Multi-objective particle swarm optimization by fusing multiple strategies

To improve the convergence and distributivity of multi-objective particle swarm optimization,we propose a method for multi-objective particle swarm optimization by fusing multiple strategies(MOPSO-MS),which includes three strategies.Firstly,the average crowding distance method is proposed,which takes into account the influence of individuals on the crowding distance and reduces the algorithm’s time complexity and computational cost,ensuring efficient external archive maintenance and improving the algorithm’s distribution.Secondly,the algorithm utilizes particle difference to guide adaptive inertia weights.In this way,the degree of disparity between a particle’s historical optimum and the population’s global optimum is used to determine the value of w.With different degrees of disparity,the size of w is adjusted nonlinearly,improving the algorithm’s convergence.Finally,the algorithm is designed to control the search direction by hierarchically selecting the globally optimal policy,which can avoid a single search direction and eliminate the lack of a random search direction,making the selection of the global optimal position more objective and comprehensive,and further improving the convergence of the algorithm.The MOPSO-MS is tested against seven other algorithms on the ZDT and DTLZ test functions,and the results show that the MOPSO-MS has significant advantages in terms of convergence and distributivity.

Differentially weighted direct simulation Monte Carlo method for particle collision in gas-solid flows

In gas-solid flows, particle-particle interaction （typical, particle collision） is highly significant, despite the small particles fractional volume. Widely distributed polydisperse particle population is a typical characteristic during dynamic evolution of particles （e.g., agglomeration and fragmentation） in spite of their initial monodisperse particle distribution. The conventional direct simulation Monte Carlo （DSMC） method for particle collision tracks equally weighted simulation particles, which results in high statistical noise for particle fields if there are insufficient simulation particles in less-populated regions. In this study, a new differentially weighted DSMC （DW-DSMC） method for collisions of particles with different number weight is proposed within the framework of the general Eulerian-Lagrangian models for hydrodynamics. Three schemes （mass, momentum and energy conservation） were developed to restore the numbers of simulation particle while keeping total mass, momentum or energy of the whole system unchanged respectively. A limiting case of high-inertia particle flow was numerically simulated to validate the DW-DSMC method in terms of computational precision and efficiency. The momentum conservation scheme which leads to little fluctuation around the mass and energy of the whole system performed best. Improved resolution in particle fields and dynamic behavior could be attained simultaneously using DW-DSMC, compared with the equally weighted DSMC. Meanwhile, computational cost can be largely reduced in contrast with direct numerical simulation.

Differentially weighted operator splitting Monte Carlo method for simulating complex aerosol dynamic processes

A differentially weighted operator splitting Monte Carlo （DWOSMC） method is developed to solve com- plex aerosol dynamic processes by coupling the differentially weighted Monte Carlo method and the operator splitting technique. This method is validated by analytical solutions and a sectional method in different aerosol dynamic processes. It is first validated in coagulation and condensation processes, and nucleation and coagulation processes, and then validated through simultaneous nucleation, coagulation, and condensation processes. The results show that the DWOSMC method is a computationally efficient and quantitatively accurate method for simulating complex aerosol dynamic processes.

Weighted Pseudo Almost Periodic Solutions of N-th Order Neutral Differential Equations with Piecewise Constant Arguments

In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.