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Abstract—In this paper, we present a new algorithm binary discrete optimization method based on cat swarm optimization (CSO). BCSO is a binary version of CSO generated by observing the behaviors of cats. As in CSO, BCSO consists of two modes of operation: tracing mode and seeking mode. The BCSO presented in this paper is implemented on a number of benchmark optimization problems and zero-one knapsack problem. The obtained results are compared with a number of different optimization problems including genetic algorithm and different versions of binary discrete particle swarm optimization. It is shown that the proposed method greatly improves the results obtained by other binary discrete optimization problems.
Keywords— Cat Swarm Optimization, Binary Discrete Cat Swarm Optimization, Zero-one Knapsack Problem, Particle Swarm Optimization
Optimization is prevalent in almost all field of science and engineering. In recent years several optimization methods are
proposed and used such as Genetic Algorithms (GAs) , , Particle Swarm Optimization Algorithm (PSO) , ,
Cat Swarm optimization (CSO)  and etc. to solve different optimization problems. PSO was originally designed and introduced by Eberhart
and Kennedy ,  in 1995. The PSO is a population based search algorithm which aims to simulate the social behavior of birds, bees or a school of fishes. Each individual within the swarm is represented by a vector of multidimensional position in the search space. The next movement of each particle is determined using a velocity vector. The velocity vector is designed such that each particle is directed towards
its best personal experience and the best experience of the whole swarm. There is also a momentum term which directs the particle according to its last velocity vector. PSO is found to be useful in different optimization problems such as optimal tuning of fuzzy systems , , clustering problem , leastcost generation expansion planning , etc. The original version of CSO is introduced in the year 2006 by Chu, Tsai, and Pan . They studied the behavior of the cats and modeled their behavior to introduce a novel optimization algorithm , . Based on their studies they suggested that cats have two modes of behavior: seeking mode and tracing mode. They notice that cat spends most of the time when they are awake on resting. While they are resting, they move their position carefully and slowly. This mode of behavior is called seeking mode. In the tracing mode, a cat moves according to its own velocities for every dimension. This algorithm will be discussed in details later in this paper. The CSO and PSO were originally developed for continuous valued spaces. But there exists a number of optimization problems in which the values are not continuous numbers but rather discrete binary integers. Classical examples of such problems are: integer programming, scheduling and routing . In 1997, Kennedy and Eberhart introduced a discrete binary version of PSO for discrete optimization problems . In binary PSO, each particle represents its position in binary values which are 0 or 1. Each particles value can then be changed (or better say mutate) from one to zero or vice versa. In binary PSO the velocity of a particle defined as
the probability that a particle might change its state to one and fails in so many binary discrete optimization problems. The original version of binary discrete optimization problem was later improved by introducing two velocity vectors . The method shows significant improvement over its previous version in .
In this paper a binary discrete cat optimization problem (BCSO) is introduced and tested. To the best of authors knowledge CSO is not used in binary discrete optimization methods. As in the original version of CSO, its binary version introduced in this paper has also two modes of operations namely: seeking mode and tracing mode. The difference between the BCSO and CSO is that the parameters of BCSO can
take the values of zero and one, this makes the algorithm totally difference. The velocity of CSO in tracing mode changes its meaning to probability of change in the bits in BCSO. The proposed BCSO is tested in a number of different benchmark optimization problems and on binary knapsack problem. The results are compared with those of genetic algorithm, BPSO and NBPSO . The results shows that the proposed method highly outperform above mentioned algorithms. This paper is organized as follows. The CSO is summarized in section II. In section III, the proposed BCSO is introduced in details. In section IV, the results of applying CSO to number of different benchmark problems are presented. Finally the concluding marks are gathered in section V
discrete binary cat swarm optimization
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