Page 32 - Fister jr., Iztok, and Andrej Brodnik (eds.). StuCoSReC. Proceedings of the 2015 2nd Student Computer Science Research Conference. Koper: University of Primorska Press, 2015

Ai ∈ [A0, Amin]. The frequency (and wavelength) can
be adjusted depending on the proximities of their tar-
gets.
• The loudness varies from a large (positive) A0 to a
minimum constant value Amin.
These three rules mimics the natural behavior of bats, while
the full basic pseudo-code is presented in Algorithm 1.
Algorithm 1 Bat algorithm
Input: Bat population xi = (xi1, . . . , xiD)T for i =
1 . . . N p, M AX F E.
Output: The best solution xbest and its corresponding value
fmin = min(f (x)).
1: init bat();
2: eval = evaluate the new population;
3: fmin = find the best solution(xbest ); {initialization}
4: while termination condition not met do
5: for i = 1 to N p do
6: y = generate new solution(xi);
7: if rand(0, 1) < ri then
8: y = improve the best solution(xbest )
9: end if { local search step }
10: fnew = evaluate the new solution(y);
11: eval = eval + 1;
12: if fnew ≤ fi and N(0, 1) < Ai then
13: xi = y; fi = fnew;
14: end if { save the best solution conditionally }
15: fmin =find the best solution(xbest );
16: end for
17: end while
The BA is a population-based algorithm, where the popu-
lation size is controlled by a parameter Np. The main loop
of the algorithm (lines 4-16 in Algorithm 1) starts after the
initialization (line 1), the evaluation of the generated solu-
tions (line 2) and determination of the best solutions (line
4). It consists of the following elements:
• generating a new solution (line 6),
• improving the best solution (lines 7-9),
• evaluating the new solution (line 10),
• saving the best solution conditionally (lines 12-14),
• determining the best solution (line 15).
The generation of a new solution obeys the following equa-
tion:
Q(it) = Qmin + (Qmax − Qmin )N (0, 1), (1)
vi(t+1) = vit + (xit − xbest )Q(it),
xi(t+1) = xi(t) + vi(t+1),
where N (0, 1) is a random number drawn from a Gaussian
distribution with a zero mean and a standard deviation of
one, and Qi(t) ∈ [Qm(ti)n , Qm(ta)x ] is the frequency determining determines the magnitude of the change and settings of pa-
the magnitude of the velocity change. The improvement
StuCoSReC Proceedings of the 2015 2nd Student Computer Science Research Conference
Ljubljana, Slovenia, 6 October
of the current best solution is performed according to the
following equation:
x(t) = xbest + A(it)N (0, 1), (2)
where N (0, 1) denotes the random number drawn from a
Gaussian distribution with a zero mean and a standard de-
viation of one. In addition, is the scaling factor and A(it) is
the loudness. The improvement is controlled by a parame-
ter ri. It is worth pointing that the parameter balances the
exploration and exploitation components of the BA search
process, where exploitation is governed by Eq. 1 and ex-
ploitation by Eq. 2.
The evaluation function models the characteristics of the
problem to be solved. The archiving of the best solution
conditionally is similar to that used in SA, where the best
solution is taken into the new generation according to a
probability controlled by the parameter Ai in order to avoid
getting stuck into a local optimum.
2.1 Control parameters in the bat algorithm
and their bottlenecks
Control parameters guide algorithms during the search space
and may have a huge influence on the quality of obtained
solutions. In summary, the BA is controlled by the following
control parameters:
• the population size NP ,
• loudness Ai,
• pulse rate ri,
• minimum frequency Qmin and
• maximum frequency Qmax .
As we can see, the BA has five control parameters that can
be difficult for users to set a proper combination of con-
trol parameter settings that are the most suitable for the
particular problem. Though some algorithms have fewer
parameters such as differential evolution [14] that employs
only three basic control parameters. However, the parame-
ter tuning can be a time-consuming task for all algorithms.
On the other hand, there are also some other robust self-
adaptive [3] BA variants that can modify the values of con-
trol parameters during the run.
The main task for us is to develop a parameterless variant
of the bat algorithm.
3. DESIGN OF A PARAMETERLESS BAT
ALGORITHM
In order to develop a new parameterless BA (PLBA), the
influence of control parameters was studied and extensive
studies revealed that some algorithm parameters can be ef-
fectively set. For example, the parameter Qi ∈ [Qmin , Qmax ]
rameters Qmin and Qmax depend on the problem of interest.
However, the rational setting of this parameter can be ap-
proximated with the lower xiLb and upper xUi b bounds of the
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