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122 Z. Li et al. / Applied Soft Computing 21 (2014) 119–138
Fig. 2. Dynamic level updating strategy of the proposed AHAIS optimization.
3.4. Suppression operator
In the proposed AHAIS optimization, a concentration-based sup-
pressor is employed, where the threshold Th
s
can be determined
by
Th
s
= ×(max{D
ij
|i /= j}−min{D
ij
|i /= j}), (6)
where the controlling coefficient ∈(0, 1). This is aimed at sup-
pressing those similar candidate antibodies.
3.5. Dynamic level updating strategy
After learning from TLEA, some candidate antibodies in BLCA
will probably become better in affinity than those in TLEA. Thus,
it is necessary to dynamically update the elements of candidate
antibodies in both BLCA and TLEA. We design a dynamic level updat-
ing strategy which allows those candidate antibodies with higher
affinity in BLCA to transfer into TLEA and allows those with lower
affinity in TLEA to return to BLCA. As shown in Fig. 2, the detailed
procedures are explained as follows.
Step 1. Sort the candidate antibodies in BLCA by their affinity in a
descending order.
Step 2. Make the first p (p = N
u
×b, b ∈(0, 1)) candidate antibodies
in BLCA transfer into TLEA.
Step 3. Sort the candidate antibodies in TLEA by their affinity in a
descending order.
Step 4. Make the last p candidate antibodies in TLEA retrograde
into BLCA.
The flowchart of the proposed AHAIS optimization is shown in
Fig. 3. The revised or redesigned operators are placed in the red
dashed-line boxes, respectively. In the initialization, the randomly
produced candidate antibodies are separated into TLEA and BLCA
based on their affinity. For TLEA, the candidate antibodies experi-
ence the affinity-based cloning and the affinity-based self-learning
mutation where the searching step length is adjusted adaptively by
a well-designed mechanism. On the other hand, for BLCA, the candi-
date antibodies undergo the elitist-learning mutation from the best
candidate antibody in TLEA after the common clone process. After
the evolutionary process, if the level updating condition is met,
the level updating strategy is triggered. Next, if the suppression
condition is met, the concentration-based suppression operator is
excited for the candidate antibodies in BLCA. Repeat this process
until it is terminated.
For the sake of clear explanation, the pseudocode of the pro-
posed AHAIS optimization is shown in Fig. 4.
4. Numerical simulations and results
In this section, a series of numerical simulations are arranged
to analyze the sensitivity of the key parameters and to examine
the solution quality and the convergence velocity of the proposed
AHAIS optimization by comparisons with DE, PSO, opt-aiNet and IA-
AIS. Furthermore, the proposed AHAIS optimization is also applied
to schedule the communication resource of an RFID reader collision
avoidance problem.
4.1. Performance experiments
4.1.1. Benchmark functions
Eight classical benchmark functions are chosen from [25] to
examine the proposed AHAIS optimization, which are listed in
Table 1. The Sphere function, the weighted Sphere function and the
Schwefel’s Problem 1.2 are simple unimodal functions and easy to
solve. The Griewank function, the Rastrigin function and the gener-
alized Schwefel’s Problem 2.26 are multimodal functions, and they
are difficult to reach the global optimum. The Rosenbrock function,
with a narrow valley from the perceived local optima to the global
optimum, can be treated as a multimodal function. The Ackley func-
tion, whose global optimum is on the bound, can be also regarded
as a multimodal function.
4.1.2. Parameter sensitivity analysis
In the proposed AHAIS optimization, three parameters, i.e., the
antibody population scale of TLEA (p
Elitist
), the controlling coeffi-
cient for suppression () and the percentage of updating antibodies
(b), need to be tuned. In this subsection, eight benchmark functions
in 10D are used to discuss the impact of these three parameters. All
the numerical simulations are run for 25 replications. The antibody