Microservice combination optimisation based on improved gray wolf algorithm

Figures & data

Figure 1. Horizontal crossover operation.

Figure 2. Vertical crossover operation.

Table

Algorithm 1. Algorithm of CGWO

Input: popNum, dim, maxIter, p1

Output: $\overrightarrow{X_{\alpha }}$, f($\overrightarrow{X_{\alpha }}$)

1: initialise($\overrightarrow{X}$); t = 1

2: $\overrightarrow{X_{\alpha }}$, $\overrightarrow{X_{\beta }}$, $\overrightarrow{X_{\delta }}$← calculateFitness($\overrightarrow{X}$)

3: while t ≤ maxIterNum do

4:  update($\overrightarrow{A}$, $\overrightarrow{C}$) // Update the parameters$\overrightarrow{C}$ and $\overrightarrow{A}$ using equation 5 and 10

5:  update(p) // Randomly generated probabilities p

6:  update($\overrightarrow{X}$) // Use equation 9 to update the location of individual grey wolves in the population

7: if (p≤p1) do

8:   rnums = randnums(popnum) //puts the integers from 1 to popnum into the rnum array after random sorting

9: for i = 1 to popnum/2 do / / horizontal cross

10:   n1 =  rnums[2i-1], n2 =  rnums[2i]

11:   for d = 1 to dim do

12:    $\overrightarrow{X_{hc}}$(n1, d) = r1*$\overrightarrow{\mathrm{X}}$(n1, d) + (1-r1) * $\overrightarrow{\mathrm{X}}$(n2, d) + c1*($\overrightarrow{X}$(n1, d)-$\overrightarrow{X}$(n2, d))

13:    $\overrightarrow{X_{hc}}$(n2, d) = r2*$\overrightarrow{\mathrm{X}}$(n2, d) + (1-r2) * $\overrightarrow{\mathrm{X}}$(n1, d) + c2*($\overrightarrow{X}$(n2, d)-$\overrightarrow{X}$(n1, d))

14:   end for

15:   if (f($\overrightarrow{X_{hc}}$(n1)) > f($\overrightarrow{X}$(n1))), $\overrightarrow{X}$(n1) = $\overrightarrow{X_{hc}}$(n1)

16:   if (f($\overrightarrow{X_{hc}}$(n2)) > f($\overrightarrow{X}$(n2))), $\overrightarrow{X}$(n2) = $\overrightarrow{X_{hc}}$(n2)

17:  end for

18:  d1 = randInt(dim); d2 =  randInt(dim) //vertical cross, d1, d2 are any integers of [1, dim]

19:  for i = 1 to popnum do

20:   $\overrightarrow{X_{vc}}$(i, d1) = r *$\overrightarrow{X}$(i, d1) + (1-r) * $\overrightarrow{X}$(i, d2)

21:   If(f($\overrightarrow{X_{vc}}$(i))>f($\overrightarrow{X}$(i))), $\overrightarrow{X}$(i) = $\overrightarrow{X_{vc}}$(i)

22:  end for

23: end if

24: $\overrightarrow{X_{\alpha }}$, $\overrightarrow{X_{\beta }}$, $\overrightarrow{X_{\delta }}$ ← calculateFitness($\overrightarrow{X}$)

25: t = t+1

26: end while

Table 1. Experimental results of the exhaustive enumeration method for microservice combination A and microservice combination B.

Combination ID	Service Instance Configuration	Search Space Complexity	Global Optimal QoSsol	Execution time (ms)
A	{20, 15, 10, 10, 5, 5}	750, 000	0.624	10297
B	{15, 15, 5, 5, 5, 5, 5, 5}	3, 515, 625	0.625	42009

Table 2. Experimental results of CGWO optimisation for microservice portfolio A.

No.	p1	Initial population size	Number of iterations	Average best QoSsol	Average execution time (ms)	Average deviation
1	0.4	200	400	0.6136	1136.74	0.0103
2	0.6	200	400	0.6154	1320.18	0.0085
3	0.8	200	400	0.6177	1591.72	0.0063
4	1	200	400	0.6185	1835.58	0.0055

Table 3. Experimental results of CGWO optimisation for microservice portfolio B.

No.	p1	Initial population size	Number of iterations	Average best QoSsol	Average execution time (ms)	Average deviation
1	0.4	200	400	0.6184	1139.36	0.0066
2	0.6	200	400	0.6198	1347.84	0.0052
3	0.8	200	400	0.6217	1520.78	0.0033
4	1	200	400	0.6215	1861.46	0.0034

Figure 3. Diagram of microservice portfolio A objective function.

Figure 4. Diagram of the microservice portfolio B objective function.

Figure 5. Adaptation values of the optimised microservice combination A for different iterations of the two algorithms.

Figure 6. Adaptation values of the optimised microservice combination B for different iterations of the two algorithms.

Table 4. Comparison of experiments for optimisation of microservice portfolio A.

Algorithm	Average best QoSsol	Average deviation
CGWO	0.6175	0.0065
GWO	0.6049	0.0191

Table 5. Experimental comparison of microservice portfolio B optimisation.

Algorithm	Average best QoSsol	Average deviation
CGWO	0.6217	0.0033
GWO	0.6074	0.0176