Optimized routing with efficient energy transmission using Seline Trustworthy optimization for waste management in the smart cities

Traveling salesman problem for shortest path discovery

The TSP is used to find the shortest path between the Truck manager and the destination (IoT nodes) to collect the wastes from the dumpster before the waste overflows. The optimized routing path deployed with the graph connectivity is given by G=(N,ξ) where, N denotes the total number of nodes in the network and ξ represents the cost function for finding the connectivity between the IoT nodes and the truck manager, where the optimal shortest distance for routing is estimated using the Seline trustworthy optimization in the smart city. The number of IoT nodes in the smart city is represented by,

where, N denotes the nodes in the smart city, N_d highlights the dth IoT node within a CH, and U denotes the total number of nodes within the wireless communication range of the smart city. The shortest path for communicating in the smart city is estimated by the cost function and it is given by,

where, ξ is the cost function to find the minimal distance between the source and destination communication terminals in the smart city and BS terms the base station. To find the optimal minimum distance with maximum energy efficiency and minimal delay to avoid congestion in traffic with proper waste management in the smart city, the proposed Seline Trustworthy Algorithm is proposed.

1. Proposed Seline-Trustworthy Optimization for solving TSP: The proposed Seline-Trustworthy algorithm is developed by integrating the hybrid features, such as foraging and Paracrine signaling behavior of the honey bees (Gao and Liu 2012) and real ants (Dorigo, Birattari, and Stutzle 2006) and the major focus of the proposed optimization relies on estimating the shortest path between the source and destination communication terminals in the smart city. The proposed algorithm locates the best position of the food source in a short time, which in heuristics terms is named as global optimal convergence. The algorithm steps for the Seline-trustworthy optimization are as follows:

Motivation: The Paracrine signaling behavior and foraging characteristics of real ants and honey bees are inherited in the proposed Seline-trustworthy algorithm solving the shortest path convergence problems. Real ants find the best food source within the neighboring location while in search of the food and it secrets a chemical known as waft, which is secreted all along the way between the source (anthill) and destination (best search space) for finding the minimal distance for other ants. This characteristic feature of the real ants is inspired for finding the minimal paths. Moreover, the characteristics of the Paracrine signaling optimization enable the convergence to the global optimal solution with the higher tendency to avoid local convergence of the optimization.

Main phases of the Seline Trustworthy Algorithm: The main phases included in the optimization are considered as the initialization phase, construction of the individual solution, and search for the local agents to find the shortest path. The phase-wise explanation of the Seline Trustworthy Algorithm is discussed below:

1. Initialization phase: The significant step is the initialization of the waft and foraging, and Paracrine signaling behavior of the Seline. The Seline forages in the transverse left waft values, while the waft is volatile over time therefore, the higher the concentration of waft, the probability of attraction towards the Seline is higher. In the beginning, ‘B’ ants are placed randomly as given by,

where, F_ij represents the amount of data transmitted between the edge of nodes, the attractiveness of edge from i to j is calculated through dividing the length of the edge, which is denoted by E_ij and α, β are the parameters used to weight the relative influence of the Seline and attractiveness of the edge and k_n represents the set of unvisited nodes.

1. Construction of solutions: A constructive heuristic probability method is used to design the construction of solutions. A constructive method helps in the assembling of solutions from finite sets of solution components. In each construction, the current partial solutions are extended by adding the feasible solution component from the set. The process of constructing the solutions is considered as a walk or path on the construction graph given by,

The above Eq. (2) is a fully connected graph, whose vertices are the solutions of the component derived from the (1) and Ω is considered as the edges of the elements, which helps in finding the direction of the food source by considering the trails of the waft. Once the graph is constructed, the minimal paths are estimated as explained in the next phase.

1. Estimation of the fitness value for the solutions: Once the solutions are constricted, the fitness of the solutions is estimated so that the optimal solutions are declared. The distance measure considered is the distance, which should be minimal between the source and the destination nodes in such a way that the truck manager uses the shortest path or the optimal distance to dispose of the wastes dumped into the dumpsters.

2. Searching for the local agents: In this phase, the solution search is done and the solution is the connectivity between the nodes or the routing path, and the solution search in the proposed Seline optimization algorithm is improved, which boosts the performance of the application. The best search agent helps in finding the nearest distance between the source and the destination in minimal time. Moreover, the convergence to the local optima is avoided through the selection of the global optimal solution for which the characteristics of the paracrine signaling characteristics and foraging characteristics play a major contribution. The optimal path based on the paracrine signaling characteristics is given by,

where, ρ denotes the evaporation parameter in different nodes. The packet finding for the optimal path ΔFijn is given below,

where, (L/Gn) denotes the ‘n’ number of search agents using the vertices of edge nodes considering the optimal arc cost-effective function acr (i, j) in its Hamiltonian tour. Once the search agent updates the position, the best source is explored through the evaluation of the fitness value. Moreover, during the signaling phase, the memory of the path traversed is stored, which assists in storing the experience of the traversing path during the routing process. The detail regarding the congestion and delay is stored as the experience factors for a routing path. Thus, the updated equation specifying the paracrine signaling characteristics with p + 1 iterations is given by,

The characteristics of foraging are explained through the Waft updation trails, which aim to increase the trails based on the foraging behavior of honey bees for an individual solution to provide high-quality solutions. The characteristics of the foraging behavior are formulated as,

where, Cbestp determines the best solution at pth iterations, φ_i,j denotes the randomly generated values, and Fi,jp is the solution obtained at pth instance. Eq. (8) is reordered as,

On substituting (11) in (7),

The finalized optimized equation for the proposed Seline Trustworthy Algorithms is given by,

In the final Eq. (15), the position update of the search agents is illustrated. The regular updates in the solutions are done iteration-wise to enable the declaration of the global optimal solution. The fitness is computed for the updated solution to find the optimal solution in such a way that the shortest path is determined for waste disposal without delay. Moreover, the experience of the track manager in the best path Cbestp of the previous iteration is recorded so that the best optimal solution of the current iteration is declared. φ_i,j represents the random value and the value ranges from [0, 1]. The solution update at the current instance is represented by Fijp+1 and ρ rate is used to reduce the unwanted redundancy.

1. Feasibility of the solutions: The feasibility of the solutions is verified by checking the fitness of the current best solution with the fitness of the best solution in the previous instance. The solution with the maximal fitness measure is considered as the best solution of the iteration, while the other solution is discarded.

2. Termination: The steps are repeated for the maximal iterations and the best solution, which is the shortest path between the trust manager and the filled dumpster of the waste management system in the smart city, is declared.

Performance metrics

The proposed method is compared with the traditional state-of-art approaches based on the performance metrics namely, Delay, Throughput, Packet Delivery Ratio (PDR), and Energy. The performance metrics mentioned above enable predicting the future and support the selection of the shortest path with less congestion in traffic, which adds sufficient value in the waste management process of the smart cities.

Delay: Delay is defined as the maximum time required by the network for the transmission of data from source to destination. A communication/routing path with minimum delay is considered as the best path for waste disposal, which minimizes energy consumption and reduces the disposal time. The delay in the network is represented in the following equation,

where, A_a represents the delay in the network and J_a, N_a denotes the number of packets received in the network and the number of packets to be transmitted.

Packet Delivery Ratio (PDR): The PDR is described as the ratio of the number of packets to be transmitted to the total number of packets being received by the destination. The PDR is mathematically represented as,

where, N_a represents the number of packets to be transmitted and N_r denotes the number of packets to be received by the network.

Throughput: Throughput is described as the quantity of data that can be transferred within a certain period between the source and destination in the smart city. The network throughput is also defined as the rate at which the bits or the packets are successfully delivered over the network channel.

where, Q_N denotes the throughput of the network and J_a represents the number of packets transmitted successfully, and R_N represents the measurement period.

Energy: The amount of energy left on each sensor node and the cluster head at the end of the communication process in the smart city is the average energy of the network In smart cities, energy is considered a very important factor since it defines the lifetime of the network and the formulation of energy for sensor nodes (24) and cluster heads (25) is represented as follows,

where, ξγ+1(ZZt) and ξγ+1(ZXt) represents the updated energy of the sensor nodes and cluster heads respectively. ξγ+1(ZZt) denotes the initial energies of sensor nodes and ξγ+1(ZXt) represents the initial energies of cluster heads. ξk(ZZt) and ξk(ZXt) denotes the energy dissipated for the nodes and cluster heads, respectively.

Using 50 nodes

Figure 4 depicts the comparative analysis of the proposed method based on the delay, throughput, PDR, and Energy with the traditional methods for 50 nodes. Figure 4a demonstrates the analysis of the comparative methods based on the delay. At round_50, the delay of 0.17, 0.37, and 0.29 s is obtained for the traditional methods, such as ACO-TSP routing, ABC-TSP routing, and PSO-TSP routing, while the proposed Seline Trustworthy-TSP routing provides a lesser delay of 0.11 s in comparison with the traditional methods. Figure 4b shows the analysis of the methods based on the energy. In terms of energy, the conventional methods, like ACO-TSP routing, ABC-TSP routing, and PSO-TSP routing dissipate more energy during the communication, while the proposed method enables the communication through the shortest routing path, which lessens the energy dissipation in the nodes comparative with the traditional methods. Figure 4c illustrates the analysis of the methods based on the PDR. The traditional methods, like ACO-TSP routing, ABC-TSP routing, and PSO-TSP routing yield a PDR value of 0.94, 0.91, and 0.96, respectively at round_50, while the proposed method provides an increased PDR of 0.99 at round_50. In Figure 4d, the throughput analysis of the methods is presented. The existing methods ACO-TSP routing, ABC-TSP routing, and PSO-TSP routing possess the throughput of 1751, 1645, and 1500 kbps, respectively, while the proposed Seline Trustworthy-TSP routing provides the throughput of 2300 kbps. On analyzing the method based on the performance metrics, it is proved that the proposed method provides better performance in comparison with the existing methods.

Figure 4:

Comparative analysis of the methods with 50 nodes in the simulation area, (a) Analysis based on Delay, (b) Analysis based on Energy, (c) Analysis based on PDR, and (d) analysis based on the Throughput.

Using 100 nodes

Figure 5 demonstrates the analysis of the comparative methods based on the performance metrics. At round_50, the delay of 0.23, 0.36, and 0.28 s is obtained for the traditional methods, such as ACO-TSP routing, ABC-TSP routing, and PSO-TSP routing, while the proposed Seline Trustworthy-TSP routing provides a lesser delay of 0.14 s in comparison with the traditional methods is illustrated in Figure 5a. In Figure 5b, the performance metrics of energy for the conventional methods, such as ACO-TSP routing, ABC-TSP routing, and PSO-TSP routing are depicted, where the traditional method used more amount of energy at the time of collecting the wastes for round_100 from the IoT nodes, whereas the proposed method dissipates lesser energy in comparison with the traditional methods. Figure 5c illustrates the analysis based on the PDR of the methods. The PDR ratio for the traditional methods, such as ACO-TSP routing, ABC-TSP routing, and PSO-TSP routing are 0.9968, 0.9947, and 0.9905, respectively for the 100th round, while the proposed method acquired an increased PDR of 0.9981. In Figure 5d, the analysis of the methods based on throughput is enumerated. The existing methods, such as ACO-TSP routing, ABC-TSP routing, and PSO-TSP routing yielded the throughput of 7600, 6892, and 5750 kbps, respectively, while the proposed Seline Trustworthy-TSP routing provides an improved throughput of 9400 kbps in comparison with the traditional methods. Based on the above analysis, it is evaluated that the proposed method exhibited improved performance than the existing ones.

Figure 5:

Comparative analysis of the methods with 100 nodes in the simulation area, (a) Analysis based on Delay, (b) Analysis based on Energy, (c) Analysis based on PDR, and (d) Analysis based on the Throughput.

Using 150 nodes

The comparative analysis of delay, throughput, Packet Delivery Ratio, and Energy for the proposed method in comparison with the traditional methods for 150 nodes is illustrated in Figure 6. The estimated delay for the existing methods, such as ACO-TSP routing, ABC-TSP routing, PSO-TSP routing is 0.46, 0.36, and 0.3 s, while the proposed Seline Trustworthy-TSP routing provides a lesser delay of 0.26 s as illustrated in Figure 6a. In Figure 6b, the performance metrics of energy is shown, where the conventional methods, such as ACO-TSP routing, ABC-TSP routing, and PSO-TSP routing dissipate more energy from the IoT nodes at the time of collecting the wastes from the dumpsters for ACO-TSP routing and ABC-TSP routing, while the proposed Seline Trustworthy methods dissipate minimal energy in comparison with the traditional methods. Figure 6c shows the performance analysis based on the PDR. The traditional methods, such as ACO-TSP, ABC-TSP, and PSO-TSP yield the PDR of 0.997, 0.99, and 0.993 respectively at the 150th round, while the proposed method achieved an increased PDR of 0.998. In Figure 6d, the throughput analysis of the routing methods is presented. The existing methods, such as ACO-TSP routing, ABC-TSP routing, and PSO-TSP routing acquired the throughput of 16,800, 16,196, and 13,635 kbps respectively, while the proposed Seline Trustworthy-TSP method provides an increased PDR value of 21,600 kbps. On analyzing the method based on the performance metrics, it is proved that the proposed method provides better performance in comparison with the existing methods.

Figure 6:

Comparative analysis of the methods with 150 nodes in the simulation area, (a) Analysis based on Delay, (b) Analysis based on Energy, (c) Analysis based on PDR, and (d) Analysis based on the Throughput.

Using 200 nodes in the simulation area

Figure 7 depicts the comparative analysis of the methods based on delay, throughput, Packet Delivery Ratio, and Energy when the simulation is established using 200 nodes. The delay acquired by the existing methods, like ACO-TSP routing, ABC-TSP routing, and PSO-TSP routing are 0.632, 0.37, and 0.422 s, respectively, while the proposed Seline Trustworthy routing provides a lesser delay of 0.23 s in comparison with the traditional methods is illustrated in Figure 7a. Figure 7b shows the analysis based on the energy remaining in the nodes. Here, the conventional method dissipates a higher amount of energy at the time of collecting the wastes from the dumpster, whereas for the proposed method, the minimal energy is dissipated in comparison with the traditional methods. In Figure 7c, the PDR analysis is enumerated, where the traditional methods, such as ACO-TSP routing, ABC-TSP routing, and PSO-TSP routing reported the PDR of 0.998, 0.997, and 0.991, respectively at 200th round, while the proposed method achieved an increased PDR of 0.99. In Figure 7d, the throughput analysis of the methods is shown. The existing methods, such as ACO-TSP routing, ABC-TSP routing, and PSO-TSP routing record the throughput of 30,400, 28,426, and 25,431 kbps, respectively, while the proposed Seline Trustworthy-TSP routing obtains the throughput of 38,400 kbps. Based on the above analysis, it is evaluated that the proposed method provides improved performance compared with the conventional methods.

Figure 7:

Comparative analysis of the methods with 200 nodes in the simulation area, (a) Analysis based on Delay, (b) Analysis based on Energy, (c) Analysis based on PDR, and (d) Analysis based on the Throughput.