# Systems, Man & Cybernetics - October 2015 - 14

```Step 6: Go to Step 2
Step 7: Done!
The complexity of GRA is O(m3) [11]. Thus, the complexity of the AC is the same as that of GRA if the number
of samples is a constant. In practice, this algorithm can be
used when we know the current group information. Based
on Definition 23, we conduct simulations with random
groups and apply (7) in Step 3:

Group Performance Increase

0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.1
-0.15

Q k [i, j] = (Q [i, j] (kx/p) + (Q [i, j] (kx/p)
- Q [i, j] ((k - 1) x/p)) /2
= (2Q [i, j] (kx/p) - Q [i, j] ((k - 1) x/p)) /2. (7)

Maximum
Average
Minimum

-0.05

0

2

4
6
8
10 12
Number of Reassignments

14

16

Figure 5. the simulation result.

changes in the internal structures, i.e., environment e.
Therefore, an ACS becomes adaptive to the internal structure changes. The role engine can incorporate rules and
policies to change the internal structures, i.e., A, R, L, W,
and AE, based on the changes in external environments.
A General Approach to ACS
From the process of RBC, we emphasize dynamic role
reassignment. From the architecture shown in Figure 4,
we emphasize that AC is implemented on the role engine.
An intuitive solution to the AC problem is reassigning
roles according to the current group state (GS(t)). If a
role assignment with a higher group qualification than
the current role assignment exists, then reassignment
occurs. If role reassignment is necessary for a group, the
reassignment must take place in time. The first step of
this algorithm is to assign roles according to the initial
group state. Then information about the group is collected and GRA is called to obtain a trial assignment matrix
at every sample point. If the trial assignment matrix gets
a higher group qualification, roles are reassigned; otherwise, nothing happens. Detailed steps are shown as follows. In this process, dynamic role assignment is
conducted according to the same intervals in period x,
i.e., x/p . We use WT to denote the current working
assignment matrix:
◆ Input: A, R, L, W, x, and p
◆ Output: Group performance
◆ AC (A, R, L, W, x, p) :
Step 1: t = 0; Q(t) = AE(A(t), R(t)), then call GRA(Q(t),
L(t), W(t)) to obtain WT = T*(t)
Step 2: Time x/p elapses, t : = t + x/p ; if t = x then go to
Step 7; otherwise, sample, and collect information about
the group, i.e., A (t), R (t), L(t), and W(t)
Step 3: AE, Q(t) = AE (A (t), R (t))
Step 4: Call GRA(Q(t), L(t), W(t)) to obtain T*(t)
Step 5: If v (Q(t), W(t), T*(t)) > v (Q(t), W(t), WT), then
WT := T*(t)
14

IEEE SyStEmS, man, & CybErnEtICS magazInE October 2015

Note that Q k [i, j] in (7) considers both the qualification value and the change of the value, kx/p expresses
the time when the kth a ssig n ment is conducted
(0 # k # p), and the 0th assignment is the initial one.
Without loss of generality, we choose m = 60, n = 10.
These choices generate a general conclusion, because we
only concentrate on the group performance trends with
the number of role assignments but not the efficiency of
the algorithm. At first, we randomly create a ij and b ij
by following (5) and (6). Second, we use four hours as
the collaboration interval because workers work 4 h
(480  min) in most factories and students study 4 h of
classes in universities or colleges before a long break,
i.e., x = 480. Because the period of the sine function in
(4) is 2r/~ ij , we choose ~ ij ! [0, r/240]. To evenly distribute the five different situations of agents' performance change, we use the following random number
generation. We take i ij ! [0, 2r/~ ij] to express that an
agent may start the work at any point of the sine function. At last, we use L[ j] (0 # L[ j] # 4 to make T(t)
workable) as a constant in [0, x ]. Based on the above
data, we create random groups with < Q[i, j](t), L[ j]> ,
compute Q k [i, j] with (7), then conduct GRA with
1 Q k, L [j]2 (0 # k 1 p) to collect the follow data: 1) Cs
that has only one assignment; and 2) C with p equal
interval role reassignments. To compute the benefits, we
use (C(p) − Cs)/ Cs (p = 2, ..., 11), where Cs = C(1) and
C(p) means the group performance with p assignments.
Figure 5 indicates that 8 -9 checks (9 -10 on the
x-axis) are sufficient to obtain the possible benefit
within the chosen period, i.e., 480 (min). It is noted
that the minimum rate is negative when there are only
1-4 role reassignments (2-5 in Figure 5). It is reasonable that in less than one period of the sine function,
1-4 reassignments do not bring in benefits. The simulation asserts that while agents' performance on roles
changes in different ways, 8-9 reassignments over regular inter vals can provide an average performance
increase of 18%.
Conclusions and Future Work
We have argued and verified that AC is beneficial. Based

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