Sustainable development of multi-media communication path of broadcasting and hosting with a dynamic environment

An improved bidirectional path search strategy

In the traditional ant colony algorithm, all ants search from the starting point to the target. We divide all the ants equally into two groups: group A and group B. Group A searches from the starting point to the ending point. In contrast, group B searches from the ending to the starting point. When two groups of ants meet, the paths of the two groups are connected to obtain a search path, which not only improves the search efficiency but also results in the global search’s insufficient ability. Therefore, we introduce the information exchange transfer factor in this article so that the two meeting ants can choose the route which has been travelled by each other or the random searching. (5)${\displaystyle mee{t}_{ij}=\left\{\begin{array}{cc}1,\hfill & ifi=joriisnearj.\hfill \\ 0,\hfill & others\hfill \end{array}\right.}$ (6)${\displaystyle op{t}_{ij}=\left\{\begin{array}{cc}1,\hfill & mee{t}_{ij}=1andrand>p_s.\hfill \\ 0,\hfill & mee{t}_{ij}=1andrand\le p_s\hfill \end{array}\right.}$

where Eq. (5) represents the conditions of the two ants meeting, in which we define the meet_ij to judge whether the ant i meets the ant j. In addition, we define the Eq. (6) to represent the judgment condition of whether two ants choose each other’s path, of which 1 is choosing and 0 represents non-choosing. Besides, we regard the random value as rand to represent the transfer probability of information exchange. p_s refers to a constant, which represents the information exchange transfer factor. If the rand is greater than this p_s, it means that two ants choose each other’s path and transfer.

Pheromone update strategy based on Wolf pack assignment

With the increase in the number of iterations, the pheromone of each path can be accumulated or returned to 0. We use the strategy of wolf allocation (Zhu, Zhu & Long, 2021; Wang & Zhang, 2022; He, Tao & Luo, 2022) to perform assignment by the updating mechanism of “survival of the strong”. In the iteration process, we refer to the “reward on merit” distribution strategy in the wolves algorithm to reward the good path and punish the poor path in each iteration. After adding the Wolf pack allocation strategy, we renew the updating rules of the pheromone, which can be shown in the following formulas: (7)${\displaystyle {\tau }_{ij}\left(t+1\right)=\left(1-\rho \right){\tau }_{ij}\left(t\right)+\sum _{k=1}^m\Delta {\tau }_{ij}^k+{\Delta }^p{\tau }_{ij}+{\Delta }^n{\tau }_{ij}}$ (8)${\displaystyle {\Delta }^p{\tau }_{ij}=\left\{\begin{array}{cc}\gamma \left(\frac{Q}{S^p}\right),\hfill & if\left(i,j\right)meetsthebestpath.\hfill \\ 0,\hfill & others\hfill \end{array}\right.}$ (9)${\displaystyle {\Delta }^n{\tau }_{ij}=\left\{\begin{array}{cc}\delta \left(\frac{Q}{S^n}\right),\hfill & if\left(i,j\right)meetstheworstpath.\hfill \\ 0,\hfill & others\hfill \end{array}\right.}$

We introduce the two parameters Δ^pτ_ij and Δⁿτ_ij for Eq. (7) where Δ^pτ_ij is the value of the pheromone that passes through the optimal route in each iteration, as shown in Eq. (8), with the optimal route evaluation value S^p of this generation. In contrast, Δⁿτ_ij is the pheromone value of the worst route for $\left(\mathrm{i},\mathrm{j}\right)$ in each iteration, as shown in Eq. (9), in which Sⁿ is the worst route evaluation value. And γ and δ are constants representing the reward coefficient for the best route and the penalty coefficient for the worst route, respectively.

Comprehensive evaluation model

We regard the heuristic function ω_ij as the expected degree of ant transfer from node i to node j, defined as Eq. (2) in the traditional ant colony algorithm. We consider the measuring method of a route to be not only the length of the reference route but also the number of listeners and the cost of consumption in transferring for the communication path of broadcasting and hosting programs. Therefore, we take the cost of business operating and the ratio of listeners’ occupancy as the optimization objective to establish a comprehensive evaluation model for the listener number and listening time constraints. The solution of the model can reflect the comprehensive consumption transferred from node i to node j, which can be applied to improve the heuristic function. (10)${\displaystyle ev{a}_{ij}=a\times di{s}_{ij}+\frac{b}{1+pe{o}_j}\times di{s}_{ij}}$ (11)${\displaystyle \sum _{j=1}^{n}pe{o}_j\le N}$ (12)${\displaystyle pe{o}_j=\sum _{i=1}^{v_j}p{t}_{ij}}$ (13)${\displaystyle {\omega }_{ij}=\frac{1}{ev{a}_{ij}}}$

Equations (10)∼(12) represent the comprehensive evaluation model and Eq. (13) represents the improved heuristic function where eva_ij denotes the comprehensive consumption of transformation from node i to node j, peo_j denotes the actual number of listeners in the next medium j, N denotes the expected number of broadcasting host programs, n is the total number of media, V _j indicates the expected audience of the medium j and pt_ji indicates the listening time of the i-th person in the medium j. Besides, $\mathrm{pt}\in \left[\mathrm{T},\mathrm{T}+\mathrm{X}\right]$ where T represents the start time of the current broadcast and X is the uncertain end time of the broadcast. In the ending, a and b is the adjustment parameter whose value is from 0 to 1. When the value of a is 1 and the value of b is 0, Eq. (13) degenerates into Eq. (2).

Parameter optimization based on improved particle swarm

The parameter value in the ant colony algorithm has a tremendous impact. Therefore, we employ the particle swarm’s strong global convergence ability to optimize the important parameters in the ant colony algorithm (Mousa & Hussein, 2022; Shami, El-Saleh & Alswaitti, 2022). Furthermore, we can complete the parameter optimization of the algorithm by repeatedly calling the ant colony algorithm in the process of multiple iterations. In this process, Eq. (15) is used as the standard to judge the quality of the parameters. (14)${\displaystyle syn\left(M_t\right)=\sum _{i,j\in M_t}ev{a}_{ij}}$ (15)${\displaystyle fit=\lambda \times \frac{1}{syn\left(M_t\right)}+\mu \times ite.}$

In Eq. (14), we set the i, j to be the connected node for the path M_t and define the eva_ij in Eq. (10). In Eq. (15), fit represents the fitness function value, $\mathrm{syn}\left({\mathrm{M}}_{\mathrm{t}}\right)$ is calculated from Eq. (14) and ite is the minimum number of iterations when the algorithm obtains the optimal solution. In addition, λ and µare constants with values from 0 to 1, representing the weight coefficient of the fitness function and the minimum number of iterations.

Firstly, we initial the particle populations. Subsequently, we bring the parameters searched by each particle to the improved ant colony algorithm. Finally, we compute the fitness of particles and select the optimal parameters following Eq. (15). During the search process, the moving speed and position of each particle are varied through the following formula: (16)${\displaystyle v_i\left(k+1\right)=\varepsilon v_i\left(k\right)+c_1{r}_1\left[pbes{t}_i\left(k\right)-x_i\left(k\right)\right]+c_2{r}_2\left[gbes{t}_i\left(k\right)-x_i\left(k\right)\right]}$ (17)${\displaystyle x_i\left(k+1\right)=x_i\left(k\right)+v_i\left(k+1\right)}$

where c₁ and c₂ denotes learning factors and ɛ represents inertia factor. In addition, r₁ and r₂ The random numbers ranging from 0 to 1 are used to adjust the search space of particles. We regard the individual and group optimal values as pbest_i and $\text{gbes}{\mathrm{t}}_{\mathrm{i}}\left(\mathrm{k}\right)$, respectively.

The shortest path planning

We consider that the communication path planning with the new media medium can be influenced by the propagation path length, listening to the number of factors and so on for the broadcasting programs. Therefore, we regard the propagation path length as the only evaluation metric to validate the simulation. To reflect the performance of the improved algorithm, we select the structure of the route network with a scale of 50 ×50 for simulation.

Firstly, we present the path results obtained by the traditional ant colony algorithm, Yunlong & Ying (2009) with bidirectional search strategy and our proposed algorithm in Fig. 2. At the same time, we show the optimal path length and the number of iterations in Fig. 3. We can demonstrate that the global search ability of the proposed algorithm is significantly improved, by which we can obtain the shorter path. However, the improvement of convergence ability is insufficient.

The traditional ant colony algorithm can achieve the optimal path length of 302.4. The path length corresponding to Yunlong & Ying (2009) is 290.94. In contrast, Yunlong & Ying (2009) improved the global search ability. Our proposed algorithm further enhances the global search ability and achieves the optimal path with a length of 285.88.

In addition, the traditional ant colony algorithm converges after 41 iterations, the algorithm used in Yunlong & Ying (2009) converges after 29 iterations and the algorithm that we propose converges after 36 iterations. Analysis shows that Yunlong & Ying (2009) and the proposed algorithm have improved the convergence speed compared with the traditional algorithm. However, the convergence speed of the algorithm that we propose is slightly less than Yunlong & Ying (2009).

The path planning of the comprehensive model

According to the conclusions above, the proposed algorithm has significantly improved compared to the traditional ant colony algorithm. In the transmission path problem of broadcasting and hosting programs, the path length is no longer the only indicator, but also the ratio of the listening should be considered. We should only reach the balance point between them to achieve the maximum profit.

To verify the superiority of the comprehensive performance for our proposed algorithm, we apply the comprehensive evaluation function as the fitness function’s evaluation metric for verification simulation. As shown in Eq. (14), the lower the overall score is, the better the path can be. To prove the algorithm’s effectiveness more intuitively, we choose a simple route network structure of 6 ×6.

Firstly, we present the path sought by the traditional ant colony algorithm and our proposed algorithm in Fig. 4. In addition, we list the various indicators of these two algorithms in Table 1. We can see from Table 1 that the path obtained by the algorithm that we propose is slightly longer than the traditional algorithm in length. But the number of listeners is significantly increased and the comprehensive score is lower than the traditional algorithm. Therefore, we can demonstrate that the algorithm in this article, which takes the comprehensive score as the standard, achieves great progress with the propagation distance and the number of listeners. At the same time, we boost the comprehensive optimization performance while comparing it with the traditional algorithm.

With the analysis, we can find that the 6 ×6 route network structure is relatively simple. These two algorithms can both traverse all paths. The traditional algorithm uses propagation distance as the only metric to obtain the shortest path of the model. However, we can achieve the optimal path of the route network model with the two indicators after considering the propagation distance and the number of listeners. With this comparison, the algorithm in this article is more satisfied with the company’s interests and achieves the unity of rapid dissemination and economic benefits.