Abstract
Particle swarm optimization (PSO) algorithm is a swarm intelligent searching algorithm based on population that simulates the social behavior of birds, bees, or fish groups. The discrete binary particle swarm optimization (BPSO) algorithm maps the continuous search space to a binary space through a new transfer function, and the update process is designed to switch the position of the particles between 0 and 1 in the binary search space. Aiming at the existed BPSO algorithms which are easy to fall into the local optimum, a new Z-shaped probability transfer function is proposed to map the continuous search space to a binary space. By adopting nine typical benchmark functions, the proposed Z-probability transfer function and the V-shaped and S-shaped transfer functions are used to carry out the performance simulation experiments. The results show that the proposed Z-shaped probability transfer function improves the convergence speed and optimization accuracy of the BPSO algorithm.
Highlights
Binary Particle Swarm Optimization AlgorithmIn the binary particle swarm optimization (BPSO) algorithm, the velocity update equation has not changed, but a new velocity transfer function has been introduced to map the original continuous search space to the binary search space. e transfer function concept was originally proposed by Kennedy and Eberhart [11], which allows PSO algorithm to run in the binary searching space
E algorithm is based on the sigmoid function used by Kennedy and Eberhart in the binary particle swarm optimization algorithm proposed in 1997 [11]
In 2017, Fei [18] proposed a V-shaped transfer function to improve the binary bat algorithm to ensure that the probability of reducing the position of the vector of the position vector of the bat is an element equal to the current best position, and increasing the probability of changing the element of their position vector to the element of the bat is the element of the unequal current optimal position, which helps to enhance the optimization of the binary bat algorithm
Summary
In the binary particle swarm optimization (BPSO) algorithm, the velocity update equation has not changed, but a new velocity transfer function has been introduced to map the original continuous search space to the binary search space. e transfer function concept was originally proposed by Kennedy and Eberhart [11], which allows PSO algorithm to run in the binary searching space. E transfer function concept was originally proposed by Kennedy and Eberhart [11], which allows PSO algorithm to run in the binary searching space In this version, particles can only be zero or 1 by taking their position vector. In 2008, Lee et al proposed another modification of BPSO algorithm [25], which allows the continuous update velocity and position of PSO algorithm In this improvement, they replace the velocity with the displacement in the transfer function. According to the characteristics of V-shaped transfer function, a series of V-shaped transfer functions are proposed by using different functional equations, whose expressions and graphs are shown in Table 2 and Figure 3, respectively. For different V-shaped functions, it is easy to find that when the slope of the function is higher, the probability of the particle position change is higher.
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