# _electronics_
## 3 Coded Packages Naming Lookup and Cache Placement
### Solving Multi-Objective Optimization Problems Based on the Multi-Colony Ant Colony Algorithm  
Since the multiple objectives of the multi-objective optimization problem are mutually constrained and exclusive, each objective cannot reach its optimal value at the same time; generally, only a set of optimal solution sets can be obtained, which is called the Pareto optimal solution [25]. This paper uses a multi-colony ant colony algorithm to solve the optimization problem. The ant colony algorithm is divided into multiple groups according to the number of objective functions, the searches are independent of each other, and the pheromone exchange between the groups is carried out according to certain rules; finally, the Pareto optimal unties. In this algorithm, the solution variable is \(O_{w_{s,i,j}}\), and the value interval of each variable is divided into \(\{0,1,\ldots,k\}\) nodes; each \(O_{w_{s,i,j}}\) has \(k+1\) selection nodes. Ant \(q\) will choose the path with a high pheromone concentration as the moving direction with a higher probability. The transition probability can be derived as follows:  
\[P_{(O_{w_{s,i,j}},O_{w_{s,i,j}})}^{q}(t)=\left\{ \begin{array}{l}\dfrac{\left[ \gamma_{O_{w_{s,i,j}},O_{w_{s,i,j}}}(t)\right]^{a}\left[\eta_{O_{w_{s,i,j}},O_ {w_{s,i,j}}}(t)\right]^{\beta}}{\sum\limits_{O_{w_{s,i,j}}\leq allowed_{q}} \left[\gamma_{O_{w_{s,i,j}},O_{w_{s,i,j}}}(t)\right]^{a}\left[\eta_{O_{w_{s,i,j }},O_{w_{s,i,j}}}(t)\right]^{b}},O_{w_{s,i,j}}\leq allowed_{q}\\ 0,\textit{otherwise}\end{array} \right. \tag{10}\]  
where \(P_{(O_{w_{s,i,j}},O_{w_{s,i,j}})}^{q}(t)\) is the probability that ant \(q\) transfers from the node with the number of \(O_{w_{s,i,j}}\) coded blocks under the satellite node \(w_{st}\) to the node with the number of \(O_{w_{s,i,j}}\) coded blocks under the satellite node \(w_{sr}\) at time \(t\). \(\gamma_{O_{w_{s,i,j}},O_{w_{s,i}}}(t)\) is the pheromone concentration on the link at time \(t\). \(\eta_{O_{w_{s,i,j}},O_{w_{s,i}}}(t)\) is the heuristic degree of the link at time \(t\), and \(\alpha\) and \(\beta\) represent the importance of pheromone and heuristic function factors, respectively; \(allowed_{q}\) is the node set of the number of coded blocks that ant \(q\) can still access under the satellite node \(w_{sr}\). \(\eta_{O_{w_{s,i,j}},O_{w_{s,i}}}(t)\) is the expected degree of the ant moving from the \(O_{w_{s,i,j}}\) coded block number node under the satellite node \(w_{st}\) to the \(O_{w_{s,i,j}}\) coded block number node under the satellite node \(w_{sr}\) at time \(t\). For the multi-objective optimization model proposed in this paper, the backhaul link load and content acquisition delay are inversely proportional to the expected degree, which can be expressed as the following formula:\[\eta_{O_{w_{Adj}},O_{w_{Adj}}}(t)=\left\{ \begin{array}{c}\frac{1}{O_{w_{Adj}} \cup_{w_{Adj}}}\\ \frac{1}{T_{O_{w_{Adj}},O_{w_{Adj}}}}\\ \end{array} \right. \tag{11}\]  
When ant \(q\) passes through a path, it will update the pheromone content on the path, so that the pheromone on the path will increase \(\Delta\tau_{\big{(}O_{w_{Adj}},O_{w_{Adj}}\big{)}}^{q}(t)\). When all ants complete an iteration, the pheromone increment on the path will be \(\sum_{q=1}^{Z}\Delta\tau_{\big{(}O_{w_{Adj}},O_{w_{Adj}}\big{)}}^{q}(t)\); \(\rho\) is the pheromone volatile factor, and \(0<\rho<1\); the local pheromone is updated by the following formula:  
\[\tau_{O_{w_{Adj}},O_{w_{Adj}}}(t+1)=(1-\rho)\tau_{O_{w_{Adj}},O_{w_{Adj}}}(t) +\sum_{q=1}^{Z}\Delta\tau_{\big{(}O_{w_{Adj}},O_{w_{Adj}}\big{)}}^{q}(t) \tag{12}\]  
Under the backhaul link load target and content acquisition delay target, when the backhaul link load and content acquisition delay of the selected path is smaller, the pheromone concentration on the selected path increases more, inspiring more ants to choose this path.