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

Tianjin Key Laboratory of Wireless Mobile Communications and Power Transmission, Tianjin Normal University, Tianjin 300387, China Department of Communication Engineering, College of Electronic and Communication Engineering, Tianjin Normal University, Tianjin 300387, China Department of Electronic Information Science and Technology, College of Electronic and Communication Engineering, Tianjin Normal University, Tianjin 300387, China Department of Intelligence Science and Technology, College of Artificial Intelligence, Tianjin Normal University, Tianjin 300387, China


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 ings (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 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][12][13]. ereby, 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][21][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.

ACO Principle.
e 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]. e 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 m(m ∈ [1, M]), the number of nodes n(n ∈ [1, N]), and the distance between any two nodes i and j as d i,j (i, j � 1, 2, . . . n). At the moment t, the pheromone concentration on a path connecting the nodes i and j is τ i,j (t). In particular, at the initial time, τ i,j (0) � τ 0 . 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 P k i,j (t) can be expressed as where η i,j (t) is the heuristic function, representing the expected degree of the ant transfer from node i to node j, and B m 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 q 0 ∈ [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 ≤ q 0 , the next node maximizes [τ i,j (t)] α [η i,j (t)] β . In contrast, if q > q 0 , the state transfer probability determined by equation (1) remains unchanged: 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. e 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.

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. e antigen-antibody affinity indicates the recognition strength of a target node. us, the affinity function could be designed as a location model of the transmission of the node: where F v is the objective function, N is the set of all nodes, M i is a subset including the nodes i away from the base station closer than s, w i is the data volume of node i, d i,j is the distance between the nodes i and j, C is a manually selected large positive constant, and Z i,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 where k v,s is the number of same bits of two antibodies v and s and L is the length (number of bits) of antibody. en, the antibody concentration can be obtained as ereby, according to the affinity A v and the concentration C v above, the reproductive probability of an individual node is determined as 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.

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. us, 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]. erefore, 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]. e 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 τ i,j (t) described by where ψ ∈ (1, 0] is a constant, τ 0 � (mF nn ) − 1 is the initial value of the pheromone trajectory between the channel nodes, and F nn is the fit value calculated by the nearest distance heuristic algorithm. en, 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 where ρ is the volatile coefficient of pheromone and τ i,j (t) 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. e pheromone parameters are adjusted according to equations (1) and (2) to prevent the local optimal solution. e affinity function A v obtained by equation (3) is used to define the final D2D algorithm pheromone update:

Security and Communication Networks
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.
en, 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 of d max � 60m. According to the Friis transmission formula, the data rate becomes a univariate function of the distance d. erefore, the data rates of station-device (R bs ) and device-device (R dv ) are expressed as follows: In equation (10), f EH � 50GHz and f SH � 2.4GHz indicate the carrier wave frequencies of base station (extreme high frequency, EHF) and wireless devices (special high frequency, SHF), respectively. Accordingly, W EH � 500 MHz and W SH � 24MHz are the typical bandwidths of EHF and SHF, P tran bs max � 400W and P tran dv max � 1W are the typical power levels of EHF and SHF, P n � 3.981 × 10 − 21 WHz − 1 is the noise background power density, c � 3 × 10 8 ms − 1 is the radiowave propagation speed, and d ≤ d max � 60m is the distance between any two nodes. e distribution of all the wireless devices, as well as the relay nodes, within a service zone is assumed to obey the Gaussian distribution. erefore, in a representative loop l containing N l nodes, the time length of D2D communication T l is deduced as Based on equation (11), the total energy consumption can be calculated using T l values (including the values of devices T l,n 1 and base station T l D2D ). erefore, the optimization constraint for energy saving is expressed as By using equation (12), the ACO/AIA algorithm can be executed as an iterative program, until the convergence indicates the minimal energy consumption.

Simulation Results and Discussion
On the basis of the algorithm and constraint we discussed above, the D2D routing for the networking of an energysaving 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.
e 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].
Following the scheme in Figure 1, 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)). e 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)).
We then executed the programming iterations based on the 30-node example ( Figure 2) 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. ese numerical simulation results imply that the ACO/AIA fusion algorithm might be valid for the avoidance of local optimization disadvantages in the conventional algorithms.
Furthermore, the iterative optimization performances were quantitatively testified in the networking of 30-node situation. As shown in Table 3, 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. e 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.
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 Figure 5, 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.

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. e authors regard that the exploration of wireless IoT networking could be moved forward following this algorithmic method, concurrent to the hardware developments.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.