Particle swarm optimization (PSO) algorithm is generally improved by adaptively adjusting the inertia weight or combining with other evolution algorithms. However, in most modified PSO algorithms, the random values are always generated by uniform distribution in the range of [0, 1]. In this study, the random values, which are generated by uniform distribution in the ranges of [0, 1] and [−1, 1], and Gauss distribution with mean 0 and variance 1 ( $U\left[0,1\right]$ , $U\left[-1,1\right]$ and $G(0,1)$ ), are respectively used in the standard PSO and linear decreasing inertia weight (LDIW) PSO algorithms. For comparison, the deterministic PSO algorithm, in which the random values are set as 0.5, is also investigated in this study. Some benchmark functions and the pressure vessel design problem are selected to test these algorithms with different types of random values in three space dimensions (10, 30, and 100). The experimental results show that the standard PSO and LDIW-PSO algorithms with random values generated by $U\left[-1,1\right]$ or $G(0,1)$ are more likely to avoid falling into local optima and quickly obtain the global optima. This is because the large-scale random values can expand the range of particle velocity to make the particle more likely to escape from local optima and obtain the global optima. Although the random values generated by $U\left[-1,1\right]$ or $G(0,1)$ are beneficial to improve the global searching ability, the local searching ability for a low dimensional practical optimization problem may be decreased due to the finite particles.

Exact kinky breather-wave solution, periodic breather-wave solution, and some lump solutions to the (2+1)-dimensional Ito equation are obtained by using an extended homoclinic test technique and Hirota bi-linear method with a perturbation parameter u0. Furthermore, a new non-linear phenomenon in the lump solution, is investigated and discussed. These interesting non-linear phenomena might provide us with useful information on the dynamics of higher-dimensional non-linear wave field.

In this paper, the sintering neck growth process of metal fibers under the surface diffusion mechanism is simulated by using the Lattice Boltzmann method (LBM). The surface diffusion model is developed considering the geometrical characteristic of metal fibers. Then, the LBM scheme is constructed for solving the developed surface diffusion model. The sintering neck growth process of two metal fibers with different fiber angles is simulated by LBM. The simulated morphologies of sintering metal fibers well agree with ones obtained by experiments. Moreover, the numerical simulation results show that the sintering neck radius of two metal fibers is increased with the increase of fiber angle, which implies that the initial geometrical characteristic plays an important role in the sintering neck formation and growth of metal fibers.

Some new solitary solutions of (3+1)-dimensional Jimbo-Miwa equation such as breather solutions, double breather solutions and mixed solutions of different forms are studied via applying Hirota's bilinear form and constructing various trial functions. Besides, the degradation phenomenon of breather solution to lump-type solution is investigated, and dynamical behaviours of the interaction between solitary solutions and lump-type solutions varying with time t is discussed. Finally, the interactive result between N-soliton solution (N takes any positive integer) and lump-type solution is studied by reducing dimension, and the detailed proof process is presented.

The (4+1)-D Fokas equation is a new and important physical model. Its Hirota's bilinear form with a perturbation parameter is obtained by an appropriate trans-formation. A class of lump solutions and three different forms of spatio-temporal structure are obtained. Meanwhile, the theoretical analysis for the change of spatio-temporal structure is discussed by using the extreme value theory of multivariate function. Finally, the interaction between a stripe soliton and lump solution is discussed, and a new wave phenomenon that the lump solution is swallowed and drowned by the stripe soliton is investigated.