## 4 System Model
### Proposed Algorithm
7:\(N_{c}\leftarrow\) Number of Container. 8:\(fit\_val\leftarrow\) Fitness value vector. 9:\(alpha\leftarrow\) alpha wolf
10:\(beta\leftarrow\) beta wolf. 11:\(delta\leftarrow\) delta wolf. 12:\(alpha\_fit\_val\leftarrow\) Fitness value of alpha wolf. 13:\(beta\_fit\_val\leftarrow\) Fitness value of beta wolf. 14:\(pop\leftarrow\) population matrix of size(\(N_{p}\),\(p\_size\)). 15:\(P\leftarrow\) Coefficient Vector. 16:\(Q\leftarrow\) Coefficient Vector. 17:\(r_{1}\leftarrow\) Random Constant. 18:\(r_{2}\leftarrow\) Random Constant. 19:\(solution\leftarrow\) represents solution of the problem. 20:\(pop\leftarrow\phi\). 21:for\(i\gets 1\) to \(N_{p}\)do
22:\(temp\leftarrow\) create_chromosome(\(N_{c},N_{t}\))
23:\(pop\gets pop\cup temp\). 24:endfor
25:return\(solution\). 26:for\(t\gets 1\) to \(N\)do
27:\(fit\_val\leftarrow\) Fitness(\(pop\)). 28: Sort the \(pop\) according to \(fit\_val\) in ascending order. 29:\(alpha\leftarrow pop[0]\). 30:\(alpha\_fit\_val\gets fit\_val[0]\). 31:\(beta\leftarrow pop[1]\). 32:\(beta\_fit\_val\gets fit\_val[1]\)
33:\(delta\_\leftarrow pop[2]\). 34:\(delta\_fit\_val\gets fit\_val[2]\). 35:for\(i\gets 2\) to \(N_{p}\)do
36:\(a\gets 2-i\cdot(2/N_{p})\). 37:\(r_{1}\gets random()\)
38:\(r_{2}\gets random()\)
39:\(P\gets 2\cdot a\cdot r_{1}-a\)
40:\(Q\gets 2\cdot r_{2}\)
41:\(D\gets|\ Q\cdot X-pop[i-1]|\)\(\triangleright\)\(X\) is \(alpha\), \(beta\), \(delta\), \(pop[i]\gets X-P\cdot D\)\(\triangleright\)\(X\) is \(alpha\), \(beta\), \(delta\), \(delta\)
42:endfor
43:Sort the \(pop\) according to \(fot\_val\) in ascending order. 44:\(solution\leftarrow pop[0]\). 45:return\(solution\). ```  
**Algorithm 2** Grey Wolf optimization Algorithm```
1:Input:\(N,T_{0},T_{end},alpha\)
2:Output:\(solution\). 3:\(N\leftarrow\) Number of Iteration. 4:\(N_{t}\leftarrow\) Number of task. 5:\(N_{c}\leftarrow\) Number of Container. 6:\(fit\_val\leftarrow\) Fitness value. 7:\(T_{0}\leftarrow\) Initial Temperature. 8:\(T_{end}\leftarrow\) Ending Temperature. 9:\(new\_fit\_val\leftarrow\) New fitness value. 10:\(solution\leftarrow\) represents solution of the problem. 11:Initialize \(solution\) randomly. 12:\(fit\_val\leftarrow\) Fitness(\(solution\)). 13:while\(T_{0}>T_{end}\)do
14:for\(i\gets 1\) to \(N\)do
15:\(rnd\_pos\gets random(0,N_{t})\). 16:\(rnd\_num\gets random(0,N_{c})\). 17:\(temp\gets solution\). 18:\(temp[rnd\_pos]=rnd\_num\). 19:\(new\_fit\_val\leftarrow\) Fitness(\(solution\)). 20:if\(new\_fit\_val<fit\_val\)then
21:\(fit\_val\gets new\_fit\_val\). 22:\(solution\gets temp\). 23:else
24:\(delta\gets e^{\frac{new\_fit\_val-fit\_val}{t_{0}}}\)
25:\(rnd\gets random()\). 26:if\(delta>rnd\)then
27:\(fit\_val\gets new\_fit\_val\). 28:\(solution\gets temp\). 29:endif
30:endif
31:endfor
32:\(T_{0}\gets T_{0}\cdot alpha\). 33:endwhile
34:return\(solution\). ```

**Algorithm 3** Simulated Annealing Algorithm

## 5 Experimental Analysis and Results

The list of parameters considered to perform our experiment with the proposed system model is presented in Table 5. All the experiments were conducted in a non-elastic environment. To fix the number of iterations for optimization algorithm, we perform our experiment with a varying number of containers from 10 to 50 and number of tasks from 1000 to 3000 and considering 1000 iterations. A constant value was observed after 1000 iterations for load variation and makespan. Therefore, for our proposed algorithm, we fix the number of iterations to 1000. The initial population size has been considered to be 1000. We performed our experiment by varying different parameters and observed the results. In most cases, more than 97% of the tasks were meeting their deadline, i.e., they could finish their execution before the deadline. We have considered two important parameters for our experiment: load variation and makespan. The makespan is the total time taken to complete the execution of all the tasks. The variance is calculated to observe the load variation. If the variance is low, it indicates the even distribution of the workload.