fv=1∑i∈N∑j∈Miωidi,jZi,j−C∑i∈Nmin∑j∈MiZi,j−1,0,where Fv is the objective function, N is the set of all nodes, Mi is a subset including the nodes i away from the base station closer than s, wi is the data volume of node i, di,j is the distance between the nodes i and j, C is a manually selected large positive constant, and Zi,j is the distribution relation of the transmission data traffic between the central base station and a relay node. In the denominator of equation (3), the second term represents the punishment for the spatial solution violating the distance constraint. In addition, the similarity among antibodies is expressed as(4)Sv,s=kv,sL,where kv,s is the number of same bits of two antibodies v and s and L is the length (number of bits) of antibody. Then, the antibody concentration can be obtained as(5)Cv=1N∑j∈NSv,s⋅Thereby, according to the affinityAv and the concentration Cv above, the reproductive probability of an individual node is determined as(6)P=αAv∑Av+1−αCv∑Cv,where α is an arbitrary constant factor. In equation (6), the individual fitness applies a positive effect on the expected reproduction probability. Higher affinity is helpful to the global optimization. However, due to the application of random searching, the efficiency of programming iteration and convergence are usually limited. On the basis of the discussion above, we considered to design a combined algorithm, which manages to concurrently take the advantages of ACO and AIA.


### 2.3. ACO/AIA Algorithmic D2D Routing

Under the current cellular network architecture, the deployment density increase of wireless devices (e.g., cellphones, unmanned equipment, and sensor array) results in the much greater data traffic pressure of the central base station. Thus, the traditional direct connection strategies are usually not available, especially on the energy consumption management aspect [28, 29]. In order to handle this difficulty, the D2D networking exploiting wireless devices as the relay nodes has to be proposed as a potentially applicable approach. Because of the requirement of routing determination in D2D networking, the algorithm performances in converging speed and accuracy are significantly important. As a result, the selection of information propagation paths has to be readily determined with the global optimization. As we discussed above, two representative algorithms (i.e., ACO and AIA) support the iterative programming for the optimal routing determination, and occupy advantages complementary to each other [30]. Therefore, we tried to combine them together to concurrently preserve their advantages. In this work, the D2D routing is discussed as a typical wireless IoT networking mission under the existing 5G architecture [25].The main idea of ACO/AIA fusion algorithm is replacing the worst antibody with the code represented by the best ant, thus to realize the information exchange between ACO and AIA. By using AIA, a series of starting times from the solution space can be selected to generate antibodies, and the ACO algorithm uses the solution space as the search range. On the basis of equation (1), we can further deduce the iterative update of pheromone τi,jt described by(7)τi,jt+1=1−ψτi,jt+ψτ0,where ψ∈1,0 is a constant, τ0=mFnn−1 is the initial value of the pheromone trajectory between the channel nodes, and Fnn is the fit value calculated by the nearest distance heuristic algorithm. Then, according to the guardian behavior in AIA, the optimal solution generated by ACO is used to stimulate the local search process. Meanwhile, the updating rules of pheromone trajectory are defined by(8)τi,jt+1=1−ρτi,jt+ρ∆τi,jt,ρ∈0,1,where ρ is the volatile coefficient of pheromone and τi,jt is the pheromone increment of at t. At the time t, the ants pass through the node once, the local and global pheromones need updates. The pheromone parameters are adjusted according to equations (1) and (2) to prevent the local optimal solution. The affinity function Av obtained by equation (3) is used to define the final D2D algorithm pheromone update:(9)pheromonei,j=1−ppheromonei,j+ρAv,nodesi,jon  path,1−ppheromonei,j+bρAv,otherwise.In equation (9), b∈0,1 is a constant, which prevents the exceeding pheromone concentrations on multipath. Before the D2D routing optimization algorithm is complete, it maintains the iteration until the final convergence is obtained.While the ACO/AIA fusion algorithm is proposed, we continue to discuss the constraint for the D2D networking optimization. Since our target is realizing a technically practical IoT scenario based on D2D routing, the optimization constraint is correspondingly set to make the total energy consumption minimized, at least lower than the traditional station-device direct communications. As the current communication techniques have almost approached the information channel capacity close to the Shannon limit, the data rate in this work is estimated by the upper limit. Then, based on the existing 5G architecture, we define the service zone covered by a single base station. Simply, we set a regular hexagon with the side length ofdmax=60m. According to the Friis transmission formula, the data rate becomes a univariate function of the distance d. Therefore, the data rates of station-device Rbs and device-device Rdv are expressed as follows:(10)Rbs=WEHlog21+PbsmaxtranGc/4πfEHd2pnWEH,d∈0,dmax,Rdv=WSHlog21+PdvmaxtranGc/4πfSHd2pnWSH,d∈0,dmax.In equation (10), fEH=50GHz and fSH=2.4GHz indicate the carrier wave frequencies of base station (extreme high frequency, EHF) and wireless devices (special high frequency, SHF), respectively. Accordingly, WEH=500MHz and WSH=24MHz are the typical bandwidths of EHF and SHF, Pbsmaxtran=400W and Pdvmaxtran=1W are the typical power levels of EHF and SHF, Pn=3.981×10−21WHz−1 is the noise background power density, c=3×108ms−1 is the radiowave propagation speed, and d≤dmax=60m is the distance between any two nodes. The distribution of all the wireless devices, as well as the relay nodes, within a service zone is assumed to obey the Gaussian distribution. Therefore, in a representative loop l containing Nl nodes, the time length of D2D communication Tl is deduced as(11)Tl=∑nl=1NlTl,nl=∑nl=1Nl1Rl,nl∑i=1nlIl,i⋅Based on equation (11), the total energy consumption can be calculated using Tl values (including the values of devices Tl,n1 and base station Tl_D2D). Therefore, the optimization constraint for energy saving is expressed as(12)E=Pdvmaxtran∑nlNlTl,nl+PbsmaxtranTlD2D⋅By using equation (12), the ACO/AIA algorithm can be executed as an iterative program, until the convergence indicates the minimal energy consumption.


## 2.1. ACO Principle

The ACO algorithm was originally developed for the vehicle routing problems (VRPs). Under this configuration, the feasible routing solutions are regarded as the paths of ants with similar mathematical models [18]. The paths of the entire ant population constitute a solution space. Here, we introduce the ACO algorithm into the D2D routing model. After each iteration, the ant colony in ACO judges the optimization feasibility of each subset in the solution space, according to the newest pheromone concentration, and finds the optimal path. To maintain the universality, we set the number of ants mm∈1,M, the number of nodes nn∈1,N, and the distance between any two nodes i and j as di,ji,j=1,2,…n. At the moment t, the pheromone concentration on a path connecting the nodes i and j is τi,jt. In particular, at the initial time, τi,j0=τ0. Considering that the next visiting node selected by ant k is determined by the pheromone concentration on the connection path between corresponding relay nodes s, the propagation probability denoted Pi,jkt can be expressed as(1)Pi,jkt=τi,jtαηi,jtβ∑s∈Bmτi,jtαηi,jtβ,nodes∈Bm,0,otherwise,where ηi,jt is the heuristic function, representing the expected degree of the ant transfer from node i to node j, and Bm represents the set of relay nodes visited by ant m. Especially, α is the pheromone factor, greater α leads to higher pheromone concentration effect in transfer. Similarly, β is the heuristic function factor; larger β suggests higher probability of a relay node being selected. Regarding the modelling of ACO in path routing, we assume that there are m ants in a quality of service (QoS) routing network, and the global and local pheromone updating rules are adopted [26]. Only the solution belongs to the global optimization path may lead to the increase of pheromone. We then select a constant q0∈0,1 as the transfer factor and define a random variable q∈0,1 to describe the determination of the next node. While an ant i in node r selects the next node s according to the following rules, if q≤q0, the next node maximizes τi,jtαηi,jtβ. In contrast, if q>q0, the state transfer probability determined by equation (1) remains unchanged:(2)ρir,s=maxpheromoner,s,nodes∈Bm0,otherwise.According to equation (2), the ant transfer state determines the output probability results, which ensure the path optimization by searching the local maxima.Following this principle, the ACO algorithms adopt the feedback mechanism and leave more concentrated pheromone in the paths, which indicates the better solutions. The positive feedback makes search processes continuously converging and finally approaching the optima. Any pheromone changes alter the surrounding environment and result in timely updates of the constraint result. Besides, if a suboptimal solution is utilized in the initial of calculation, the iterative convergence could be significantly accelerated. However, the rapid converging advantage may also induce a potential local optimum issue. As a result, other algorithms for the speed-optimum trade-off are necessary.


## 2.2. AIA Principle

To get rid of the local optimum hindrance, the node prediction step planning for the more effective global routing suggests the AIA principle [27]. Under the classical AIA configuration, the antigens represent the subsets of a solution space, and the antibodies represent the coding sets of corresponding relay nodes. The antigen-antibody affinity indicates the recognition strength of a target node. Thus, the affinity function could be designed as a location model of the transmission of the node:(3)Av=1Fv=1∑i∈N∑j∈Miωidi,jZi,j−C∑i∈Nmin∑j∈MiZi,j−1,0,where Fv is the objective function, N is the set of all nodes, Mi is a subset including the nodes i away from the base station closer than s, wi is the data volume of node i, di,j is the distance between the nodes i and j, C is a manually selected large positive constant, and Zi,j is the distribution relation of the transmission data traffic between the central base station and a relay node. In the denominator of equation (3), the second term represents the punishment for the spatial solution violating the distance constraint. In addition, the similarity among antibodies is expressed as(4)Sv,s=kv,sL,where kv,s is the number of same bits of two antibodies v and s and L is the length (number of bits) of antibody. Then, the antibody concentration can be obtained as(5)Cv=1N∑j∈NSv,s⋅Thereby, according to the affinityAv and the concentration Cv above, the reproductive probability of an individual node is determined as(6)P=αAv∑Av+1−αCv∑Cv,where α is an arbitrary constant factor. In equation (6), the individual fitness applies a positive effect on the expected reproduction probability. Higher affinity is helpful to the global optimization. However, due to the application of random searching, the efficiency of programming iteration and convergence are usually limited. On the basis of the discussion above, we considered to design a combined algorithm, which manages to concurrently take the advantages of ACO and AIA.


## 2.3. ACO/AIA Algorithmic D2D Routing

Under the current cellular network architecture, the deployment density increase of wireless devices (e.g., cellphones, unmanned equipment, and sensor array) results in the much greater data traffic pressure of the central base station. Thus, the traditional direct connection strategies are usually not available, especially on the energy consumption management aspect [28, 29]. In order to handle this difficulty, the D2D networking exploiting wireless devices as the relay nodes has to be proposed as a potentially applicable approach. Because of the requirement of routing determination in D2D networking, the algorithm performances in converging speed and accuracy are significantly important. As a result, the selection of information propagation paths has to be readily determined with the global optimization. As we discussed above, two representative algorithms (i.e., ACO and AIA) support the iterative programming for the optimal routing determination, and occupy advantages complementary to each other [30]. Therefore, we tried to combine them together to concurrently preserve their advantages. In this work, the D2D routing is discussed as a typical wireless IoT networking mission under the existing 5G architecture [25].The main idea of ACO/AIA fusion algorithm is replacing the worst antibody with the code represented by the best ant, thus to realize the information exchange between ACO and AIA. By using AIA, a series of starting times from the solution space can be selected to generate antibodies, and the ACO algorithm uses the solution space as the search range. On the basis of equation (1), we can further deduce the iterative update of pheromone τi,jt described by(7)τi,jt+1=1−ψτi,jt+ψτ0,where ψ∈1,0 is a constant, τ0=mFnn−1 is the initial value of the pheromone trajectory between the channel nodes, and Fnn is the fit value calculated by the nearest distance heuristic algorithm. Then, according to the guardian behavior in AIA, the optimal solution generated by ACO is used to stimulate the local search process. Meanwhile, the updating rules of pheromone trajectory are defined by(8)τi,jt+1=1−ρτi,jt+ρ∆τi,jt,ρ∈0,1,where ρ is the volatile coefficient of pheromone and τi,jt is the pheromone increment of at t. At the time t, the ants pass through the node once, the local and global pheromones need updates. The pheromone parameters are adjusted according to equations (1) and (2) to prevent the local optimal solution. The affinity function Av obtained by equation (3) is used to define the final D2D algorithm pheromone update:(9)pheromonei,j=1−ppheromonei,j+ρAv,nodesi,jon  path,1−ppheromonei,j+bρAv,otherwise.In equation (9), b∈0,1 is a constant, which prevents the exceeding pheromone concentrations on multipath. Before the D2D routing optimization algorithm is complete, it maintains the iteration until the final convergence is obtained.While the ACO/AIA fusion algorithm is proposed, we continue to discuss the constraint for the D2D networking optimization. Since our target is realizing a technically practical IoT scenario based on D2D routing, the optimization constraint is correspondingly set to make the total energy consumption minimized, at least lower than the traditional station-device direct communications. As the current communication techniques have almost approached the information channel capacity close to the Shannon limit, the data rate in this work is estimated by the upper limit. Then, based on the existing 5G architecture, we define the service zone covered by a single base station. Simply, we set a regular hexagon with the side length ofdmax=60m. According to the Friis transmission formula, the data rate becomes a univariate function of the distance d. Therefore, the data rates of station-device Rbs and device-device Rdv are expressed as follows:(10)Rbs=WEHlog21+PbsmaxtranGc/4πfEHd2pnWEH,d∈0,dmax,Rdv=WSHlog21+PdvmaxtranGc/4πfSHd2pnWSH,d∈0,dmax.In equation (10), fEH=50GHz and fSH=2.4GHz indicate the carrier wave frequencies of base station (extreme high frequency, EHF) and wireless devices (special high frequency, SHF), respectively. Accordingly, WEH=500MHz and WSH=24MHz are the typical bandwidths of EHF and SHF, Pbsmaxtran=400W and Pdvmaxtran=1W are the typical power levels of EHF and SHF, Pn=3.981×10−21WHz−1 is the noise background power density, c=3×108ms−1 is the radiowave propagation speed, and d≤dmax=60m is the distance between any two nodes. The distribution of all the wireless devices, as well as the relay nodes, within a service zone is assumed to obey the Gaussian distribution. Therefore, in a representative loop l containing Nl nodes, the time length of D2D communication Tl is deduced as(11)Tl=∑nl=1NlTl,nl=∑nl=1Nl1Rl,nl∑i=1nlIl,i⋅Based on equation (11), the total energy consumption can be calculated using Tl values (including the values of devices Tl,n1 and base station Tl_D2D). Therefore, the optimization constraint for energy saving is expressed as(12)E=Pdvmaxtran∑nlNlTl,nl+PbsmaxtranTlD2D⋅By using equation (12), the ACO/AIA algorithm can be executed as an iterative program, until the convergence indicates the minimal energy consumption.


## 3. Simulation Results and Discussion

On the basis of the algorithm and constraint we discussed above, the D2D routing for the networking of an energy-saving IoT was testified via the programming iteration. After each iteration, the constraint result is calculated and fed back to the next iteration for the asymptotic minimization of constraint [30]. In particular, according to the existing 5G standard, the D2D sequence information amount sent by a base station is set as a constant of 10 Mb, and the data amount of a device is randomly generated obeying the Gaussian distribution within the range of 50–200 Mb. The programming scheme of out ACO/AIA fusion algorithm is illustrated in Figure 1, and the parameters used in the programming are provided in Table 1. In addition, to verify the performance advantage of our new algorithm, the classical ACO and AIA algorithms are also testified under the completely same conditions for comparisons [31].Figure 1
Programming scheme of the ACO/AIA algorithm for energy-saving optimization.Table 1
Algorithm programming parameters.
ParametersValuePopulation size100Memory capacity10Crossover probability0.5Mutation probability0.1Diversity evaluation parameter0.95Pheromone index2Heuristic index3Pheromone volatility coefficient0.1Pheromone enhancer1Following the scheme in Figure1, we first generate the information nodes (wireless devices) within a hexagonal cellular network service zone. As shown in Figure 2, the node positions including data amounts are randomly generated (30 nodes as a representative example in Figure 2(a)). The positions and data amounts of 30 nodes are also detailed in Table 2. While all the nodes are covered by a central base station, a traditional station-device direct connection model is constructed (Figure 2(b)).Figure 2
A representative wireless networking model containing 30 nodes. (a) Random generation of information nodes within a service zone. (b) Traditional direct communication strategy.
(a)(b)Table 2
Node position and data amount information corresponding to Figure2.
Nodex-coordinate (m)y-coordinate (m)Data size (Mb)00001−29.75076725−21.145198228.8074986−32.371182339.513467952.8557669348.864290527−17.86911115−26.04441642−28.50671196−12.298411770.593461897−21.6799826224.5320698810.2703786314.2535886948.777410111.93168611010−10.4339343336.8657126111.760926681−4.1052880122.5529069146.706503521316.18910379−9.73259791425.227759352.95136701525.233759023.78786610416−37.3286405517.5382412017−34.73651287−16.57198318−5.951438079−25.81988619−41.53044014−2.107418320−19.18381344−22.3525822121.7005287620.786928922−34.21303177−18.425582330.45716541−6.4209711224−17.23243667−25.56317625−16.96341148−4.05674612618.3806822524.1265610127−4.98049597−7.19577143284.651289738−25.77341082926.9371720433.0504610230−20.95107025−24.637759We then executed the programming iterations based on the 30-node example (Figure2) and presented the routing results in Figure 3. Comparing with the classical ACO and AIA algorithms, our novel fusion algorithm significantly reduces the large-span connections. And, the interferences between loops are also reduced. These numerical simulation results imply that the ACO/AIA fusion algorithm might be valid for the avoidance of local optimization disadvantages in the conventional algorithms.Figure 3
D2D routing results acquired from ACO, AIA, and ACO/AIA fusion algorithms (30 nodes in Figure2).Furthermore, the iterative optimization performances were quantitatively testified in the networking of 30-node situation. As shown in Table3, all the results acquired from three algorithms approach stability after around 300-time iterations. However, the ACO/AIA algorithm exhibits much higher energy efficiency than the other two algorithms, as shown in Figure 4. The much higher energy consumption levels of ACO and AIA algorithms, especially the classical ACO algorithm, provide the relatively high final results, which imply the local optimization issue as we mentioned above.Table 3
Optimization trends of energy-saving D2D networking (30-node) along with the iterations of ACO, AIA, and ACO/AIA fusion algorithms.
The number of iterationsTotal energy consumptionACOAIAACO/AIA1292150.8678325210.4059242842.10092194461.987325210.4059242842.10093194461.987325210.4059240157.053⋯⋯⋯⋯⋯⋯⋯⋯100194461.987227245.520998898.74869⋯⋯⋯⋯200194461.987128434.194676446.35832⋯⋯⋯⋯300194343.9423125626.134573241.97747301194343.9423125626.134573241.97746302194343.9423125626.134573241.97746303194343.9423125626.134573241.97746Figure 4
Energy efficiency optimization trends of ACO, AIA, and ACO/AIA fusion iterations.Moreover, in order to further verify the universality of our algorithm in the energy-saving optimization, the cases including more devices (information nodes) were tested. As shown in Figure5, the representative examples of D2D networking of 70, 150, 200, and 300 nodes optimized by using the ACO, AIA, and ACO/AIA fusion algorithms, respectively, are compared with each other. We discovered the consistent regularity that the ACO/AIA algorithm possesses the best energy efficiency and the convergence performance.Figure 5
D2D routing results of 70, 150, 200, and 300 nodes optimized by ACO, AIA, and ACO/AIA fusion algorithms. Obviously, the ACO/AIA fusion algorithm provides much high iteration efficiency in the optimization for energy saving.Besides, we would like to note that although D2D routing significantly enhances the energy efficiency, the time latency in indirect connections is an inevitable issue hindering the practical applicability. To overcome the time-delay hindrance, the final solution may still focus on the hardware developments, together with the algorithm investigations.


## 4. Conclusion

In summary, we investigated the D2D routing scenarios for the energy-efficient networking from the algorithm aspect. Based on the numerical simulation results, we illustrated that the program iteration is a technical option for the construction of primitive D2D wireless IoTs, under the current hardware developing level. More importantly, we proposed a D2D routing algorithm based on the classical ACO and AIA algorithms. By testing the iterative optimization under the energy-saving constraint, the novel ACO/AIA fusion algorithm provides more satisfactory converging performances than traditional algorithms. The authors regard that the exploration of wireless IoT networking could be moved forward following this algorithmic method, concurrent to the hardware developments.



---

*Source: 5781166-2021-09-07.xml*