Cat Swarm Optimization

Abstract

In this paper, we present a new algorithm of swarm intelligence, namely, Cat Swarm Optimization (CSO). CSO is generated by
observing the behaviors of cats, and composed of two sub-models, i.e., tracing mode and seeking mode, which model upon the
behaviors of cats. Experimental results using six test functions demonstrate that CSO has much better performance than Particle
Swarm Optimization (PSO).

Full text

Q. Yang and G. Webb (Eds.): PRICAI 2006, LNAI 4099, pp. 854 – 858, 2006.
© Springer-Verlag Berlin Heidelberg 2006
Cat Swarm Optimization
Shu-Chuan Chu1, Pei-wei Tsai2, and Jeng-Shyang Pan2
1 Department of Information Management,
Cheng Shiu University
2 Department of Electronic Engineering,
National Kaohsiung University of Applied Sciences
Abstract. In this paper, we present a new algorithm of swarm intelligence,
namely, Cat Swarm Optimization (CSO). CSO is generated by observing the
behaviors of cats, and composed of two sub-models, i.e., tracing mode and
seeking mode, which model upon the behaviors of cats. Experimental results
using six test functions demonstrate that CSO has much better performance than
Particle Swarm Optimization (PSO).
1 Introduction
In the field of optimization, many algorithms were being proposed recent years, e.g.
Genetic Algorithm (GA) [1-2], Ant Colony Optimization (ACO) [6-7], Particle
Swarm Optimization (PSO) [3-5], and Simulated Annealing (SA) [8-9] etc. Some of
these optimization algorithms were developed based on swarm intelligence. Cat
Swarm Optimization (CSO), the algorithm we proposed in this paper, is motivated
from PSO [3] and ACO [6].
According to the literatures, PSO with weighting factor [4] usually finds the better
solution faster than the pure PSO, but according to the experimental results, Cat
Swarm Optimization (CSO) presents even much better performance.
Via observing the behavior of creatures, we may get some idea for solving the
optimization problems. By studying the behavior of ants achieves ACO, and with
examining the movements of the flocking gulls realizes PSO. Through inspecting the
behavior of cat, we present Cat Swarm Optimization (CSO) algorithm.
2 Behaviors of Cats
According to the classification of biology, there are about thirty-two different species of
creatures in feline, e.g. lion, tiger, leopard, cat etc. Though they have different living
environments, there are still many behaviors simultaneously exist in most of felines.
In spite of the hunting skill is not innate for felines, it can be trained to acquire. For
the wild felines, the hunting skill ensures the survival of their races, but for the indoor
cats, it exhibits the natural instinct of strongly curious about any moving things.
Though all cats have the strong curiosity, they are, in most times, inactive. If you
spend some time to observe the existence of cats, you may easily find that the cats
spend most of the time when they are awake on resting.

Cat Swarm Optimization 855
The alertness of cats are very high, they always stay alert even if they are resting.
Thus, you can simply find that the cats usually looks lazy, lying somewhere, but
opening their eyes hugely looking around. On that moment, they are observing the
environment. They seem to be lazy, but actually they are smart and deliberate.
Of course, if you examine the behaviors of cats carefully, there would be much
more than the two remarkable properties, which we discussed in the above.
3 Proposed Algorithm
In our proposed Cat Swarm Optimization, we first model the major two behaviors of
cats into two sub-models, namely, seeking mode and tracking mode. By the way of
mingling with these two modes with a user-defined proportion, CSO can present bet-
ter performance.
3.1 The Solution Set in the Model -- Cat
No matter what kind of optimization algorithm, the solution set must be represented
via some way. For example, GA uses chromosome to represent the solution set; ACO
uses ant as the agent, and the paths made by the ants depict the solution sets; PSO
uses the positions of particles to delineate the solution sets. In our proposed algorithm,
we use cats and the model of behaviors of cats to solve the optimization problems, i.e.
we use cats to portray the solution sets.
In CSO, we first decide how many cats we would like to use, then we apply the
cats into CSO to solve the problems.
Every cat has its own position composed of M dimensions, velocities for each di-
mension, a fitness value, which represents the accommodation of the cat to the fitness
function, and a flag to identify whether the cat is in seeking mode or tracing mode.
The final solution would be the best position in one of the cats due to CSO keeps the
best solution till it reaches the end of iterations.
3.2 Seeking Mode
This sub-model is used to model the situation of the cat, which is resting, looking
around and seeking the next position to move to. In seeking mode, we define four
essential factors: seeking memory pool (SMP), seeking range of the selected dimen-
sion (SRD), counts of dimension to change (CDC), and self-position considering
(SPC).
SMP is used to define the size of seeking memory for each cat, which indicates the
points sought by the cat. The cat would pick a point from the memory pool according
to the rules described later.
SRD declares the mutative ratio for the selected dimensions. In seeking mode, if a
dimension is selected to mutate, the difference between the new value and the old one
will not out of the range, which is defined by SRD.
CDC discloses how many dimensions will be varied. These factors are all playing
important roles in the seeking mode.
SPC is a Boolean variable, which decides whether the point, where the cat is al-
ready standing, will be one of the candidates to move to. No matter the value of SPC

856 S.-C. Chu, P.-w. Tsai, and J.-S. Pan
is true or false; the value of SMP will not be influenced. How the seeking mode works
can be described in 5 steps as follows:
Step1: Make j copies of the present position of catk, where j = SMP. If the value of
SPC is true, let j = (SMP-1), then retain the present position as one of the
candidates.
Step2: For each copy, according to CDC, randomly plus or minus SRD percents of
the present values and replace the old ones.
Step3: Calculate the fitness values (FS) of all candidate points.
Step4: If all FS are not exactly equal, calculate the selecting probability of each
candidate point by equation (1), otherwise set all the selecting probability of
each candidate point be 1.
Step5: Randomly pick the point to move to from the candidate points, and replace
the position of catk.
minmax FSFS
FSFS
Pbi
i−
−
=, where 0 < i < j (1)
If the goal of the fitness function is to find the minimum solution, FSb = FSmax, oth-
erwise FSb = FSmin.
3.3 Tracing Mode
Tracing mode is the sub-model for modeling the case of the cat in tracing some tar-
gets.
Once a cat goes into tracing mode, it moves according to its’ own velocities for
every dimension. The action of tracing mode can be described in 3 steps as follows:
Step1: Update the velocities for every dimension (vk,d) according to equation (2).
Step2: Check if the velocities are in the range of maximum velocity. In case the
new velocity is over-range, set it be equal to the limit.
Step3: Update the position of catk according to equation (3).
(
)
dkdbestdkdk xxcrvv ,,11,, −××+= , where d = 1,2,…,M (2)
xbest,d is the position of the cat, who has the best fitness value; xk,d is the position of
catk. c1 is a constant and r1 is a random value in the range of [0,1].
dkdkdk vxx ,,, += (3)
3.4 Cat Swarm Optimization
As we described in the above subsection, CSO includes two sub-models, the seeking
mode and the tracing mode. To combine the two modes into the algorithm, we define
a mixture ratio (MR) of joining seeking mode together with tracing mode.
By observing the behaviors of cat, we notice that cat spends mot of the time when
they are awake on resting. While they are resting, they move their position carefully
and slowly, sometimes even stay in the original position. Somehow, for applying this
behavior into CSO, we use seeking mode to represent it.

Cat Swarm Optimization 857
The behavior of running after targets of cat is applied to tracing mode. Therefore, it
is very clear that MR should be a tiny value in order to guarantee that the cats spend
most of the time in seeking mode, just like the real world.
The process of CSO can be described in 6 steps as follows:
Step1: Create N cats in the process.
Step2: Randomly sprinkle the cats into the M-dimensional solution space and ran-
domly select values, which are in-range of the maximum velocity, to the ve-
locities of each cat. Then haphazardly pick number of cats and set them into
tracing mode according to MR, and the others set into seeking mode.
Step3: Evaluate the fitness value of each cat by applying the positions of cats into
the fitness function, which represents the criteria of our goal, and keep the
best cat into memory. Note that we only need to remember the position of
the best cat (xbest) due to it represents the best solution so far.
Step4: Move the cats according to their flags, if catk is in seeking mode, apply the
cat to the seeking mode process, otherwise apply it to the tracing mode
process. The process steps are presented above.
Step5: Re-pick number of cats and set them into tracing mode according to MR,
then set the other cats into seeking mode.
Step6: Check the termination condition, if satisfied, terminate the program, and
otherwise repeat step3 to step5.
4 Experimental Results
We applied CSO, PSO and PSO with weighting factor into six test functions to com-
pare the performance. All the experiments demonstrate the proposed Cat Swarm Op-
timization (CSO) is superior to PSO and PSO with weighting factor. Due to the space
limit of this paper, only the experimental results of test function one shown in Fig. 1.
Fig. 1. The experimental result of test function 1

858 S.-C. Chu, P.-w. Tsai, and J.-S. Pan
References
1. Goldberg, D.E.: Genetic Algorithm in Search. Optimization and Machine Learning. Addi-
son-Wesley Publishing Company (1989)
2. Pan, J. S., McInnes, F. R., Jack, M. A. : Application of Parallel Genetic Algorithm and
Property of Multiple Global Optima to VQ Codevector Index Assignment. Electronics Let-
ters 32(4) (1996) 296-297
3. Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. Sixth International
Symposium on Micro Machine and Human Science (1995) 39-43
4. Shi, Y., Eberhart, R.: Empirical study of particle swarm optimization. Congress on Evolu-
tionary Computation. (1999) 1945-1950
5. Chang, J. F., Chu, S. C., Roddick, J. F., Pan, J. S. : A Parallel Particle Swarm Optimization
Algorithm with Communication Strategies. Journal of Information Science and Engineering
21(4) (2005) 809-818
6. Dorigo, M., Gambardella, L. M.: Ant colony system: a cooperative learning approach to the
traveling salesman problem. IEEE Trans. on Evolutionary Computation. 26 (1) (1997) 53-
66
7. Chu, S. C., Roddick, J. F., Pan, J. S.: Ant colony system with communication strategies.
Information Sciences 167 (2004) 63-76
8. Kirkpatrick, S., Gelatt, Jr. C.D., Vecchi, M.P.: Optimization by simulated annealing. Sci-
ence (1983) 671-680
9. Huang, H. C., Pan, J. S., Lu, Z. M., Sun, S. H., Hang, H.M.: Vector quantization based on
generic simulated annealing. Signal Processing 81(7) (2001) 1513-1523