GenACO a multi-objective cached data offloading optimization based on genetic algorithm and ant colony optimization

Related works

Cached data offloading is an extraordinary capability required to be owned by an application, workstation, server, and network to manage data storage considered to be larger than its capacity (Zulfa, Hartanto & Permanasari, 2020). It is a very common method used in cloud computing (Wang et al., 2019; Li et al., 2020a; Li et al., 2020b), mobile computing (Dutta & Vandermeer, 2017; Zhu & Reddi, 2017), operating system (Silberschatz, Galvin & Gagne, 2008; Tian & Liebelt, 2014), and telecommunication Prerna, Tekchandani & Kumar (2020).

Luo et al. (2017) examined the energy consumption optimization in Mobile Edge Computing (MEC) by formulating objective functions based on the variables of energy consumption, backhaul capacities, and content popularity. The research utilizes the GA algorithm with the optimization function to minimize the energy consumption value and validated by measuring the system average delay and average power toward adding the MEC servers and backhaul capacity. Moreover, Xu et al. (2019) also proposed a data offloading optimization framework named COM, designed to optimize mobile devices execution time and energy consumption. The COM framework was used to model a multi-objective optimization solved using the NSGA-III algorithm. It was validated by calculating the maximum value of the utility and resource utilization functions achieved.

Pescosolido, Conti & Passarella (2019) developed a Content Delivery Management System (CDMS) method for device-to-device data offloading in cellular networks. It was proposed to predict system performance in transmission distance and energy consumption using simulations configured with Infrastructure-to-Device (I2D) transmission and Base Stations. The research was validated through the efficiency of data offloading and Physical Resource Block (PRB). Furthermore, Zhao et al. (2019) proposed mobile data offloading by predicting the real-time traffic Small Base Station (SBS) on MEC using a multi-Long Short-Term Memory (LSTM) algorithm. The results predicted were further used for data offloading by utilizing the Cross-Entropy (CE) algorithm. The research formulated the problem with an optimization approach to determine the maximum value from the system throughput.

Huang et al. (2019) also developed the Deep-Q Network (DQN) framework to solve data offloading optimization and resource allocation in MEC using energy costs, computation costs, and delay costs as variables. The optimization was modeled with mixed-integer non-linear programming solved by Reinforcement Learning (RL) algorithm, and the DQN was validated by calculating the minimum total cost generated. Another research by Elgendy et al. (2019) focused on resource allocation optimization and computation offloading with additional data security protection in MEC. The security protection was conducted by adding the Advanced Encryption Standard (AES) algorithm to prevent cyber-attacks. At the same time, the optimization problem was modeled based on the knapsack problem and solved using a branch and bound algorithm. Its implementation was further validated by determining the smallest value of time and energy consumption.

Kuang et al. (2021) modeled data offloading and resource allocation in one cooperative scheme to optimize power allocation and CPU cycle frequency in MEC and, subsequently, to make appropriate data offloading decisions. The research was measured by calculating the smallest possible task latency value and also adopted the Convex optimization method, dual Lagrangian decomposition, and ShenJing Formula. Another study by Zhong et al. (2021) discussed a caching strategy framework to optimize traffic load, and QoS in Multi-access Edge Computing named GenCOSCO. The aim was to minimize the task execution time as a Mixed Integer Non-Linear Programming (MINLP) optimization problem by considering the heterogeneity of task requests, pre-storage of application data, and cooperation of the base station variables. The GenCOSCO was used to propose the FixCS algorithm and was validated by calculating the average latency.

Moreover, Peng et al. (2021) proposed an application paradigm as a service chain for detailed data offloading and location caching mechanisms. Each service chain was limited by leasing costs and designed according to the queuing theory in computer networks. The research was further validated by calculating the average response delay towards increasing cache server time and capacity.

Wang et al. (2019) also studied the cached data offloading optimization on the edge network to reduce requests made to the origin server for the same data. The focus was on the cache capacity on the limited edge network, which means each cached data needed to be prioritized. The optimization problem was proposed using a knapsack problem. This research used cyclic ACO-GA with three variables: access count, access time, and data size. Research by Wang et al. (2019) is used as the baseline in our study because, based on our manual calculations, there is an opportunity to improve the value of the formulated objective function. The previously generated objective function value is 0.4374, but this value can be even more optimal up to 0.4350. This is a strong basis for us to improve the performance of CGACA.

Genetic algorithm (GA)

GA was first introduced by John Holland in a publication entitled Adaptation in Natural and Artificial Systems Holland (1992) and observed to have adopted several phenomena such as natural selection and mutation for survival. GA used these adaptation principles to improve solutions in each generation Purnomo (2014). One other main principle is a crossover, a cross-breeding mechanism between two individuals (parents) to produce better quality offspring than both parents. It illustrates in Fig. 2, where two individual chromosomes (parents) create new offspring working in groups with other genes to form a chromosome. This chromosome represents a solution vector from the completed case study, with each gene can mutate based on a certain probability, as illustrated in Fig. 3.

Meanwhile, the quality of the genetic algorithm solution vector was measured by a fitness value. The highest value among the existing chromosomes is selected when the genetic algorithm finds the maximum optimization value. This fitness value was, calculated using the following Eq. (1). GA also uses elitism to maintain one or several of the best individuals in the next generation to produce other individuals with better fitness values Santosa & Ai (2017). (1)${\displaystyle fitness=\frac{1}{f_{\left(x\right)}+\varepsilon }}$

Ant colony optimization (ACO)

Dorigo first introduced ACO to find the shortest path in the Travelling Salesman Problem case study (TSP) (Dorigo, Maniezzo & Colorni, 1996). This algorithm adopts the behavior of ant colonies from the nest to the food source. Each ant can leave a pheromone trail on each of its paths. The pheromone substances are from endocrine glands, which can identify fellow ants or their groups by serving as a solid signal to influence other ants to follow in the footsteps of this pheromone. At first, each ant can determine its route and leave a pheromone trail to identify others, as indicated in Fig. 4.

Moreover, the pheromone can evaporate, which means its path is lost faster on longer routes than shorter ones. It is difficult for other ants to follow the path on a longer route due to the evaporation of the pheromone trail. In comparison, the shorter route still has traces even though the first pheromone has disappeared, but it regains the path through the pheromone from other ants. The stronger signal attracts other ants to follow the same trail, as shown in Fig. 5. An ant k at node r can select a route s(i,j) based on a certain probability, and those that have completed a route leaves a pheromone trail (τ) of τ_i,j←τ_i,j + Δτ^k while the vaporized pheromone is calculated using ${\tau }_{i,j}\leftarrow \left(1-\rho \right){\tau }_{i,j}$ where ρ is a predetermined constant.

Cyclic ACO-GA

The performance of the Cyclic ACO-GA (CGACA) proposed by Wang et al. (2019) was improvised in this study to improve its final result by obtaining a more optimal objective function value. It is important to note beforehand that CGACA conducts cyclical algorithmic exchange between ACO and GA with the ACO algorithm run in the first iteration. At the same time, the next solution search process is implemented through GA. ACO is applied when GA experiences stagnation in five successive iterations until the maximum iteration is achieved. Moreover, The ACO algorithm in CGACA used the roulette wheel, which has an unfavorable impact due to its production of random solutions and superior individuals (Moodi, Ghazvini & Moodi, 2021; Lipowski & Lipowska, 2012). However, the CGACA framework proposed by Wang et al. (2019) does not provide settlement action in a situation where the GA does not experience stagnancy. It means the GA does not have a full role in exploiting the solution to the fullest.

The results of our initial research showed that the ACO algorithm takes the longest time when compared to GA and binary Particle Swarm Optimization (BPSO) in completing the cached data optimization. The worst-case scenario in CGACA will occur if the GA algorithm experiences a solution stagnation at the beginning of the iteration so that ACO will be rerun until the iteration is complete. Such a situation makes the ACO iteration dominate, so the total CGACA time consumption becomes very large. Table 1 explains the important weakness points to be considered in improving the CGACA performance.

GenACO

GenACO is an optimization framework that we propose to improve the performance of CGACA produced by Wang et al. (2019). GenACO was proposed using the constant r0 to overcome the roulette wheel weakness in solution probabilities. The r0 value is used to balance exploring candidate solutions in the early iterations and focuses on exploiting the optimum solution at the end of the iteration. In addition, GenACO has two execution modes, namely cyclic and non-cyclic. Both managed to improve the quality of the solution.

Table 2 describes the rationale of GenACO maintaining the cyclic ACO-GA hybrid method. Figure 6 illustrates the step of the proposed hybrid GenACO. The ACO algorithm is needed to generate the best initial population for GA. The r0 has been used in this step. If the GA has a stagnant solution, the last ACO will run again until the iteration ends. Detail explanation about r0 will be explained further in the next section.

The Knapsack problem is a classic optimization problem that can be solved using brute force or greedy methods. However, the greedy method does not guarantee an optimal solution, while the brute force has a very high time complexity of O(2ⁿ). Based on Fig. 6, assuming n is cached data, m is the number of GenACO ants, and Nc is the iteration used, then the complexity of GenACO is O(Nc*n*m). Consequently, the time complexity of GenACO is better than the classical method.

Solution probability

The ACO algorithm plays an essential role in generating the solution required by the GA to produce the best population. However, the disproportionate use of trace pheromones can cause the best solution of Eq. (4) not always to appear. The ACO algorithm in GenACO no longer uses the roulette wheel to select a solution from all the ants. It was replaced by adding r0 as a constant to be compared with a random number r [0,1], such that when r0 > r, the ant selects the cached data with the enormous pheromone value and selects the cached data randomly when otherwise. (2)${\displaystyle {\tau }_i\left(t\right)=w_1\ast \frac{ct\left(i\right)}{total\left(ct\right)}+w_2\ast \frac{fr\left(i\right)}{total\left(fr\right)}+w_3\ast \frac{sz\left(i\right)}{total\left(sz\right)}}$

The initialization of the pheromone value (τ) follows Eq. (2) by using three cached data property values, which include the access count (ct), access time (fr), and data size (sz) with each multiplied by its respective weight w1 = 0.3 w2 = 0.3 w3 = 0.4 Wang et al. (2019). Moreover, the visibility function in Eq. (3) also influences the choice of solutions made by the ant colony. Therefore, the probability of cached data is selected and entered into the cache server follows Eq. (4). (3)${\displaystyle {\eta }_i\left(t\right)=w_1\ast \frac{ct\left(i\right)\ast fr\left(i\right)}{sz\left(i\right)}}$ (4)${\displaystyle P_i\left(t\right)=\frac{{\tau }_i{\left(t\right)}^{\alpha }\ast {\eta }_i{\left(t\right)}^{\beta }}{{\tau }_i{\left(t\right)}^{\alpha }\ast {\eta }_i{\left(t\right)}^{\beta }+{\tau }_i{\left(t\right)}^{\alpha }\ast {\eta }_i{\left(t\right)}^{\beta }}}$

The r0 constant value becomes very important in determining the direction of ACO algorithm solution selection in GenACO. The simulation showed the r0 = 0.5 is suitable for placing in the first iteration of ACO to make the GenACO explore as many potential solutions as possible and not easily trapped on the local optimum in the initial iterations. In addition, r0 = 0.9 is planned to be set in the second part of ACO when the GA experiences a solution stagnation. This part is expected to focus more on exploiting the search for the optimum value. Based on experience, it will be difficult for the random number r[0,1] to be greater than 0.9. Therefore setting this value seems to force ACO always to choose the cached data with the most significant probability. The use of r0 in GenACO is illustrated in Table 3.

Table 3:

Illustration on the use of r0 in the three cyclic GenACO steps.

DOI: 10.7717/peerjcs.729/table-3

Cyclic and non-cyclic GenACO

GenACO proposed two modes, cyclic and non-cyclic, to improve CGACA performance. The first mode is described in Table 3. In contrast, the second mode only runs the ACO algorithm once in the first iteration, after which the GA algorithm continues fully up to the maximum iteration. The non-cyclic mode does not use r0 = 0.9 to avoid the local optimum in the initial iteration. Therefore we used r0 = 0.7, which is expected to balance the exploration and exploitation of solutions in the first iteration, as illustrated in Table 4.

Table 4:

Illustration on the use of r0 in the two GenACO non-cyclic steps.

DOI: 10.7717/peerjcs.729/table-4

Cached-data representation

The ACO and GA algorithms have different solution vector representations in modeling cached data. In the GA algorithm, a chromosome creates as much array space as the total data, with each representing the 0/1 condition of one cached data. A value of 1 indicates that the selected cached data will be entered into the cache server. At the same time, 0 means it will not be included. Meanwhile, in the ACO algorithm, the array space only consists of several routes selected by the ants. One ant and another may have a different number of selected routes.

Moreover, the route chosen by this ant represents a collection of cached data to be entered into the cache server, and the ACO solution representation on GenACO duplicates how ACO works in solving TSP. Figures 7 and 8 illustrate an example solution of GA and ACO, respectively.

Multi-objective function

GenACO can solve the cached data offloading optimization problem using the knapsack problem approach as a multi-objective optimization model. Its multi-objective optimization is built using three property values which include access count (ct), access time (fr), and data size (sz) contained in each cached data. However, not all data can enter the cache server due to the limited capacity. Therefore, their priority value was determined based on these three property values.

These three variables also have their respective objective functions. The objective function of access count is in line with Eq. (8); access time with Eq. (9); and data size with Eq. (10), Wang et al. (2019), multiplied by their respective weights w₁ = w₂ = 0.3, and w₃ = 0.4, which is then calculated the final objective function as profit (Fx) following (Eq. 11), Wang et al. (2019).

The smaller Fx indicates high priority. The n dataset consists of cached data candidates of x₁, x₂, x₃, …, x_j that can be entered by the cache server with capacity S and profit F_x. Meanwhile, each x_j consists of access count (ct), access time (fr), and data size (sz). Furthermore, the GenACO is expected to determine the solution vector x_j when x_j = 1 to calculate objective function. The cached data is ignored when x_j = 0 and will not be included in the objective function calculation following Eq. (11). Therefore problem definition following Eq. (7).

(7)${\displaystyle \sum _{j=1}^{n}profit\left(F_x\right)x_j\le S}$ (8)${\displaystyle f_{CT}=\frac{1}{n}\sum _{j=1}^n\frac{D_{c{t}_{\left(j\right)}}-D_{c{t}_{\left(min\right)}}}{D_{c{t}_{\left(max\right)}}-D_{c{t}_{\left(min\right)}}}}$ (9)${\displaystyle f_{FR}=\frac{1}{n}\sum _{j=1}^n\frac{D_{f{r}_{\left(j\right)}}-D_{f{r}_{\left(min\right)}}}{D_{f{r}_{\left(max\right)}}-D_{f{r}_{\left(min\right)}}}}$ (10)${\displaystyle f_{SZ}=\frac{1}{n}\sum _{j=1}^n\frac{D_{s{z}_{\left(j\right)}}-D_{s{z}_{\left(min\right)}}}{D_{s{z}_{\left(max\right)}}-D_{s{z}_{\left(min\right)}}}}$ (11)${\displaystyle F_x=w_1\ast \left(1-f_{CT}\right)+w_2\ast \left(1-f_{FR}\right)+w_3\ast f_{SZ}}$

Performance measurement

Evolutionary algorithms such as ACO and GA are widely used to complete optimization work. Generally, the optimization performance measurement through the continuous domain is usually measured by the optimum value of the objective function and the solution convergence time achieved (Sahu, Panigrahi & Pattnaik, 2012; Sun, Song & Chen, 2019). Meanwhile, the knapsack problem belongs to a discrete domain. Therefore, additional performance indicators are the best and worst profit, the average profit achieved, and the total number of items in the knapsack (Rizk-Allah & Hassanien, 2018; Li et al., 2020a; Li et al., 2020b; Liu, 2020). However, the best solution in the cached data offloading optimization case study was selected based on the highest number of knapsack items with the lowest objective function value.

Dataset

GenACO was tested by datasets used in Wang et al. (2019) with three cached data property: access count (ct), access time (fr), and data size (sz) with their respective sizes in Mbit, decimal, and second. Moreover, the maximum capacity of the cache server was 950 Mbit. The dataset can be accessed through the given GitHub repository.

Simulation setup

The single ACO and GA scenario was divided into four scenarios. Moreover, the CGACA scenario was repeated three times to observe the solution stagnation position experienced by GA. The results were compared with the proposed cyclic and non-cyclic GenACO. The simulation was conducted using 10 particles and 20 iterations with the parameter settings of the six scenarios presented in Table 5. Both parameters were adopted from Wang et al. (2019) then simplified because the best solution average has been found in such particles and iterations range. The simulation was conducted using PHP programming language and Mysql database to facilitate our subsequent research in implementing fog computing architecture.

Results and discussion

Comparison of stagnant solution CGACA and GenACO

Figure 9 showed the solution stagnation of the three ACO–GA hybrid simulations. The first ACO on CGACA obtains an initial solution that is not very good. This situation impacts GA performance which fails to improve the initial solution so that it is quickly trapped in the local optimum. Moreover, the roulette wheel mechanism and the probability of crossover and mutation cause GA to fail to improve this initial solution. In the end, GA stuck to the solution stagnation from iterations 2 to 5. The GA algorithm, which stagnated the solution far from the best known, caused the last ACO hard to improve the solution and achieve solution convergence. However, the roulette wheel mechanism used by the last ACO at CGACA failed to fix this until the maximum iteration.

The GA algorithm on Cyclic GenACO also suffers from a solution stagnation. However, before solution stagnation occurred, GA had a better initial solution. GA successfully maximized the initial solution of the first ACO to become an optimal solution. However, because the optimal solution is equal in five consecutive iterations, it is considered a stagnation of the solution. In the end, the last ACO on cyclic GenACO was executed, but the optimal solution previously generated could not be maintained. We suspect this situation was caused by set r0 = 0.9, so the solution fell out from the previous optimum. In future work, this will be our concern so r0 in the last ACO can be more adaptive to the previous solution.

The use of r0 = 0.7 in the non-cyclic GenACO simulation succeeded in obtaining a better initial solution than CGACA and cyclic GenACO. This situation makes GA job easier. In addition, the proper parameter setting on the probability of mutation and crossover makes GA performance more reliable. It can be seen in the performance of GA, which can maintain the optimal solution until the maximum iteration.

Based on Fig. 9, non-cyclic GenACO is the best solution for average solution quality and total time consumption. However, GenACO cyclic and non-cyclic modes did not have a significant difference in total time consumption. Non-cyclic GenACO is only 4.5 s ahead of cyclic mode. Based on Tables S4, the saving time obtained by GenACO can be calculated using Eq. (12). (12)${\displaystyle Savin{g}_{time}=\frac{\left(CGACAexec.time-GenACOexec.time\right)}{CGACAexec.time}\ast 100\text{\%}.}$

Therefore, we calculated cyclic GenACO saving time consumption by up to 38%, while non-cyclic GenACO saving it by 47%. Both GenACO modes can be accepted as a solution to the problem of cached data offloading. The ACO algorithm is very appropriate to use in the first iteration to create an excellent and reliable initial population, making it easier for GA to find the optimal solution quickly and good average quality of the solution.